Mainstream economics portrays individual agents as choosing rationally. Many of its generalizations concerning how people actually choose are also claims about how agents ought rationally to choose. This fact distinguishes economics from the natural sciences, whose particles do not choose and are neither rational nor irrational, and whose theories have no similar normative aspect. Chemists offer no advice to benzine molecules, which would not listen to advice if given. I have a good deal to say in Chapters 4, 13, and 16 about the significance of this distinctive feature of economics. In this chapter, my goal is to describe the fundamental elements of models of both rational and actual choice. Most of the chapter is devoted to the simplest model: “ordinal utility theory.” However, Section 1.3 provides a sketch of expected utility theory, which is central to decision theory and plays an important role in mainstream economics.

1.1 Rational Choice with Perfect Knowledge: Preferences and Ordinal Utility Theory

What is it to choose rationally? This is an old philosophical question, which, like other old philosophical questions, is hard to answer. One can say, accurately, albeit unhelpfully, that rational choice consists in choice that is properly responsive to reasons. There are many ways to fail to be properly responsive to reasons and thus many kinds of irrationality. Furthermore, the notion of choice is ambiguous. It can refer to deliberating, or it can refer to the action that is the outcome of deliberation. Economists regard choice as action and regard it as determined by three factors: physical constraints, beliefs (or expectations), and preferences. Choices are rational if they are governed by rational preferences and rational beliefs. Noneconomists take “preferences” to be subjective states of individuals, which are reflected in their words and actions. Although preferences in economics differ from preferences in ordinary discourse in ways to be explained later, this chapter argues that preferences in economics, like preferences in ordinary discourse, are subjective states that combine with beliefs to cause choices.

If people are approximately rational, then a model of rational choice can be used to predict actual choice. A normative theory is concerned with value – that is, with what is good or bad – and with which actions are obligatory, permissible, or impermissible. Unlike “positive” theories that describe, predict, and explain what actually happens, normative theories evaluate what happens and say what ought to happen. Rationality is a normative notion, although not a moral notion. To fail to do what one rationally ought to do is foolish or self-defeating rather than evil.

This sketch of the distinction between positive and normative inquiries is subject to caveats. Among other difficulties, there is no sharp boundary between positive and normative. Just consider statements such as “members of the SS were cruel” or “Margaret Thatcher was shrewd.” They state matters of fact, but they also offer evaluations. However, for our purposes, the rough distinction between what is, on the one hand, normative, prescriptive, or evaluative and, on the other hand, positive or factual will serve. As we shall see, the normative model of rational preference, belief, and choice this chapter presents can also play a central role in positive economics when joined with the hypothesis that people are largely rational.

The objects of choice can be many different things. In consumer choice theory, they are limited to bundles of commodities and services. In the theory of the firm, the alternatives may be combinations of inputs. Preferences range more widely. An individual, Marty, may have preferred that Hillary Clinton be elected president in 2008, that Apple stock double in value, or that no hurricane strikes Puerto Rico, but none is a state of affairs that Marty can choose.

The description of the objects of both choice and preference must include “everything that matters to the agent” (Arrow Reference Arrow1970, p. 45). Otherwise, preferences would change with context. For example, I have no preference among the alternatives described merely as “a cup of coffee” or “a bottle of beer.” Which I prefer depends on the time of day, what I am eating, what the weather is like, and many other things. The states of affairs ranked by preferences must instead be described as “drinking a cup of coffee versus a bottle of beer at 7 a.m. with cereal and …” or “drinking a bottle of beer versus a cup of coffee on a hot afternoon after mowing the lawn and … . ” I often simplify and speak of a preference for beer rather than speaking of a preference for the complete state of the world with drinking a beer versus the complete state of the world without doing so.Footnote ¹

The economist’s model of rational choice largely abstracts from deliberation: constraints and beliefs fix which alternative actions are feasible and believed to be feasible, and agents choose whatever action is at the top of their already given preference ranking of the actions they believe to be feasible. Taken by itself, Yolanda’s preference for blueberries over strawberries is not subject to rational appraisal, but there are rational constraints on sets of preferences. For example, if she also prefers cherries to blueberries, then she ought to prefer cherries to strawberries. The model of rational choice does not condemn as irrational Peter’s preference for a side serving of mouse droppings over a portion of carrots, but it does find it irrational if Peter also prefers being healthy to being unhealthy.

1.1.1 Certainty and Perfect Knowledge

In unusual circumstances in which agents possess complete knowledge and there is neither risk nor uncertainty, what agents believe coincides with the facts, and nothing need be said about belief, rational or otherwise. The account of rationality in these circumstances is called “ordinal utility theory.” Economists have a simple model of rational choice shown in Figure 1.1. Agents who have complete knowledge rank the alternatives among which they choose (represented here by different foods). Constraints may rule out some alternatives (bread in this case). Agents choose from the remaining options whatever is at the top of their preference ranking. In positive economics, an agent’s preference ranking governs the agent’s choices. In normative (welfare) economics, the objective is to help people move up their preference ranking. The principles of positive microeconomics are mainly generalizations concerning preferences and their implications for choice. The imperatives of normative economics specify how best to satisfy preferences. Preferences lie at the core of mainstream economics.

Figure 1.1 Preference and choice.

1.1.2 Preference Axioms

Mainstream economists agree on the following axioms concerning preferences in the special circumstances in which there is no uncertainty and agents possess perfect knowledge. Because, as Section 1.1.3 explains, preferences that satisfy these axioms can be represented by an ordinal utility function, these are called the axioms of ordinal utility theory. Although economists agree on these axioms, few think these axioms are universal truths. Some economists believe that the axioms of ordinal utility theory are good approximations and that the violations can be regarded as unsystematic noise. Many question whether these axioms are generally true of people and regard them more as a point of comparison than as a guide to reality. Even those who have the fewest qualms about the model recognize that these axioms are simplifications of a more complicated reality. This is not just an armchair observation. As discussed in Chapters 13 and 14, there are experimental data revealing systematic violations of these axioms, and psychologists and behavioral economists have formulated generalizations concerning preferences that explain these violations. Nevertheless, for most economists, even behavioral economists, these axioms are the standard starting place for theorizing concerning individual choice.

The following two axioms (quoted from Mas-Colell et al. 1995, p. 6) are ubiquitous:

$(Completeness\text{)}\text{For all}x,y\text{in}X,\text{either}x⪰y\text{or}y⪰x\text{or both}.$

$(Transitivity)\text{For all}x,y,\text{and}z\text{in}X\text{if}x⪰y\text{and}y⪰z,\text{then}x⪰z.$

“$X$” is the set of alternatives over which agents have preferences – commodity bundles in the case of consumer choice theory – and $x$, $y$, and $z$ are alternatives in $X$. According to Mas-Colell et al., “[w]e read $x⪰y$ as ‘$x$ is at least as good as $y$’” (1995, p. 6; see also Varian Reference Varian1984, p. 111). This definition of “$x⪰y$” might seem surprising, since the axioms are supposed to govern preferences within the (positive) science of economics, not judgments of goodness. It is better to read “$x⪰y$” as “the agent either prefers $x$ to $y$ or is indifferent between $x$ and $y$.” “$x\succ y$” means “the agent prefers $x$ to $y$,” and “$x\sim y$” means that the agent is indifferent between $x$ and $y$. Employing the weak preference relation “$⪰$” is convenient, because one does not have to specify separately the transitivity of strong preference, indifference, and mixtures of the two, such as the claim that if $x\succ y$ and $y\sim z$, then $x\succ z$.

Varian (Reference Varian1984, pp. 111–12) includes two additional axioms, which, as I explain shortly, are needed to prove a crucial theorem:

(Reflexivity) For all $x$ in $X$, $x⪰x$.

(Continuity) For all $y$ in $X\{x:x⪰y\}$ and $\{x:x\le y\}$ are closed sets.Footnote ²

Reflexivity is trivial and arguably a consequence of completeness, while continuity is automatically satisfied for any finite set of alternatives.

In contrast to Varian, who presents the axioms as assumptions about people’s actual preferences, Mas-Colell et al. maintain that completeness and transitivity are axioms of rationality: people’s preferences are rational if they satisfy the axioms (1995, p. 6). Since Mas-Colell and his co-authors are concerned to offer an account of people’s actual preferences, they must also maintain that to some extent people’s preferences are in this sense rational.

1.1.3 Utilities and the Ordinal Representation Theorem

The ordinal representation theorem proves that when people’s preferences satisfy these axioms,Footnote ³ then they can be represented by a continuous utility function that is unique up to a positive monotone (order-preserving) transformation (Debreu Reference Debreu1959, pp. 56–7). The “utility” of an alternative merely indicates the alternative’s place in an agent’s preference ranking. It is not something people seek or accumulate.

Here is a simple way to understand how a utility function “represents” preferences and what it means for it to be unique up to a positive order-preserving transformation. Suppose that an agent, Jill, who has preferences over a finite set of alternatives, adopts the convention of listing the alternatives on lined paper with preferred alternatives in higher rows and alternatives among which she is indifferent in the same row. Since Jill’s preferences are complete, every alternative must find a place in the list. Since Jill’s preferences are transitive, no alternative can appear in more than one row. Given such a list, one can assign numbers arbitrarily to rows, with the proviso that higher numbers are assigned to higher rows. Any numbering of the rows that is consistent with the ordering is an ordinal utility function. The numbers – the utilities – merely indicate where alternatives are located in Jill’s preference ranking. Utility is not pleasure or usefulness or anything substantive at all. It is merely an indicator of an alternative’s location in a preference ranking. Figure 1.2 provides an illustration of how ordinal utilities represent preferences.

Figure 1.2 Ordinal utility.

The pictures of food represent the ordered list of alternatives. $U$ and $U\prime$ are two of the infinite number of utility functions that assign higher numbers to alternatives in higher rows, and the same number to alternatives in the same row. The numbers are arbitrary apart from their order. In Figure 1.2, Jill chooses the banana rather than an apple because she prefers it to the apple. The picture says nothing about why she prefers the banana to the apple; it certainly does not say that the reason is that the banana has more utility. That claim mistakenly supposes that utility is something like pleasure, which is found in different quantities in the objects of preference. Utility is an indicator of preference. It is not an object of preference.

Jill does not choose the bread, despite preferring the bread to the banana, because she cannot have the bread, perhaps because the store has run out of bread or because she cannot afford to purchase it. Because she is indifferent between the banana and the pineapple, she could just as well have chosen the pineapple.

1.2 Revealed Preference Theory

Revealed preference theory is an interpretation of formal results explored initially by Paul Samuelson (Reference Samuelson1938, Reference Samuelson1947), generalized and developed by many others (especially Houthakker Reference Houthakker1950), and elegantly summarized by Arrow (Reference Arrow1959), Richter (Reference Richter1966), and Sen (Reference Sen1971). Samuelson sought to reformulate the positive theory of consumer choice so as to eliminate reliance on a subjective notion of preference. His motivation appears to have been philosophical. The empiricism (see §A.1) prevalent in the 1930s made reference to subjective preferences methodologically suspect. Apart from some technicalities, Samuelson succeeded in showing that if choices among commodity bundles satisfy a consistency condition, then a complete and transitive preference ranking can be constructed from the choices. Preferences can be “revealed” by choices, and the empirical legitimacy of talk of preferences can be secured by reducing it to talk of observable choices. In this work, Samuelson is concerned with the positive theory of choice, not with the normative theory of rationality, but his results apply to both. For further discussion of Samuelson’s methodological views, see Section 11.2.

The basic idea of revealed preference theory is that, if Mimi chooses option $x$, when she might have chosen option $y$, then she has revealed that she prefers $x$ to $y$ or is indifferent between them. Her choices are consistent if they satisfy the “weak axiom of revealed preference” (WARP). It says that if $x$ and $y$ are both in the set of alternatives among which Mimi chooses, and she chooses $x$, then she never chooses only $y$ from any set including both $x$ and $y$. In consumer choice theory, the statement of WARP is somewhat more complicated, because prices influence choices by determining which bundles of commodities are available rather than by influencing preferences. If choices satisfy sufficiently strong consistency conditions, then, in principle, economists can construct a complete and transitive revealed preference ordering from them (Sen Reference Sen1971, Reference Sen1973). Samuelson’s hope was to purge economics of unobservable and hence (in his view) unscientific content by replacing the axioms governing subjective preferences with an axiom requiring consistency of choice.Footnote ⁵ His view is still popular. For example, in an influential essay, Faruk Gul and Wolfgang Pesandorfer write, “[i]n the standard approach, the terms ‘utility maximization’ and ‘choice’ are synonymous” (2008, p. 7).

In fact, revealed preference theory mischaracterizes the notion of preferences that economists employ. Economists do not and cannot employ a notion of preference defined in terms of choices. Economists in fact employ a conception of preferences as subjective states that determine choices only in conjunction with beliefs.

This argument may appear beside the point to economists, who often take “revealed preference” to mean nothing more than inferring preferences from market data given often implicit assumptions about people’s beliefs. For example, Boardman et al. write that “[t]he indirect market methods discussed in this chapter are based on observed behavior, that is, revealed preference” (2010, p. 341). No one doubts that claims about preferences are inferred from behavior (including verbal behavior) and assumptions about beliefs. If only that were all that is meant by speaking of revealed preference theory. Samuelson is after bigger game.

The central claim of revealed preference theory can be formulated as: $A$ prefers $x$ to $y$ if and only if $A$ sometimes chooses $x$ from sets of alternatives that include $y$, and $A$ never chooses $y$ from any set that includes $x$. Many economists mistakenly believe that this claim has been proven. For example, Henderson and Quandt write, “the existence and nature of her [an agent’s] utility function can be deduced from her observed choices among commodity bundles” (1980, p. 45).

The theorem that Henderson and Quandt have in mind is the following. Suppose that $R$ is a two-place relation such that for some set of alternatives $S$, available to an individual, Jeff, $xRy$ if and only if Jeff chooses $x$ from $S$ that includes $y$ – that is, if and only if $x$ is in $C(S)$, the set of choices that Jeff makes when he repeatedly chooses from $S$.

$\text{“}R\text{”}$ is supposed to be interpreted as “weak preference” $(x\ge y)$. If Jeff weakly prefers $x$ to $y$, then he satisfies the WARP if and only if Jeff’s choice set for any set of alternatives including both $\text{x}$ and $\text{y}$ never includes $y$ unless it also includes $x$. The revelation theorem establishes that if Jeff’s choices satisfy WARP, then there is a relation $R$ that is complete and transitive and that implies Jeff’s choices. In other words, Jeff acts as if maximizing $R$.

On the intended interpretations, the revelation theorem establishes that preferences can be defined in terms of choices when choice behavior satisfies WARP. Some economists take the revelation theorem to show that economists can dispense with the notion of preference. On this view, the theorem shows that anything economists need to say about the behavior of individuals can be said in the language of choice (Mas-Colell et al. 1995, p. 5). Other economists regard the correspondence between choice and preference as legitimating talk of subjective preferences. In Sen’s words, “[t]he rationale of the revealed preference approach lies in the assumption of revelation and not in doing away with the notion of underlying preferences” (1973, p. 244).

These interpretations of the theorem are not defensible. The binary relation that the revelation theorem proves to be implicit in choices that satisfy the WARP is not the preference relation and cannot serve the functions that the preference relation serves in economic theory and practice. The identity between ${\text{Max}}^{\text{R}}(\text{S})$ and $\text{C(S)}$ does not reveal “underlying preferences.” Talk of preferences cannot be eliminated from economics without gutting the discipline.

Among the many objections to revealed preference theory,Footnote ⁷ two stand out. First, if preference is defined by choice, then where there is no choice, there is no preference. Revealed preference theory limits preferences to those alternatives among which agents choose. It thus denies that an agent has preferences among infeasible alternatives or among of states of affairs among which the agent faces no choice. Restricting preferences to those alternatives among which people have chosen would cripple economics.Footnote ⁸ Nothing could be said about how preferences among the consequences of choices affect choices, because preferences are limited to the objects of choice themselves. The only thing economists could say to predict an agent’s choice would be that the agent chooses whatever the agent has chosen.

The obvious response to this serious problem is to reinterpret the theory. Rather than maintaining that an agent such as Jessica prefers $x$ to $y$ if and only if she never chooses $y$ when $x$ is available, revealed preference theorists might say that Jessica prefers $x$ to $y$ if and only if she would never choose $y$ if $x$ were available (Binmore Reference Binmore1994). On this interpretation of revealed preference theory, whether agents actually face a choice between $x$ and $y$ is irrelevant to their preferences, which are defined by how they would choose, if they were to face such a choice.

In switching from actual to hypothetical choice, economists abandon the empiricist project of avoiding references to anything that is not observable. How King Charles would choose if it were up to him whether the USA remains in NATO is no easier to observe than his preference. Hypothetical choices are not choices. They can be predicted, but not observed. Predictions about how Charles would choose rely on no different or better evidence than claims about what he prefers. Notice, in addition, that claims about what he would do in a hypothetical situation cannot be answered until his beliefs are specified. Suppose that Charles were given an apparatus with a blue button that keeps the USA in NATO and a red button that leads it to leave. Without knowing what Charles believes about the buttons, we cannot predict what he would do.

The second problem with revealed preference theory, whether it attempts to define preference in terms of actual or hypothetical choices, is that its fundamental claim is false. It is not the case that if Martha prefers $x$ to $y$, then she never chooses $y$ or would never choose $y$, when she could have chosen $x$. If Martha mistakenly believes that $x$ is not among the available objects of choice, then she may choose $y$ despite preferring $x$ to $y$. For example, at the end of Romeo and Juliet, Romeo enters the tomb of the Capulets and finds Juliet apparently dead. He does not know that she took a potion that simulates death. Unwilling to go on living without Juliet, Romeo takes poison and dies. He chooses death from a set of alternatives that in fact includes eloping with Juliet. If choice defines preference, then Romeo prefers death to eloping with Juliet. In fact, of course, he prefers eloping with Juliet to death and chooses death only because he does not know that eloping with Juliet is a (so-to-speak) live option.

Defenders of revealed preference might respond as follows:

On this view, economists employ a technical concept, preference*, that is defined in terms of choice. It is unfortunate that their use of the same term confuses outsiders, but the economist’s notion of preference* is defined by choice.

Economists are entitled to define their own technical concepts and to proscribe the use of everyday concepts, but only if they actually use the concepts they define rather than the concepts they proscribe. In fact, economists rely on a concept of preferences that is not revealed by choices and they cannot avoid doing so without eviscerating their theories. For example, when Donald Trump was elected, the price of stock in private prisons, which Hillary Clinton had proposed shutting down, shot upward. To explain and predict this, economists need to cite the beliefs of investors as well as their preference for higher returns. But earning a higher return is not an object of choice, and the preference for higher returns is not a revealed preference. Preferences, as understood by economists, explain behavior only in conjunction with beliefs.

Moreover, if economists took preferences to be revealed preferences, they could not do game theory. Consider, for example, the scene from Pride and Prejudice where Darcy, overcome by his love for Elizabeth, proposes marriage to her, despite her lack of dowry, her mother’s vulgarity, and her younger sister’s silliness and impropriety. Regarding Darcy as arrogant and unfeeling, Elizabeth turns him down. Their interaction can be modeled as a game (Figure 1.3).

Figure 1.3 Darcy and Elizabeth.

The numbers in Figure 1.3 are ordinal utilities – that is, indicators of preference order. Higher numbers indicate more preferred alternatives. The first number in each pair expresses Darcy’s utility, and the second number expresses Elizabeth’s utility. Darcy moves first and can either propose (P) or not propose (~P). Not proposing ends the game with the second-best outcome for both players.Footnote ⁹ If Darcy proposes, then Elizabeth gets to choose whether to accept (A) or reject his proposal (~A). Rejecting the proposal is the best outcome for Elizabeth (at this point in the novel) and the worst for Darcy, while accepting is best for Darcy and worst for Elizabeth.

Some of the preferences in Figure 1.3 are revealed by choices. For example, Elizabeth’s refusal reveals that she prefers rejecting to accepting the proposal. However, other preferences, which are needed to define the game, rank alternatives between which agents do not and cannot choose. For example, Darcy cannot choose whether Elizabeth accepts, but the game is not well defined without specifying his preference over her acceptance or rejection. To predict whether Darcy will propose, a game theorist needs to know Darcy’s preferences among the outcomes, including outcomes between which he cannot choose, as well as his beliefs about whether Elizabeth will accept his proposal. Preferences in games are not preferences* (Rubinstein and Salant 2008, p. 119).

Beliefs mediate the relationship between choices and preferences. Economists can infer preferences from choices or choices from preferences only given premises concerning beliefs. Neither beliefs nor preferences can be identified from choice data without assumptions about the other. Choices can be evidence of preferences, but they cannot define them.Footnote ¹⁰

Economists have paid little attention to these objections because they often restrict their models to circumstances where what people believe coincides with what is truly the case. If beliefs match the reality, then economists need not mention them. That fact makes beliefs no less important.Footnote ¹¹ Preferences cannot be defined by choices, because preferences cannot be limited to the immediate objects of choice and because they cannot be inferred from choices without premises concerning beliefs.

1.3 Rationality and Uncertainty: Expected Utility Theory

The theory of rationality can be extended to choices involving risk and uncertainty. Economists and decision theorists commonly speak of risk when agents know the possible outcomes of their choices and their probabilities. In situations involving uncertainty, it is not known what are the probabilities of the outcomes of the alternatives or even what the outcomes may be.Footnote ¹² I treat the cases of risk and uncertainty together by allowing the probabilities mentioned in Section 1.3.1 to be either limits to relative frequencies or subjective degrees of belief. This simplification begs the question against those who maintain that situations of uncertainty involve more radical ignorance and different principles of rational decision-making.

1.4 What Are Preferences?

The discussion of the axioms of ordinal and expected utility theory, the implicit assumptions concerning preferences, and the mistakes of revealed preference theory jointly pin down the conception of preferences that lies at the heart of mainstream economics.Footnote ¹⁸ One can read off an interpretation of preferences from the following assumptions about preferences: preferences are (at least to some degree of approximation) complete, transitive, reflexive, and continuous; and they satisfy the independence condition. They are given and largely stable over time and across contexts, and the alternatives that they rank are complete states of the world. These assumptions imply:

1. 1. Preferences are comparative evaluations. They are evaluative, because they can be expressed in the form of a ranking in terms of better or worse. They are comparative: to say that Mary prefers to go dancing is elliptical. She prefers dancing to something else.

2. 2. Preferences are “total” comparative evaluations that motivate choices. They rank states of affairs, including the immediate objects of choice, as better or worse with respect to everything the agent considers to be relevant. Note that I make no assumption concerning what the agent considers to be relevant, nor concerning whether the agent is rational or well informed concerning her judgment of what is relevant to a choice. An agent’s preference ranking may depend on a few largely irrelevant properties of alternatives, or it may reflect an exhaustive investigation of the options.

3. 3. Preferences are subjective states that determine choices in combination with beliefs and constraints. As subjective states, they are not directly observable. They can be inferred from choices – but only with the help of premises concerning beliefs.

4. 4. Preferences are subject to rational criticism. They are not just gut feelings, even if sometimes they depend on nothing else.

Preferences must be total evaluations (point 2) because in combination with beliefs and constraints, they determine choices. They thus cannot be “partial” comparative evaluations of alternatives. From the agent’s perspective, preferences rest on a comparison in every relevant regard. I take it as implicit in the notion of an evaluation that it motivates choices. As total comparative evaluations, preferences in economics differ from preferences in everyday conversation, in which obligations and commitments compete with preferences in determining choices and the value of alternatives. Whereas noneconomists might say, “Bonnie preferred to go out with her friends to staying home; nevertheless, she stayed home because she promised to babysit,” economists would say that Bonnie preferred to stay home because she promised to babysit. In economic models of rational choice, whatever influences choices, other than beliefs and constraints, does so via influencing preferences.

More should also be said about the vulnerability of preferences to rational criticism, because many economists have denied it. Although in their famous paper “De Gustibus Non Est Disputandum” (“There is no arguing about tastes”) (1977), George Stigler and Gary Becker deny that preferences among commodity bundles should be regarded as primitives in economics, beyond explanation, they attribute to most economists the belief that “when a dispute has been resolved into a difference of tastes,” “there is no further room for rational persuasion” (1977, p. 76). They are right that such a view is prevalent among economists. Nevertheless, it is mistaken. Although Margaret may regard taste as the only factor that is relevant to her preference for a strawberry ice cream cone over a coffee ice cream cone, even a preference such as this one lays hostages to rational criticism. A newspaper article concerning an $E$. coli outbreak caused by eating strawberry ice cream may change Margaret’s preferences.Footnote ¹⁹ With new experiences and information, she may change the list of factors that she considers to be relevant to her preference. Satisfying the axioms of ordinal or cardinal utility theory can sometimes be a demanding cognitive task. Mas-Colell et al. maintain that “[i]t takes work and serious reflection to find out one’s own preferences” (1995, p. 6). In short:

The models of rational and actual choice employed by economists explain and predict behavior by citing the constraints on choices and the agent’s beliefs and preferences. Constraints on choices typically limit choices via beliefs. People who are late to an appointment do not flap their arms in a futile attempt to fly. Because they know that flying unassisted is not possible, they do not try. The axioms concerning preferences say nothing about what people prefer. Unusual people, who long for pain and suffering, could satisfy the axioms. Positive economic theory supplements the axioms of ordinal utility theory with axioms concerning the content of preferences, such as the claim that people prefer more commodities to fewer. These additional axioms are among the subject matter of Chapters 2 and 3.

1.5 Preferences and Self-interest

Neither ordinal utility nor expected utility say anything about the extent to which individuals are self-interested. However, the fact that the standard models of rational choice take an agent’s choices to be determined by the agent’s own preferences has misled economists and commentators on economics into thinking otherwise. Even the Nobel laureate, Amartya Sen, has on occasion mistakenly taken preference to imply self-interest. He maintains that “preference in the usual sense” has “the property that if a person prefers $x$ to $y$ then he must regard himself to be better off with $x$ than with $y$” (1973, p. 67). “Preference can be … defined so as to keep it in line with welfare as seen by the person in question” (1973, p. 73), and “the normal use of the word permits the identification of preference with the concept of being better off” (1977, p. 329). Similarly, Daniel Kahneman maintains that economists typically equate what people choose with what they anticipate will result in the most enjoyment (2006, pp. 489, 501).

Self-interest or expected advantage cannot be what people mean by preference, because there is no contradiction in maintaining that people’s preferences may depend on things that people do not expect to influence their own well-being. Most people do not apportion their donations to disaster relief by considering how much those donations will contribute to their own well-being. Drivers in the grip of road rage, who have shot and killed other drivers, are focused on harming others rather than benefiting themselves. Consider the humdrum instrumental decisions that fill one’s life. People often have no idea how they bear on their interests. When deciding among shoes for a seven-year-old, parents are thinking about which pair would be best for the seven-year-old, not for themselves. The mere possibility that people have preferences among alternatives, without considering how they influence their own interests or that people sometimes sacrifice their interests in order to accomplish something that matters more to them, shows that doing as one prefers is not by definition acting in one’s self-interest or promoting one’s expected benefits.

And these are not mere possibilities: apart from sociopaths, people are capable of distinguishing what they want most of all from what they judge to be best for themselves, and most people sometimes carry out actions whose consequences they believe to be worse for themselves than some feasible alternative. Moreover, if, as many welfare economists assume, well-being is defined as preference satisfaction, then preferences cannot be defined by expected well-being.

What leads to the conflation of preference and self-interest is that one’s preferences reflect one’s interests, and speaking of acting on one’s interests invites an equivocation between acting “in pursuit of one’s objectives (whether self-benefiting or not)” and acting “in pursuit of one’s own advantage.” There may be some individuals whose objectives are limited to benefiting themselves. But most people have all sorts of objectives. The pursuit of some project that is not intended to benefit oneself may of course wind up benefiting oneself. Indeed, venerable advice for living well counsels devoting oneself to something other than one’s own interests. But there is nothing in this good advice that equates preference and self-interest.

Many economic models take people to be self-interested, and for specific purposes, such models are often useful. I would be skeptical of a model of private equity companies that attributes to the executives of those firms entirely altruistic preferences. But self-interest is not built into the meaning of preferences. Utility theory places no constraints on what individuals may want; it only requires consistency of preferences and that choices manifest preference, given belief. Utility theory has a much wider scope than economics. As is appropriate in a theory of rationality, it says nothing specifically about commodities or services. It says nothing about people’s aims, about whether agents are acquisitive and self-interested or generous and otherworldly, or about whether humans are saints or sinners.

1.6 Conclusions

Mainstream economists employ a model of rational choice, which they also take to be an approximate characterization of actual choice. In this model, choice is determined by constraints, beliefs, and preferences. While not providing an explicit definition of preferences, economists are committed to a set of axioms and standard assumptions concerning preferences that together imply that preferences are total subjective comparative evaluations. Preferences are not beyond criticism, nor is it the case, as some economists have maintained, that economists have nothing to say about their formation and modification. Ordinal utility theory is a convenient way of expressing the consequences of the conditions economists impose on choices and preferences (and, in the case of expected utility theory, beliefs as well). As Chapters 2 and 3 show, this model of rational choice is embedded in microeconomics, general equilibrium theory, and macroeconomic models.

Although the normative model of rationality discussed in Chapter 1 is central to microeconomics, microeconomics is a positive theory describing, predicting, and explaining actual choices and their consequences. This chapter examines the microeconomic theory of consumer choice. Along the way we shall see an example of an economic model and, in reflecting on the theory of consumer choice and the explanation of demand, many questions will arise concerning the structure of economic theory and whether the propositions of economic theory are in accord with the evidence. The material here should be familiar to economists.

2.1 Market Demand for Consumption Goods

One central generalization of economics is the law of demand, which can be stated as: higher prices diminish demand for commodities and services, while lower prices increase demand. For example, an increase in the price of gasoline leads consumers to purchase less gas.

There are several things to note about the law of demand:

1. 1. It is not mysterious or deeply theoretical. It is part of the experience of retailers who hold sales to eliminate excess inventory.

2. 2. It is a generalization about markets, not about individuals.

3. 3. The law of demand cannot be stated simply as: price and quantity demanded are inversely correlated. For example, in August, when many families take car trips, both the price of gasoline and the amount purchased may be larger than in February. Economists distinguish between the effects of a change in the price of gasoline, which is a movement “along a demand curve” and the effects of other factors, such as whether families go on vacation, which imply a shift in the demand curve. The law of demand is a causal claim that price increases cause decreases in quantity demanded, and price decreases cause increases in quantity demanded. Unlike inverse correlation, which is a symmetric relation, there is an asymmetric causal relation here.

How is one to make a generalization such as the law of demand more precise and serviceable? One might start by attempting to list the major factors that influence market demand:Footnote ¹

• Demand for any commodity or service causally depends on its price: $p_x\text{}\uparrow \to q_x^{}{}^d\text{}\downarrow$; $p_x\text{}\downarrow \to q_x{}^d\text{}\uparrow$.Footnote ²

• Demand depends on the price of substitutes. If $x$ and $y$ are substitutes then $p_y\text{}\uparrow \to q_x^{}{}^d\text{}\uparrow ss$ and $p_y\text{}\downarrow \to q_x^{}{}^d\text{}\downarrow$. For example, demand for tea causally depends not only on the price of tea but also on the price of coffee. Groups of commodities or services such as coffee and tea that meet similar needs or satisfy similar wants are called “substitutes” by economists.

• Demand causally depends on the price of complements. If $x$ and $y$ are complements, then $p_y\text{}\uparrow \to q_x^{}{}^d\text{}\downarrow$ and $p_y\text{}\downarrow \to q_x^{}{}^d\text{}\uparrow$. For example, people want jam with bread and DVDs with their DVD players. Groups of commodities or services that are consumed together are called “complements” by economists.

• Demand causally depends on income and wealth. If $x$ is a normal good, then income $\uparrow \to q_x{}^d\text{}\uparrow$ and income $\downarrow \to q_x{}^d\text{}\downarrow$. An increase in the average income and wealth of buyers causes people in societies such as ours typically to demand more of “normal” goods and less of “inferior” goods.Footnote ³

• Demand causally depends on tastes or fads. When I was a child in the suburbs of Chicago, yogurt was an unusual specialty item and kiwifruit were unheard of. Demand for these commodities increased because people came to want them.

These additional generalizations provide a more detailed grasp of market behavior than does the law of demand by itself. However, without further generalizations about the strength and stability of these different causal factors, economists have no general way to predict even the direction of a change in demand in response to price changes. Furthermore, even if economists were able to use these generalizations to predict changes in prices and quantities purchased, these generalizations provide little theoretical depth. If economists stopped here, they would have no explanation for why these generalizations obtain, and their explanations of market phenomena would be superficial.

Empirical research can flesh out these generalizations. With sufficient data, it is possible to estimate the magnitude of the change in demand for $\text{x}$ with respect to changes in the price of $x$, ceteris paribus or the changes in demand ceteris paribus, in response to changes in the prices of substitutes or complements. Large firms devote substantial resources to the empirical study of market behavior, and there is a well-established body of econometric techniques that are employed to estimate the responsiveness of demand (and supply) to various causal influences.

Market generalizations, rendered quantitative by econometric inferences from statistical data and by empirical research are precarious. Fads are quirky. The introduction of new products can disrupt settled patterns of consumption. Although it is possible that incomes, tastes, and the prices of complements and substitutes happen not to change so that the change in demand $(\Delta q_x^d)$ ceteris paribus with a change in the price of $\mathrm{x }(\Delta p_x)$ is the actual change in demand, it is more often the case that ceteris is not paribus – that is, other things apart from the particular causal variable one is interested in also change. So, in addition to determining the causal relations between individual causal variables and $q^d{}_x^{}$, economists need to know how to combine the effects of multiple causes.

Moreover, no matter how useful generalizations relating $q^d{}_x^{}$ to various causal factors may be to firms who seek advice concerning how to price or package their products, these generalizations by themselves must be disappointing to economic theorists who aspire to imitate the great achievements of the natural sciences. For, apart from statistical techniques and empirical research methods, there is little theory here.

Those economists interested in theory – and not all economists are or should be interested in theory – have attempted to put demand and consumer choice on a deeper and more secure theoretical footing. Starting with the basic model of rational choice, they have attempted to find further generalizations concerning the choice behavior of individuals that explain, systematize, and unify causal generalizations concerning market behavior. Just as Newton’s theory of motion and gravitation accounts for (and corrects) Galileo’s law of falling bodies and Kepler’s laws of planetary motion, so a deeper theory of the economic behavior of individuals might account for and possibly correct generalizations concerning market behavior. This strategic choice is neither inevitable nor guaranteed to succeed. More superficial and less unified models seem to be lesser scientific achievements than a deeper and more unified model of consumer choices, but the deeper account may not be attainable or more useful.

2.2 The Theory of Consumer Choice

Consumer choice theory is supposed to explain the causal generalizations discussed in Section 2.1 concerning market demand. It is made up of the following three “behavioral postulates” or “laws” (§A.4):

1. 1. Consumers are rational – that is, they have complete, transitive, reflexive, and continuous preferences and do not prefer any known (affordable) option to the one they choose.

2. 2. Consumers are acquisitive – that is:

   1. a. the objects of every individual $i$’s preferences are bundles of commodities consumed by $i$,

   2. b. there are no interdependencies between the preferences of different individuals,

   3. c. up to some point of satiation (that is typically unattained), individuals prefer larger commodity bundles to smaller (bundle $y$ is larger than bundle $x$ if $y$ contains at least as much of every commodity or service as does $x$ and more of some commodity or service), and

   4. d. although a consumer may be acquisitive because of some ultimate altruistic aim (of no interest to consumer choice theory), the proximate goals of acquisitive consumers are self-interested.

3. 3. The preferences of consumers for commodities and services show diminishing marginal rates of substitution – DMRS. For all individuals $i$ and all commodities or services $x$ and $y$, $i$ is willing to exchange more of $y$ for a unit of $x$ as the amount of $yi$ has increases relative to the amount of $xi$ has.Footnote ⁴

In Chapter 1, I discussed the definition or model of rationality that is used here. An individual $A$ is rational if and only if $A$’s preferences are complete, transitive, reflexive, and continuous, and $A$ never prefers any option $A$ knows to be available to the option $A$ chooses. In the context of consumer choice theory, an available option is an affordable commodity bundle. Whether taken as normative or positive, utility theory has a much wider scope than economics. The second “law,” which asserts that consumers are acquisitive, brings utility theory to bear on economic behavior.Footnote ⁵ This generalization is a cluster of claims. One might call it “nonsatiation,” but doing so overemphasizes one element in the cluster. One might call it “self-interest,” but doing so would not highlight the limitation of preferences to commodity bundles. One might speak of “greed,” but that would sound pejorative. To say that it regards consumers as acquisitive seems the best compromise, although the label may misleadingly suggest a preference for money rather than what money can buy.

To say that consumers are acquisitive is to say that, unless satiated, they want more of all commodities and services. As economists recognize, this claim is a caricature of human behavior. Like the other generalizations, it might be defended as a reasonable first approximation; as a harmless distortion of reality that is required for the construction of a manageable theory. One might argue that it captures a causal “tendency” that is central to economic behavior. Alternatively, one might argue that, given the presence of markets, to regard people as acquisitive is not such a gross exaggeration after all. Since one can always sell one’s fifth computer and donate the money to a favorite charity, even altruists might prefer a commodity bundle containing five computers to one containing only four. The objection that selling a used computer is not costless in terms of time and hassle misses the mark, because, to the extent that it is correct, it is not the case that the five-computer commodity bundle differs from the four-computer bundle only in the number of computers. On the contrary, the five-computer bundle arguably possesses less leisure.Footnote ⁶

If individuals are acquisitive, then their immediate objectives are self-interested, for their preferences are over bundles of goods and services, and by denying any interdependence of preferences economists rule out commodities or services such as food for starving Ethiopians, which might be on sale from Oxfam. Acquisitiveness demands that the satisfaction of the preferences of others not be included, even implicitly, among the arguments of my utility function.Footnote ⁷ Acquisitiveness identifies options with commodity bundles and implies that choices are based on wanting more of everything. Whereas utility theory is perfectly consistent with altruism, the claim that people are acquisitive rules out immediately altruistic objectives. It is the assumption that consumers are acquisitive that confines attention not only to “rational man” but to “economic man,” who is motivated by the pursuit of what money can buy. The claim that people are acquisitive rules out both direct concern with the plight of others and envious concern with the successes of others. Although overly cynical economists and students of economics may believe that people are exclusively acquisitive, a more charitable interpretation attributes to economists the view that, although false, acquisitiveness is a useful exaggeration with respect to market behavior.

The “law” of DMRS implies that the amount that a consumer such as Penelope will pay for a portion of some good or service $x$ diminishes as the amount of $x$ that Penelope possesses increases. She is willing to pay less for her second bag of French fries than for her first. It is difficult to state DMRS in its full generality without the help of mathematics. A helpful way to grasp what it says is to use some old-fashioned language. Suppose that rather than merely indicating preferences, utility functions measure some quantity, such as pleasure, and that, as is the case in expected utility theory, utilities have cardinal, not merely ordinal, significance – that is, differences between the utilities of different alternatives are not arbitrary.

Employing a cardinal notion of utility, nineteenth-century economists formulated a law of diminishing marginal utility. This law, which was independently discovered by several economists, was one cornerstone of the so-called neoclassical or marginalist revolution in economics in the last quarter of the nineteenth century. If commodity bundle $b\text{'}$ differs from bundle $b$ only in containing more of some commodity $x$, then acquisitive consumers will prefer $b\prime$ to $b$. The law of diminishing marginal utility offers the further generalization that the size of this (positive) increment in the utility of $b\prime$ as compared to $\text{b}$ is a decreasing function of the amount of $x$ already in $\text{b}$. As Penelope keeps eating French fries, the amount by which an additional French fry increases her total pleasure becomes smaller and smaller.

Apart from qualms about identifying utility with some substantive good such as pleasure, the law of diminishing marginal utility seems plausible. There are grounds to deny that it is universally true (see Karelis Reference Karelis1986), but it is plausible in many contexts. It neatly explains the paradoxical fact that useful but plentiful goods, such as water, are often cheaper than relatively useless but scarce goods, such as diamonds – a fact that bothered eighteenth- and early nineteenth-century economists. But if, as in contemporary economics, utility functions are no more than a means of representing preference rankings, differences in utilities are arbitrary, and one cannot sensibly speak of diminishing marginal utility.

The law of DMRS is Edgeworth’s (Reference Edgeworth1881) and Pareto’s (Reference Pareto1909, chapters 3 and 4) trick for capturing the implications of diminishing marginal utility for consumer choice without commitment to cardinal utilities. The idea was rediscovered and popularized by J. R. Hicks and R. G. Allen (Reference Hicks and Allen1934). The essence is that an individual is willing to trade away more of $y$ to get a unit of $x$ when he or she has little of $x$ than when he or she has a great deal of $x$. Instead of looking at the utility increment provided by an additional unit of $x$ as a function of the amount of $x$, economists can look at the terms of exchange between $x$ and other commodities. The notion of marginal utility may still be lurking in the background as an explanation for DMRS, but all that consumer choice theory needs are ordinal utilities, acquisitiveness, and diminishing marginal rates of substitution.

One no more understands consumer choice theory by learning its constituent generalizations than one understands quantum theory by learning the Schrödinger equation. One needs to see how rationality, acquisitiveness, and DMRS are used together and what simplifications and mathematical techniques are required to bring them to bear on economic phenomena. When we see how the theory of consumer choice accounts for market demand, we shall have a better sense of the theory.

Regardless of its success in accounting for market phenomena, the theory of consumer choice is a troubling theory, for it is hard to regard its basic claims as “laws” without the scare quotes. This problem lies at the heart of most methodological discussion concerning economics and is discussed in Part II.

In treating theories as sets of “laws” or “lawlike” statements, I am assuming the answer to the philosophical question, “what is a scientific theory?” (§A.4). This view of scientific theories is defended Chapter 6.

2.3 Market Demand and Individual Demand Functions

Economists explain market demand in terms of individual demand. With preferences, prices, and budgets already fixed, consumers possess, as it were, a shopping list for commodities and services upon which they can spend their budgets. The market demand for each commodity or service $(x,y,\dots )$ is the sum of all the individual demands – that is, the sum of the quantities of $x$, $y$, etc. that are on the shopping lists. The market demand function (for $x$) is a mapping from prices, incomes, and preferences to amounts of $x$ demanded. As in many elementary treatments, the discussion here oversimplifies and takes market demand functions to be the sum of individual demand functions (for a careful treatment, see Friedman Reference Friedman1962).

A more substantive step in the explanation of market demand is the derivation of individual demand functions from consumer choice theory and from further statements concerning the institutional and epistemic (belief or knowledge) circumstances in which consumers choose. An individual demand function for a commodity or service $x$ states how much of $x$ (as a flow of $x$ per unit time) is demanded by an individual $i$ as a function of causal variables, some of which may be left implicit within a ceteris paribus condition. For example, when economists treat the quantity of $x$ that $i$ demands as a function only of the price of $x$ (ceteris paribus), they are not denying that $i$’s demand for $x$ also depends on income, tastes, and other prices. When these other causal determinants of $i$’s demand for $x$ change, the demand curve – that is, the functional relationship between the price of $x$ $(p_x)$ and the quantity of $x$ demanded by $\mathrm{i }(q_i^{}{{}^d}_x)$ will shift. Suppose for concreteness that $\text{x}$ is coffee and that there is a change in both its price and in the price of a substitute for coffee such as tea. The change in demand for coffee with a change in the price of coffee will differ from what it would have been had the price of tea not changed. If in a particular application such changes are small or rare, it is handy to consider explicitly only the causal dependence of $q_i^{}{{}^d}_x$ on $p_x$ and to hide the impact of the other causal influences in a ceteris paribus clause.

The simplest models of demand, which suppose that individuals can choose among quantities of only two commodities, have special limitations and serve as pedagogical devices much more than explanatory or predictive tools. I focus on them here, because they permit a graphical treatment and are easy to understand. They also illustrate central features of economic modeling and how fundamental theory is employed to derive and to explain useful but more superficial economic generalizations.

2.4 The Model of a Two-Commodity Consumption System

To derive features of individual demand functions from the generalizations of consumer choice theory, economists employ models of consumer choice. I call the simplest of these models a “two-commodity consumption system.” This is my terminology. You will not find it in any economics textbooks.

A two-commodity consumption system is supposed to model the behavior of some individual agent, $A$, faced with a choice between bundles of only two commodities $x$ and $z$ in the context of a market economy, where prices are already posted and $A$’s income is already determined. Obviously, consumption possibilities include many more than two commodities or services, but one might treat all commodities except one as a single composite commodity. Let us suppose that Alice chooses a consumption bundle consisting of coffee ($X$) and “everything-else-Alice-consumes” ($Z$). One then formulates the model of a two-commodity consumption system as follows.

A quadruple $<A,x,z,Y>$ is a two-commodity consumption system if and only if:

1. 1. $A$ is an agent, $x$ and $z$ are kinds of commodities or services, and $Y$ is the agent’s income.

2. 2. $A$ faces a choice over a convex set of bundles of commodities $(q_x,q_z)$, where $q_x$ and $q_z$ are non-negative real numbers representing quantities of $x$ and $z$ respectively.Footnote ⁸

3. 3. $A$’s income, $Y$, is a fixed amount known to $A$, and it is entirely spent on the purchase of a bundle $(q_x,q_z)$.

4. 4. The prices of $x$ and $z$, $p_x$ and $p_z$, are fixed and known to $A$.

5. 5. $A$’s utility function is a strictly quasi-concave, increasing, and differentiable function of $q_x$ and $q_z$ (or, alternatively, $A$’s indifference curves are continuous and convex to the origin).

6. 6. $A$ chooses the bundle $(q_x,q_z)$ that maximizes $A$’s utility function subject to the constraint that $p_x{q}_x\text{}+\text{}{p}_z{q}_z\le Y$ (or the bundle $(q_x,q_z)$ is on the highest attainable indifference curve).Footnote ⁹

These six assumptions fall into three classes: (a) simplified specifications of the institutional and epistemic setting – for example, fixed and known prices and income; (b) restatements or specifications of the “laws” of consumer choice theory – for example, maximization of utility functions that show acquisitiveness and DMRS; and (c) further simplifications whose role is to make the analysis easy and determinate – for example, only two infinitely divisible commodities. The model is not an uninterpreted mathematical structure. It defines a quadruple of agent, commodities, and income.

Here are some further details concerning the three groups of assumptions that define a two-commodity consumption system:

1. (a) Institutional and epistemic assumptions. The highly simplified specification of the institutional and epistemic setting in the two-commodity consumption system is common in many economic models. By attributing perfect knowledge to individuals, economists spare themselves any inquiry into the beliefs of agents (§1.2). The assumption that the agent is a “price taker” – that is, that the agent cannot intentionally influence prices – is common and part of the definition of what economists call “perfect competition.” Introducing the possibility of bargaining would make the outcome depend on bargaining power and skill, which would complicate the model and reduce its determinacy.

2. (b) Specifications of the “laws.” The generalizations concerning preference and choice that make up the theory of consumer choice appear in mathematical dress. Assumption 6 of the model says that $\text{A}$ chooses a commodity bundle that maximizes $A$’s utility, subject to the constraint that the value of $A$’s consumption must not exceed $A$’s income. This is just a restatement of what I called the choice determinacy axiom. It means nothing more than that, subject to the budget constraint, $\text{A}$ chooses what $A$ most prefers.

   The continuous utility function mentioned in assumptions 5 and 6 is an ordinal utility function and is definable only if $A$’s preferences are complete, transitive, reflexive, and continuous. Stipulating that $A$’s utility is an increasing function of both $q_x$ and $q_z$ is asserting that $A$ is acquisitive. Demanding that the utility function be differentiable is merely a mathematical convenience.Footnote ¹⁰ Finally, to stipulate that the utility function must be strictly quasi-concave restates the law of DMRS. Suppose that for any bundles of the two commodities $b\text{'}\left[=(q_x\text{'},q_z\text{'})\right]$ and $b\text{*[=(}{q}_x\text{}\text{*},q_z\text{}\text{*)]}$, $U(b\prime )\ge U(b*)$. Then the function $U(b)$ is strictly quasi-concave if and only if for all $b$ strictly between $b\text{'}$ and $b\text{}*, U(b)>U(b*)$ (Malinvaud Reference Malinvaud1972, p. 26). The alternative formulation of assumption 5 in terms of indifference curves is discussed in the next section.

3. (c) Further simplifications in the model. Although the institutional and epistemic specifications and the restatements of the “laws” of the theory of consumer choice are problematic, what seems strange or perhaps even bizarre (until one becomes accustomed to the habits of economists) are the extreme simplifications – a convex consumption set containing only two commodities and all income spent. (A set is convex if a line between any two points in the set is entirely contained in the set. So, among other things, the convexity of the set of commodity bundles implies that commodities are infinitely divisible.)

Despite the extreme simplifications, models such as the two-commodity consumption system are not silly. Some of the simplifications are avoidable and one can investigate whether those that are not avoidable are likely to lead to significant error. At the cost of mathematical complexities and some indeterminacies, one can analyze consumer choice among indivisible commodities. Taking income as fixed separates decisions to consume from decisions to devote resources to increasing income or future consumption. Depending on which questions the model is intended to answer, economists may regard this separation as a helpful first approximation. When at the supermarket, people typically take their incomes as given.

2.5 Deriving Individual Demand

In principle, it is possible to derive a fully specified demand function for a particular individual from information about the individual’s preferences and incomes and the price and availability of commodities and services. However, economists never know enough to carry out such a derivation. Instead, they show how such a derivation could be carried out, and they show that axioms concerning preferences specified by consumer choice theory imply the generalizations concerning market demand with which this chapter began.

Since the commodity bundles among which $A$ chooses contain only two infinitely divisible commodities, the whole set of consumption possibilities may be represented by the portion of the $q_x\text{}–q_z$ plane bounded below and to the left by the lines $q_x\text{}=0$ and $q_z\text{}=0$ (see Figure 2.1). Each point $(a,b)$ in this quadrant represents a commodity bundle consisting of $a$ units of commodity $x$ and $b$ units of commodity $z$. This is an instance of what economists call a “commodity space,” and $A\text{’s}$ utility function assigns a utility (ranking) to each point. If commodity bundle $b_1$ is northeast of $b_2$ (above and to the right of it), then because $A$ is acquisitive, $A$ prefers $b_1$ to $b_2$.

Figure 2.1 Indifference curves.

One can represent $A$’s budget constraint by the line, $p_x{q}_x+p_z{q}_z=Y.$ It is a straight line with the slope $-p_x\text{}/\text{}{p}_z$ that intersects the $q_x$ axis at $Y\text{}/\text{}{p}_x$ and the $q_z$ axis at $Y\text{}/\text{}{p}_z$. $A$ wants to move as far northeast as possible but cannot spend more than $Y$, which means that $A$’s consumption lies somewhere along the budget line.

$A$’s preferences, in the form of $A$’s “indifference curves,” determine where $A$’s consumption lies along the budget line. A point in the commodity space $(q_x,q_z)$ lies on the indifference curve through the point $(a,b)$ if and only if $A$ is indifferent between $(q_x,q_z)$ and $(a,b)$. Since commodities are infinitely divisible and $A$’s utility function is continuous, $A$’s indifference curves will be continuous. If $(a\prime ,b\prime )$ is northeast (or southwest) of $(a,b)$, then $(a\prime ,b\prime )$ cannot lie on the indifference curve passing through $(a,b)$, and, given the transitivity of indifference, the indifference curve including $(a,b)$ cannot intersect the indifference curve including $(a\prime ,b\prime )$.

Because $A$’s utility function depends on two variables, $q_x$ and $q_z$, its graph would require three dimensions, but, since the values of the utilities, apart from the ordering, do not matter, one loses nothing by representing $A$’s preferences by indifference curves, which can be drawn in two dimensions. Instead of relying on the strict quasi-concavity of the utility function to draw inferences concerning $A$’s consumption choice, economists can make use of the closely related claim that $A$’s indifference curves are convex to the origin, that is, that they have the shape represented in Figure 2.1. The claim that $A$’s indifference curves are everywhere convex to the origin is a perspicuous mathematical restatement of the law of DMRS. The absolute value of the marginal rate of substitution, given that $A$ possesses commodity bundle $(a,b)$, is the slope of the indifference curve passing through $(a,b)$ at point $(a,b)$. As $q_x$ relative to $q_z$ increases, the magnitude of the slope of the indifference curve increases ever more slowly. If $q_z/q_x$ is small, a small amount of $z$ sacrificed for a large amount of $x$ keeps $A$ on the same indifference curve.

$A$ does what he or she most prefers if and only if $A$ chooses a bundle on the highest indifference curve that intersects the budget line. That indifference curve will be tangent to the budget line, except in the case of a so-called corner solution, where the highest indifference curve intersects the budget line at one of the axes.

Suppose $x$ were coffee and $z$ were “$ee$” (the composite commodity consisting of everything else that $A$ consumes). Suppose also that $A$ is some particular person, Alice. Economists could predict exactly how much coffee Alice buys if they knew Alice’s income, the price of coffee, some index price for $ee$, and Alice’s indifference curves. However, economists obviously do not know enough to make such quantitative applications.

Knowing little beyond what is stipulated in the assumptions of the model, economists would like to be able to predict or explain changes in consumption as a consequence of changes in prices or income. To do this, further assumptions about the shape of Alice’s indifference curve are necessary. Almost anything is possible in general. A larger income may lead to a smaller demand for inferior goods, and a price decrease can even go with a decrease in demand for “Giffen goods.”Footnote ¹¹ Given indifference curves shaped like those in Figure 2.1, which are reasonable in the case of many consumers and goods such as coffee, more definite conclusions can be reached. If income decreases to $Y\text{’}$ in Figure 2.1, Alice will consume less of both coffee and $ee$. If the price of coffee decreases, then Alice will consume more coffee and less of $ee$. Alice’s demand for coffee is a decreasing function of the price of coffee, an increasing function the price of $ee$ (which is a substitute), and an increasing function of Alice’s income, and, of course, it depends upon Alice’s preferences. These claims say nothing about the dynamics of adjustment (see §3.4). They state how demand would differ, as it were, after the dust has settled.

Since market demand is the sum of individual demands, economists can explain the generalizations concerning market demand. And, moreover, just as economists who sought to emulate Newton might have hoped, economists also have corrections for these market generalizations. The theory of consumer choice shows how those generalizations, including even the law of demand, can break down. It would be nice to have a quantitative account of market demand, and it would be nice to make use of a less idealized model, but the descent from the level of market generalization to theoretical underpinnings appears to be a success.

This success is modest, because data concerning market demand provide weak support for consumer choice theory. For example, as Gary Becker has shown (1962), completely random behavior could account for downward-sloping demand curves and the influence of income on demand; and habitual behavior could account for all of the market generalizations discussed earlier. So the theory of consumer choice is only weakly confirmed by its ability to explain the general facts concerning market demand.

2.6 Conclusions

This chapter has sketched the basic components of consumer choice theory and shown how they imply relatively superficial generalizations concerning market demand. In describing the way that microeconomics characterizes the demand side of markets, this account has also been accumulating philosophical debts. It has spoken of rational choice theory and consumer choice theory, without saying much about what constitutes a “theory.” It has taken the fundamental constituents of those theories to be laws, albeit typically with scare quotes, since presumably false claims are not really laws. But I have said nothing about what a law might be. Chapter 1 spoke of models of rational choice, and this chapter delineated one simple model. But little has been said about what a model is or how models, laws, and theories are related. And Section 2.5 ended with some concerns about confirmation, which has also not yet been discussed.

Consumer choice theory purports to predict and explain the demand “side” of markets. To understand markets, one must also consider supply. A theory is also needed to account for how the “forces” of supply and demand jointly determine economic outcomes. In this chapter, I fill in these pieces of microeconomic theory, before turning in Chapter 4 to normative economics. The material here – especially in Sections 3.1–3.4 – should again be familiar to economists. Sections 3.5–3.7 make more controversial claims.

3.1 Market Supply of Consumption Goods and the Theory of the Firm

Just as market demand depends on prices, incomes, and tastes, so market supply depends on the prices of outputs and inputs and on technology. A higher price for $x$ brings forth a larger supply; a lower price diminishes supply.Footnote ¹ Higher prices of inputs either increase the price of output or decrease its supply. Improvements in technology can make it cheaper to produce something and increase the supply of it at a given price. The fate of older coal-fired electric-generating plants illustrates these claims. Changes in technology, especially in fracking and in wind turbines, have lowered electricity-generating costs, and many older coal-fired plants with high operating costs have shut down.

As in the case of generalizations concerning demand, empirical work and statistical analysis can add a quantitative dimension; and the results can be of practical use. Just as in the case of demand, economists seek more than such superficial theorizing. They aim to uncover deeper laws and provide a more systematic explanation of the behavior of firms and the owners of resources.

In theorizing about the supply of unproduced services, such as labor, the theory of consumer choice can itself be adapted, with quantity supplied depending on the choices of individuals between leisure, job amenities, and consumption goods and services. However, most consumer goods and services are produced by firms. Because firms (unlike consumers) are abstractions, standing in for entities as unlike one another as Microsoft and the corner locksmith, economists focus on generalizations concerning the transforming of inputs into outputs rather than characteristics of specific enterprises. The point is to clarify how changes in technology and prices of inputs and outputs influence supply.

As in the case of consumer choice theory, I characterize the theory of the firm in terms of the substantive generalizations that, together with simplifications about the circumstances, explain more superficial generalizations about supply. The presentation here may appear less familiar to economists than in the case of consumer choice theory. For example, in their influential microeconomics text, Mas-Collel et al. (Reference Mas-Collel, Whinston and Green1995) list eleven fundamental characteristics of “production sets,” making no distinction between (1) those that characterize specific markets such as free entry; (2) those, like infinite divisibility of inputs and outputs, that are simplifications needed for the application of mathematical tools; (3) those that are everyday generalizations, such as the general impossibility of transforming outputs back into inputs; and (4) substantive generalizations or “laws” that economists have identified in order to advance the understanding of the supply of goods and services. Unlike their presentation, the account presented here emphasizes the distinction between “laws,” background knowledge, and simplifications, although the central content is the same.

The theory of the firm is made up of two (or arguably three) “laws”:

1. 1. Diminishing returns. In the neighborhood of the actual levels of a firm’s output and inputs, output increases with increases in the quantity of each input. However, holding fixed all but any one input, output increases with additional units of that input at a decreasing rate.Footnote ²

2. 2. Profit maximization. Firms attempt to maximize net returns.Footnote ³

There is a third generalization whose status as a law in the theory of the firm is more questionable:

1. 3. Constant returns to scale. In the neighborhood of the actual levels of a firm’s output and inputs, if all of the inputs into production are increased or decreased in the same ratio, then output will increase or decrease in that ratio.

Just as acquisitiveness and diminishing marginal utility state that utility increases at a decreasing rate when consumption increases, so the law of diminishing returns, or diminishing marginal productivity, states that the increase in output from an increase in the quantity of input $k$ is a decreasing function of $q_k$. At extremely low levels of input $k$, relative to the other inputs there may be increasing returns, and, with enough of any input, output can actually be reduced, as excess quantities of an input get in the way and gum up the works. Diminishing returns does not deny these facts; it merely claims that they do not obtain within the range of mixes of inputs found in actual firms. Just as in the case of marginal utility, one speaks of diminishing marginal productivity because it is claimed that the marginal product (the marginal increase in output due to an increase in the quantity of some input) decreases, not that total product decreases.

Constant returns to scale says roughly that if one doubles all inputs, one gets double the output. There is no conflict between constant returns to scale and diminishing returns, although the terminology might suggest otherwise. Constant returns to scale is a troubling generalization. Some, such as Samuelson (Reference Samuelson1947, p. 84), regard it as a trivial definitional truth – whenever it appears not to hold, economists invent some further input that has not been augmented enough or has been augmented too much. There is no reason why returns to scale should be constant, unless the economy is always in equilibrium. If there were increasing or decreasing returns to scale, then, contrary to the assumption of equilibrium, firms would wish to be larger or smaller than they in fact are. Constant returns to scale helps make economic models coherent and mathematically tractable rather than functioning as a substantive generalization concerning economies.

Profit maximization has been controversial. From the armchair, it appears to be a reasonable approximation, but profit maximization by firms may conflict with utility maximization by individuals. What happens when, as is usually the case, managers have preferences for other things in addition to higher profits for the firms they manage? How can individuals be motivated so that firms will aim to maximize profits? Much work in agency theory has been done on this question (Fama Reference Fama1980; Jensen and Meckling Reference Jensen and Meckling1976; Williamson Reference Williamson1985).

By themselves, these “laws” provide the skeleton of a theory of the firm. As was the case in consumer choice theory, one needs to see how the laws are used together and what sorts of simplifications and mathematical techniques are needed to bring them to bear on particular problems. Although the law of diminishing returns is relatively solid, the “laws” that make up the theory of the firm give rise to qualms (to be addressed in Chapter 9) like those that consumer choice theory provokes.

3.2 Market Supply and the Model of a Two-Input Production System

Just as economists explain market demand in terms of individual demand, so they explain market supply in terms of the supply of individual firms, treating the quantity supplied in markets for consumer goods as the sum of the quantities firms supply. The substantive step is the derivation of a firm’s supply function from the theory of the firm and from additional premises concerning the institutional and epistemic circumstances in which production decisions are made. Some firms transport, distribute, or market goods rather than produce them, but these activities can be regarded as kinds of production. The supply function relates the output of a firm (as a flow per unit time) to its inputs. To simplify the discussion, assume that the firm buys its inputs and sells its single output in competitive markets. There are many complexities here and, as in the case of demand, I confine my treatment to the simplest case.

In the most elementary treatments, economists employ a simple model of the firm, which I call a “two-input production system.” This model, like the two-commodity consumption system discussed in Section 2.2, illustrates characteristic features of models in economics:

$<f,z,a,b>$ is a two-input production system if and only if:

1. 1. $f$ is a firm; $z$ is its output; and $a$ and $b$ are its inputs.

2. 2. In “the short run” $q_b$ is fixed as $q_b\text{}*$.

3. 3. $q_z=g(q_a,q_b)$, where $g$ is continuous and differentiable and known to $f$. The first partial derivatives of $g$ are positive, and the second partial derivatives are negative.

4. 4. The prices, $p_z$, $p_a$, and $p_b$, are given and known to $f$.

5. 5. $f$ aims to maximize net returns: $p_z{q}_z-[p_a{q}_a+p_b{q}_b]$.

Only two of the laws of the theory of the firm are employed here: diminishing returns and profit maximization. Since the quantity of one of the inputs of production, $b$, is fixed, the scale is unchanging, and returns to scale are irrelevant. The analysis makes use of Marshall’s insight (1930, book V, chapters 1–5; see also Boland Reference Boland1982a) that economists can regard factors that take a long time to adjust as fixed “in the short run.” The institutional and epistemic assumptions mirror those in the two-commodity consumption system. The firm is operating in a competitive market, where it cannot influence the price it must pay for inputs or the price it can get for its output.Footnote ⁴ The firm knows these prices, which is a stronger assumption than in the case of consumption, since firms often make their production decisions well before they sell their product. This model leaves out capital, time, and uncertainty. It simplifies by assuming infinite divisibility (implicit in 3), one output, and only one variable input into production.

3.3 Deriving a Competitive Firm’s Supply Function

With the quantity of $b$ fixed at some $q_b\text{}*$, output is a function only of $q_a$, or, alternatively, economists can regard the input requirements of a as a function of the level of output. Economics can thus think about a firm’s decision-making technologically, with output determined by input, or economically, with the level of input determined by the desired level of output.

Economists can then graph the partial derivative of $g$ with respect to $q_a$ (with $q_b$ fixed at $q_b\text{}*$) or the derivative of the inverse function relating $q_a$ to the desired level of $q_z$. In other words, one can consider the marginal productivity of $a$ – the marginal difference in output owing to a marginal increment of $a$ – as a function of $q_a$, or one can consider the marginal input requirements as a function of $q_z$. If one multiplies by $p_z$ in the first case and $p_a$ in the second, one can, as in Figure 3.1, graph the relationship between $q_a$ and the value of the marginal product of $a$ and, as in Figure 3.2, one can graph the relationship between marginal cost and $q_z$.

Figure 3.1 Marginal productivity.

Figure 3.2 Marginal cost.

As diminishing returns implies, the marginal productivity curve will have a negative slope over the relevant range of input mixes. Figure 3.1 also shows the fixed price firm $f$ must pay per unit of $a$, ${\text{p}}_{\text{a}}$, as a horizontal line. Since $f$ attempts to maximize profits and knows both $p_a$ and the marginal productivity of $a$, the amount of input $a$ employed will be $q_a\text{*}$, and the level of output is then $g(q_a*,q_b\text{*)}$. If the firm, $f$, were to employ less of $a$ than $q_a\text{*}$, then it could increase its profits by increasing production, for an additional unit of $a$ will result in an increment of output that is worth more than the cost of the additional input. If more than $q_a\text{*}$ is employed, then $f$ is decreasing its net return by employing units of input that cost more than the value of output they produce.

In Figure 3.2, diminishing returns implies that the marginal cost curve (the marginal input requirements of $a$ multiplied by $p_a$) is upward sloping. Just as one can represent the given input price, $p_a$, as a horizontal line Figure 3.1, so one can represent $p_z$ as a horizontal line in Figure 3.2. The intersection of the price and the marginal cost curves represents the profit-maximizing output, $q_z\text{*}$. If output is less than this, further net revenue can be obtained by producing more units, since their cost is less than their price. If more than $q_z\text{*}$ is produced, revenue is being lost on producing units that cost more than their price.

It is possible to derive a supply function from the production function $(q_z=g(q_a,q_b))$, the specifications of institutional and epistemic conditions, and the various simplifications. Moreover, firms may sometimes know their production functions. However, as in the case of demand, the object is not usually to derive a precise supply function. Instead, the goal is to derive and explain features of the supply functions of firms that do not depend on idiosyncratic details of a particular firm’s production function.

Economists can predict changes in the quantity of output supplied by a firm as a consequence of changes in prices or technology without knowing much about the firm’s production function except that its first partial derivative with respect to a variable input such as $q_a$ is positive and its second partial derivative negative. If the price of its output increases, the horizontal line representing this price in Figure 3.2 shifts upward and $q_z$ increases. A change in $p_z$ causes (other things being equal) a change in the same direction in the quantity of output. If, on the other hand, $p_a$ increases, the marginal cost curve shifts upward and its intersection with the line representing the price of $z$ is shifted left. $q_z$ is a decreasing function of $p_a$. A change in $p_b$ has no effect at all on marginal cost and no effect at all on $q_z$. Since a technological change will only be adopted by a profit-maximizing firm if it lowers costs, technological changes that affect prices in the short run will tend to lower them. As in the case of consumer theory, economists are mainly concerned with properties of equilibria, not with the dynamics of adjustment.

Since market supply is the sum of the supplies of individual firms, economists can thus explain the generalizations concerning market supply sketched earlier. And, moreover, just as in the case of demand, they have learned how to refine these generalizations. For it is not the case that changes in input prices always affect supply. If the price change concerns a relatively fixed factor, then its influence on output will not register immediately. It would be nice to have a quantitative account of market supply, and indeed, with further information concerning the production functions of actual firms, such a quantitative account would appear to be possible. It would also be nice to transcend such a simple model. But, again, as in the case of demand, the descent from the level of market generalization to supposed theoretical underpinnings seems to be a success.

3.4 Market Equilibrium and Price Determination

The accounts of supply and demand take prices to be among the causes of quantities demanded and supplied. Firms and consumers take prices as given and unalterable. But, in a market economy, prices arise as a consequence of the choices of firms and households. We still need a theory of how market economies coordinate individual behavior, and not merely how, given that coordination, prices separately influence the quantities supplied and demanded.

Showing how the behavior of firms and consumers determine prices is a task for general equilibrium theory as well as microeconomics.Footnote ⁵ However, before turning to general equilibrium theory, one can sketch the basic story about how prices are determined. Even though economies are characterized by general interdependence among markets, it can still be reasonable sometimes to focus on markets singly or in small groups. Such theorizing has been aptly called “partial equilibrium theory,” for one is abstracting from the general interdependencies among markets.

A good explanation of price determination, whether in a particular market or in a whole economy, requires a well-articulated theory of how demand and supply at the currently prevailing prices give rise to changes in prices. In models of perfect competition, in which buyers and sellers cannot influence prices, bargaining is ruled out.Footnote ⁶ In equilibrium there can be no excess demand and no excess supply (unless the price is zero). That means that no buyer has an incentive to offer to pay more than the going price and no seller has an incentive to lower the price. Individual buyers who offer to pay less than the going price will find no sellers, and individual sellers who attempt to charge more than the going price will find no buyers. An account of price determination thus requires a consideration of dynamic disequilibrium processes.

Although there are sophisticated attempts at modeling disequilibrium processes, the basic story concerning price determination in individual markets is essentially Adam Smith’s:

If at any given price there is an excess demand, competition among those who want the commodity or service will bid up the price until the excess demand is eliminated. Because Smith supposes that the equilibrium price, which he calls “the natural price,” is determined entirely by supply, he describes the competitive bidding that changes the price entirely from the side of demand. Contemporary economists tell a similar story on the supply side: if at any given price there is an excess supply, competition between those who supply the commodity or service will bid down the price until the excess inventories of the suppliers have been eliminated (see Arrow and Hahn Reference Arrow and Hahn1971, chapters 11–13). Thus, economists draw the famous graph shown in Figure 3.3.Footnote ⁷ At any price above the equilibrium price $p_e$, such as $p_o$, there will be an excess supply ($q_o{}^D<q_o{}^S$), and competition among those who supply the commodity or service will lower the price.

Figure 3.3 Supply and demand: price determination.

Economists do not have a theory describing in detail how such competition among buyers or sellers determines prices, and presumably in reality there are many different mechanisms of price adjustments. It might be argued that Smith’s account of price determination is ruled out in models in which buyers and sellers are all price takers and hence incapable of adjusting the prices they personally offer or require. In a notable paper, Robert Aumann (Reference Aumann1964) shows that in a model with a continuum (an uncountable infinity) of buyers and sellers it is possible to reconcile the determination of prices through the behavior of buyers and sellers with the inability of any buyer or seller to influence the price he or she pays. Whether this helps understand actual markets may be questioned. The tension between the models of competitive market supply or demand and models of price determination by competitive bidding illustrates the fact that models can be useful and enlightening, even if they are not consistent with one another.

Moreover, despite the apparent inconsistency between the models determining quantities supplied and demanded and the sketchy model of price determination, economists in fact combine the two into an account of how prices adjust to changes in determinants of supply or demand. Each price determines a supply and a demand as explained by the theories of consumer choice and of the firm. For example, a shift in demand as in the movement from $D$ to $D\text{’}$ in Figure 3.3 causes a price shift. The new prices call forth new supplies and demands and the hypothetical process that begins with a change in some factor affecting supply or demand iterates until (partial) market equilibrium is restored. A market is in “equilibrium” when there is no excess demand or (unless the price goes to zero) excess supply. Little more is said about the real (processes of) equilibration within a single market, although there has been a good deal of discussion of hypothetical mechanisms such as Walras’ “tâtonnement” and Edgeworth’s “recontracting.”

“Comparative statics” supply and demand explanations can easily get confusing. Economists are often reluctant to regard them as causal, because they are inclined to distinguish a comparison of equilibrium states from an explicitly dynamic causal account. To be sure, comparative statics accounts skip over the intricate causal details of adjustments to shocks such as shortages of Covid-19 tests. Moreover, it is bound sometimes to be the case that the details of adjustment processes influence outcomes. That is certainly the case in adjustments to Covid-19. But qualitative causal claims about how prices will change can be made without describing the dynamic processes. Indeed, in many markets, such as those for commodity futures, it seems entirely reasonable to ignore the dynamics of adjustments, which occur nearly instantaneously in response to second-by-second fluctuations in demand and supply.

In abstracting from the actual sequence of events and time ordering, comparative statics accounts differ from paradigm cases of causal explanation. But they may be causal nonetheless. Supply and demand functions and the market institutions may causally explain equilibrium prices and quantities. Although the distinction between dynamic and comparative statics accounts is important, both may be causal.

The causal structure of comparative statics analysis is straightforward. In the background is an implicit temporal story in which the shift whose effects one is exploring precedes the establishment of a new equilibrium. Figure 3.4 depicts the implicit story that economists have in mind.

Figure 3.4 Implicit dynamics.

Except in the equilibrium conditions at the beginning and end, all the causal arrows point to the right from previous to later times. The supply function $f_S$ and the equilibrium price $p_e$ determine the quantity of the commodity supplied, $q_{}^S{}_e$. Suppose it is corn. The demand function $f_D$ and the equilibrium price determine the quantity of corn demanded $q_{}^D{}_e$. $q^S$ and $q^D$ are equal in equilibrium, and so there is nothing to cause the equilibrium price, $p_e$, to change. There is then some shock to supply or demand – in Figure 3.4, it is a shock, $X$, to the supply of corn. Perhaps there is an outbreak of corn blight. Because of the blight, the function relating the quantity of corn supplied to the market price of corn changes at $t+1$ from $f_S$ to $f{’}_S$. The changed supply function and the as-yet unchanged price lead jointly to a new quantity of corn supplied $q_{}^S{}_{t+2}$. However, at $t+2$, price and demand have not yet changed. $q_{}^D{}_{t+2}$ and $q_{}^S{}_{t+2}$ combine with the workings of the market mechanism, $M$, to give rise to a changed price, $p_{t+3}$. Jointly with $f_D$ and $f{’}_S$, $p_{t+3}$ gives rise to $q_{}^D{}_{t+4}$ and $q_{}^S{}_{t+4}$ – that is, new quantities of corn demanded and supplied. Jointly with the market mechanism, $q_{}^D{}_{t+3}$ and $q_{}^S{}_{t+3}$ give rise to a new price $p_{t+4}$. Although nothing in the story so far guarantees that the process will ever reach an equilibrium, if it does, the new equilibrium price of corn coupled with the supply and demand functions will give rise to quantities supplied and demanded that are equal to one another at a new equilibrium price. The comparative statics account shown in Figure 3.5 greatly simplifies the story.

Figure 3.5 Comparative statics.

In abstracting from the actual course of adjustment to the shock, as Figure 3.5 does, economists are assuming that the adjustment process will not appreciably affect those aspects of the final outcome that are of interest to them. When this assumption is mistaken, a comparative statics account of shifts in market equilibrium explanation will be incorrect. But making such an assumption and then leaving the intermediate steps out does not preclude a causal interpretation.

In the comparative statics account, the explanatory factors consist of the supply and demand functions ($f_D$ and $f_S$), the unspecified market mechanisms, $M$, and the shock, $X$, that initiates the change in $f_S$. Supply and demand functions, unlike specific quantities supplied or demanded, can have a role in explaining prices if, as in Figure 3.4, they do not shift as other prices and tastes and production processes evolve over time. In a paradigm case of a supply and demand explanation, such as explanation for a lower price of soybeans in the United States owing to the imposition of restrictions on the importation of American soybeans by the Chinese government (which shifts the demand function), the other factors that determine the supply and demand functions – that is, how the supply and demand for soybeans are functionally related to the price of soybeans (factors such as the price of fertilizer or the popularity of Chinese food) – do not themselves depend appreciably on the price of soybeans or the amount of them sold. Thus, the explanation for the new lower price of soybeans in terms of market mechanisms, the shift in the demand function for soybeans owing to the import restrictions, and the more or less unchanging supply function makes good causal sense.Footnote ⁸

3.5 Microeconomic Theory

Both the microeconomic problems and analytical techniques economists work with are more sophisticated than the simple examples mentioned so far. Nevertheless, this chapter and Chapter 2 have set forth the basics of microeconomic theory. It consists in my view of seven laws:Footnote ⁹ those of the theory of consumer choice, those of the theory of the firm, and the assertion that markets reach equilibrium. Economists generally regard the claim that markets are in equilibrium as a theorem rather than an axiom; they formulate their models in order to prove that equilibria obtain. When economists have not yet succeeded in proving that an equilibrium obtains in some new economic model, they are inclined to assume that it does. I have more to say about the commitment to equilibrium in later chapters.

There are disquieting aspects to the claim that microeconomic theory consists of these seven “laws.” First, not all microeconomic models employ all of these laws, even when they are relevant to the explanatory and predictive tasks at hand. Some models, such as the two-input production system, leave out laws (constant returns to scale in this case) that have no implications for the case at hand. More disturbingly, others incorporate contraries to some of the fundamental laws of microeconomic theory. There are models with satiation, models with increasing or decreasing returns to scale, models without profit maximization, and even models without completeness, models without continuity, and models with intransitive preferences. It is as if physicists supposed that force is sometimes proportional to acceleration and sometimes not.

These facts suggest two conclusions: economic models need not be consistent with one another, and the “laws” of microeconomics do not have the same status as fundamental natural laws. Economists regard many as expedient first approximations, which theorists may supersede or reject in particular investigations. Some, such as transitivity, choice determination, DMRS, and diminishing returns, are more central than others. Theoretical work that rejects these may cross the boundaries dividing economics from other social inquiries. These facts raise difficult questions about what unites the discipline and explains its boundaries, which I address in Chapter 7. What sort of a science can economics be?

A further problem with identifying microeconomic theory with these seven generalizations is that other claims are also distinctive features of microeconomic models. For example, although general equilibrium theory and microeconomics rely on the same behavioral generalizations, they are distinct from one another.Footnote ¹⁰ What distinguishes them are not their laws, but the explanatory questions they address and the simplifications they employ. Microeconomics focuses on single markets or small groups of markets and thus on partial equilibrium, while general equilibrium theory is concerned with the economy as a whole. I call the behavioral generalizations that form the core of both microeconomics and general equilibrium theory simply “equilibrium theory.” Microeconomics and general equilibrium theories are augmentations of equilibrium theory.

Figure 3.6 summarizes the view of equilibrium theory or the basic behavioral generalizations of equilibrium models presented in Chapters 1–3.

Figure 3.6 The basic equilibrium model.

In addition to its laws and questions, microeconomics is characterized by distinctive simplifications. Buyers and sellers are price takers, monopolists, or monopsonists. Commodities are infinitely divisible. Economic agents have perfect knowledge of all relevant data. Many models distinguish between the “short run” in which some inputs are fixed and the “long run” in which all inputs can be adjusted. These simplifications are prevalent and characteristic of microeconomic models, even though they are less essential to them than equilibrium theory. Economists do not regard them as truths, let alone economic discoveries. If anything, economists seek to relax or to avoid such assumptions, not to maintain them in the face of criticism.

3.6 General Equilibrium Theories

General equilibrium theories aim in principle to explain how market economies coordinate individual behavior via the price system. Markets do not work flawlessly, but the fact that the goods people want are produced and distributed without central direction is amazing, and in need of explanation. To some extent, general equilibrium models are continuous with microeconomic models, and they are built upon the same “laws.” Some idea of general equilibrium goes back to the eighteenth century, but Leon Walras (Reference Walras1926) was the first economist to take seriously the task of elucidating an abstract general equilibrium theory.

Models that can justifiably be called “general equilibrium models” come in at least six varieties:

1. 1. models of highly simplified fictional economies with few commodities, resources, and individuals;

2. 2. models of the interrelations between aggregates such as total consumption and the money supply;

3. 3. structural macroeconomic forecasting models;

4. 4. input–output models with dozens or hundreds of commodities;

5. 5. DSGE (dynamic stochastic general equilibrium) models; and

6. 6. abstract models of economies with few constraints on individual choices, production, endowments, etc.

These six kinds of general equilibrium model differ in complexity, level of aggregation, and especially their purposes. In attempting to address large-scale questions, it can be helpful to employ highly aggregative general equilibrium models in which there are, for example, only two commodities (a consumption good and a capital good), only one unproduced input into production (labor), and only two kinds of agents (workers and capitalists). Such models of whole “toy” economies can explore the interdependencies among the three markets for labor and the two commodities. By representing the myriad actual commodities as merely one capital and one consumption good, such models assume away many of the complexities of the relations among markets. When such simplified “small” general equilibrium models are built around equilibrium theory, as they typically are, these models are similar in intention to the partial equilibrium work characteristic of microeconomics.

Simple Keynesian models, such as John Hick’s IS-LM model, which is discussed in Chapter 5, are instances of the second kind of general equilibrium theorizing. They describe a general – that is, economy-wide – equilibrium, but it is an equilibrium among aggregates such as total savings and output; these models do not attempt to show how the choices of individuals generate a general equilibrium. The third variety of general equilibrium models – large-scale macroeconomic forecasting models, such as those developed in the 1950s and 1960s by economists such as Lawrence Klein (Reference Klein1980) – are elaborations of modeling such as IS-LM relying on a wider set of decision rules and aggregate relations.

The fourth variety, input–output models, are directed toward narrower practical, predictive ends (Whalley Reference Whalley, Aaron, Galper and Pechman1988). By assuming, for example, that there are constant production coefficients and that demands for different commodities and services satisfy certain constraints, economists can construct a model of an economy with dozens or hundreds of commodities and industries and investigate how the outputs of some commodities are affected by government policies and shocks of various kinds. Economists might, for example, use input–output models to predict how a drop in oil prices would affect the cost of clothing.

General equilibrium models of the fifth variety play a large role in contemporary macroeconomics, which models the economy as stochastic – that is, subject to random shocks – and dynamic, in the sense of examining how shocks are propagated through the economy, typically via the choices of a single immortal representative agent. Thus the name “dynamic stochastic general equilibrium” models. Although driven by the rational choices of the representative agent, these models are implicitly highly aggregative, because the choices of the representative agent implicitly aggregate the choices of actual individuals.

That brings us to the sixth variety of general equilibrium theorizing, which many economists have regarded as the theoretical foundations for mainstream economics, while others regard it as having instead cast those foundations in doubt.

3.7 Abstract General Equilibrium Models

Abstract general equilibrium theories are augmentations of (some substantial subset of) the eleven laws that together make up the theories of rationality, consumer choice, and the firm. Furthermore, abstract general equilibrium models, unlike other applications or augmentations of the basic equilibrium model, involve many commodities and investigate a fully general interdependence among the markets in an economy. What distinguishes general equilibrium models from microeconomic models are assumptions of this last kind and the apparent explanatory task of accounting for the operation of whole economies.

Abstract general equilibrium models are puzzling, since they abstract so radically from the details of real economies. Gerard Debreu in his classic Theory of Value states that his theory is concerned with the explanation of prices (1959, p. ix). Others as distinguished as Kenneth Arrow and Frank Hahn deny that general equilibrium theories are explanatory (1971, pp. vi–viii). Some prominent economists (Blaug Reference Blaug1980a, pp. 187–92) and philosophers (Rosenberg Reference Rosenberg1983) have argued that abstract general equilibrium theory is not empirical science at all.

Abstract general equilibrium theories place no limitations on the interdependence of markets or on the nature of production and demand beyond those implicit in the “laws” of equilibrium theory. Given the abstractness and lack of specification in abstract general equilibrium theory, many economists regard it as the fundamental theory of contemporary economics. As the previous discussion suggests, I contend that equilibrium theory is the fundamental theory. Abstract general equilibrium theory is one way to apply the fundamental theory.

What good are abstract general equilibrium theories? Owing to their abstraction and simplifications, they do not appear able to explain or predict anything. For example, models of intertemporal general equilibrium commonly assume that agents have complete knowledge concerning production possibilities and the availability and prices of commodities for the whole of the future. They also stipulate that there is a complete set of commodity futures markets on which present commodities and titles to future commodities of all kinds and dates can be freely exchanged (see Koopmans 1957, pp. 105–26; Malinvaud Reference Malinvaud1972, chapter 10; Bliss Reference Bliss1975, chapter 3). Because economic reality does not satisfy, even approximately, such extreme assumptions, abstract general equilibrium theories have little predictive worth and are consequently untestable. In that case, what role can they play within an empirical science?

Abstract general equilibrium theorizing aimed to prove that under idealized circumstances there exist stable and unique economy-wide equilibria that render compatible the choices of individual producers and consumers and that also have desirable welfare features. In the 1950s and 1960s, this project had some major successes. In particular, economists proved that equilibria exist for perfectly competitive markets and that those equilibria are optimal in the sense that no alternative to a perfectly competitive equilibrium $E$ exists that satisfies some preferences better and everyone else’s preferences at least as well as $E$ does. These proofs appeared to justify Adam Smith’s view that it is as if there is an invisible hand coordinating the actions of individuals, leading them to promote the public good in the course of pursuing their private interests. These abstract inquiries have the form of explanatory arguments where the explanandum is the existence of an economic equilibrium. Yet, construing general equilibrium theories as explanations of general equilibria is problematic, because they rely on false premises and because it is questionable whether actual economies are in equilibrium.

Whatever else one can say on its behalf, abstract general equilibrium theorizing has played a powerful critical role. Indeed, it bears some responsibility for the transformation of economics over the past generation. Although proofs of the existence of equilibria were a triumph for abstract general equilibrium theorizing, further investigation led to theoretical disaster. General equilibrium theorists failed to show that the equilibria whose existence they proved were unique or stable, except under such restrictive conditions as to make the demonstrations irrelevant to actual economies. In addition, in a series of theorems proven in the 1970s, theorists showed that the conditions imposed on individuals – the generalizations that I called equilibrium theory – have virtually no implications concerning aggregate phenomena. These theorems also cast serious doubt on the reliance on representative agents in DSGE models. They show that the assumption that individual preferences satisfy axioms such as transitivity or DMRS does not imply that market behavior (or the preferences of a representative agent) will be consistent with these axioms. Unlike what we saw in the case of partial equilibrium (where, crucially, incomes are independently fixed), economists cannot prove that market demand curves are downward sloping from the fact that individual demand curves are downward sloping. As Shafer and Sonnenschein (Reference Shafer, Sonnenschein, Arrow and Intriligator1982, p. 672) put it:

The only constraints on aggregate demand functions implied by the conditions on individual demand and preference are that they must be continuous and homogeneous of degree zero, and they must obey Walras’ law.Footnote ¹²

General equilibrium theory is downtown Econville, where macroeconomics, microeconomics, and normative economics cross paths. Extremely abstract theorem proving rubs shoulder with rough and ready simple models. General equilibrium models have appeared to many economists to be the starting point on an endless voyage to sublime climes, while others believe that the roads in the center of town are in such bad repair that there is nowhere to go and a new starting place must be found. Many questions remain.

3.8 Conclusions

This chapter completes the sketch of equilibrium theory that began with the theory of rationality in Chapter 1, its embedding in consumer choice theory in Chapter 2, and its account of production and supply in this chapter, culminating in partial equilibrium accounts of price determination and general equilibrium forays into extending the account of price determination into an account of what determines the overall coordination of the actions of market participants.

In the course of this chapter, the list of philosophical IOUs has grown. Questions about the nature of models have become more pressing, and philosophically minded readers may by now be thoroughly annoyed at my apparently arbitrary shifting between talking about models and talking about theories. How do they differ, and how are they related? How can economists sensibly make use of models that contradict one another? Are models of individual interactions superior to models that specify relations among aggregates? Does it make sense to regard variables as simultaneously cause and effect? What is causation and how does it differ from mere association? What is the role of theorem proving in an empirical science?

Before tackling these questions, we need a more complete picture of mainstream economics. Welfare economics is the topic of Chapter 4. Chapter 5 discusses macroeconomics.

The central aim of normative economics is to help guide economic policy. There are many kinds of economic policies: taxes, transfers, tariffs, licensing, and patents, plus regulations on employment, housing, transportation, retirement benefits, immigration, food safety, land use, drugs and medical procedures, and many other things. These policies matter deeply to people. They affect people’s freedoms and opportunities. They contribute to or mitigate inequalities. They limit or aggravate discrimination against disfavored social groups. They shore up or threaten individual rights and political voice. Economic policies clearly matter to individual welfare, which is the central concern of mainstream normative economics. Indeed, normative economics is often called “welfare economics.”

Talk of “welfare” is ambiguous. In everyday political discussion, “welfare” consists of programs for the poor such as nutritional or housing assistance. Welfare economics is concerned with a different sense of the term. In this sense, “welfare” is a matter of how well people’s lives are going. Welfare in this sense is synonymous with “well-being” – the overall metric in terms of which to judge how well people’s lives are going.

What counts as well-being is a matter of philosophical controversy. There are three main views: (1) well-being is, as the classical utilitarians believed, a matter of mental states or, for short, happiness; (2) well-being is constituted by the satisfaction of preferences (cleansed of false beliefs and irrationality); and (3) well-being consists in possessing some set of “objective” goods, such as happiness, close friends, good health, and achieving worthwhile goals. These accounts of well-being are problematic. Those who are happy because they are deluded about their lives are not living well. Satisfying my preference for an end to the Covid-19 pandemic in 2023 may not make me better off if I die first. Taking well-being to consist in a list of goods does not explain why some things are on some people’s lists while others things are not, or how to make trade-offs among items on the list.

If one steps back from these philosophical theories of well-being and lowers one’s expectations, it is obvious that people do not need an adequate philosophical theory in order to know something about well-being. We know, for example, that generally people live better if they are healthy or have intimate friends than if they are ill and friendless. Platitudes such as these do not constitute a satisfactory philosophical theory, and they leave many questions about well-being unanswered. But sets of such platitudes, which I call a “folk theory” of well-being, provide some meaning for the term “welfare” and a touchstone against which to test more detailed claims about welfare.

Specifically, economic welfare is that portion of an individual’s well-being that depends upon the institutions, policies, and outcomes with which economists are concerned. It is tempting to identify economic welfare with wealth, but the connection between wealth and economic welfare needs to be examined. There is a correlation between economic welfare and overall welfare, and very low levels of economic welfare make it impossible to live well. Yet, economic welfare and overall welfare do not always go together. Wealth is no guarantee of well-being.

Mainstream normative economics is an offspring of utilitarianism (see Bentham Reference Bentham and Harrison1789; Mill Reference Mill1863; Sidgwick Reference Sidgwick1901). Utilitarianism maintains that the evaluation of policies and individual actions depends on their consequences for the welfare of individuals. One can summarize the view as follows:

This formulation hides many complexities. Should one be concerned with total welfare or average welfare? The answer is crucial to the evaluation of population growth. Whose welfare counts? Only people currently alive? All people in the present and future? All sentient beings? Should moral appraisal focus on the consequences of actions and policies or instead on the consequences of rules governing policies and actions? What constitutes welfare? Bentham took welfare to consist in pleasure. Mill claims that welfare is happiness, but sometimes it sounds as if he regards welfare as preference satisfaction. Sidgwick takes welfare to consist in desirable mental states. Utilitarian policy evaluation depends on how all these questions are answered. What best satisfies preferences often differs from what most contributes to happiness.

Despite its utilitarian roots, contemporary mainstream normative economics is not utilitarian, mainly because economists are skeptical about comparing the welfare gains and losses of different people, and, of course, there is no way to judge whether the benefits policies bring to some people are larger than the harms they cause others without the ability to compare benefits and harms across individuals. It may seem odd that welfare economists deny that interpersonal comparisons of welfare are possible. Who would deny that indigent children impressed into the Lord’s Resistance Army are worse off than the typical child born into a middle-class Japanese home? Sections 4.2.1 and 4.3 will have more to say about welfare economics and interpersonal comparisons.

The problems that welfare economics must address are diverse and difficult. A broad social consensus in affluent societies supports providing minimum amounts of food, housing, medical care, and education to everyone, because these appear to be universal or nearly universal prerequisites to living well. But how much of these should be provided and by means of which institutions? While most people support ensuring that people’s basic needs are met, they also believe that it is not the state’s responsibility to hold the hands of individuals and make their lives successful. When someone’s spouse dies, it is not up to the state to console them or to provide a replacement. It may not be entirely up to those individuals who suffer tragedies to pick up the pieces of their life, but it is not mainly up to public policy. Provided that people’s basic needs are met and they have the necessary physical and mental capabilities, people should be responsible for their own well-being. Economic policy has narrower goals than the flourishing of individuals.

Consider just a few examples. First, what, if anything, should be done about the breathtakingly unequal distribution of income and wealth within the United States and across the world? Fewer than 100 individuals (some estimate as few as five or eight individuals) have more wealth than half the world’s population combined – nearly four billion people! While international inequalities have diminished, owing especially to rapid economic development in China and India, inequalities within those two nations are glaring and growing. Income and wealth inequalities in the United States, after narrowing in the middle third of the twentieth century, have exploded over the past four decades. What, if anything, should be done?

Second, to what extent does international trade exacerbate or mitigate inequalities, and how does this bear on welfare? While economists have generally been enthusiastic supporters of lowering tariff barriers, there are costs to lessening the protection of domestic enterprises. Some firms, facing competition from abroad, go bankrupt. Workers in some industries lose their jobs. Are the benefits sufficient to justify harms such as these?

Third, consider the challenges of macroeconomic policy. By 2009, with an official end to the severe recession that began in 2008, economic activity in the USA was no longer shrinking, but the unemployment rate was about 10 percent and the budget deficit was $1.3 trillion. Economists disagreed about what to do, with some arguing for additional government expenditures, especially on infrastructure, in the hope of getting the economy moving again, while others argued that governments needed to cut back on their budgets to lower deficits and thereby reassure investors that there was no risk of fueling inflation or defaulting on the debt. Whether “stimulus” or “austerity” was the correct policy had enormous consequences both for economic recovery and for the well-being of the least well-off members of society, who would suffer in the immediate future from austerity, even if the policy were successful.

In all these examples, positive theory is challenged to explain the relevant phenomena and make predictions about the consequences of policies, and normative theory is challenged to appraise proposed policies and their consequences. As these examples illustrate, the challenges for economic policy differ greatly. Normative economists need to analyze and evaluate long-lasting economic trends. They need to defend general conclusions concerning perennial questions such as how to evaluate international trade policies. They need to help answer pressing policy questions around which political controversies swirl.

To address the many challenges, normative economics requires a great deal of positive economic knowledge. Economists cannot appraise economic inequalities, determine whether lower tariffs are on the whole beneficial, or favor stimulus or austerity without knowledge of the effects of the phenomena of concern and of the policies under discussion. But positive theorizing is not enough. Even if economists reduce the normative appraisal of economic outcomes to a consideration of their consequences for welfare, economists still need some normative theorizing to get from the conclusions positive economics establishes concerning prices, quantities, and incomes to judgments concerning what most promotes welfare.

This chapter lays out the normative theory employed by mainstream economics. Section 4.1 begins with the fundamental question: what is welfare or, synonymously, well-being? Section 4.2 explains why the answer that economists give led them to eschew utilitarianism, and it links this chapter to Chapters 1–3, presenting the fundamental theorems of welfare economics, the grounds for the admiration economists have for the operation of perfectly competitive markets, the problems of markets that are not perfectly competitive, and further theorems concerning social choice and welfare. Section 4.3 turns to practical work in welfare economics and the foundations of cost–benefit analysis. Section 4.4 is concerned with the peculiar moral authority of economists. Section 4.5 ends with an overview, including some remarks about alternatives to mainstream normative economics.

4.1 Welfare and the Satisfaction of Preferences

As Chapters 1–3 document, preferences are the central concept that economists employ to predict and explain the choices of economic agents. To assert that preferences motivate choices says nothing by itself about welfare. However, if economists assume, as they often do, that individuals are self-interested – that is, that they usually aim to benefit themselves – then the rankings by individuals of the objects of choice reflect their evaluation of how beneficial those objects of choice are for themselves. Choice determination implies that an agent such as Penelope chooses an alternative $x$ if and only if she believes there is no feasible alternative that she prefers to $x$. If Penelope is trying to benefit herself in her choices, then she chooses $x$ if and only if she believes there is no feasible alternative that is better for her than $x$. If her beliefs are true and her judgments of value are sound, then what best satisfies Penelope’s preferences coincides with what most enhances her well-being. In other words, for any two alternatives $x$ and $y$, Penelope prefers $x$ to $y$ if and only if $x$ is better for her than $y$. Since, in addition, the same word, “utility,” is used both to refer to an indicator of preferences and as a synonym for welfare, the identification of welfare and preference satisfaction strikes many economists as unproblematic.

One important implication of identifying welfare with preference satisfaction is that it rules out paternalism – that is, overruling the preferences of an individual with the intention of benefiting that individual. For example, laws requiring that people wear seat belts are largely paternalistic even if they may have small or indirect benefits for others. If whatever Morrie chooses is best for him, then it is impossible to make Morrie better off by overruling his choice. Although this implication of identifying preference satisfaction and welfare may be attractive to economists, who typically strongly oppose paternalism, the claim that one can never benefit individuals by overruling their choices is false. For example, suppose Morrie is a tourist in London. Looking the wrong way, he steps in front of a speeding bus. Clare grabs him and pulls him back on to the curb. She overrules his mistaken choice, much to Morrie’s benefit.

Note that to say that welfare is preference satisfaction is to say only that those states of affairs that are higher up in Penelope’s preference ranking are better for her. It says nothing about feelings of satisfaction. Satisfying a preference need not result in any feeling of satisfaction (or any feeling at all). Whether Penelope finds out that some preference of hers is satisfied and is pleased at the information is a separate question from whether her preference is satisfied. Satisfying preferences is like satisfying degree requirements: preference satisfaction obtains when states of affairs that are ranked more highly come about, whether or not those outcomes are known or enjoyed.

4.2 How Is Welfare Economics Possible?

4.3 Welfare Economics in Practice

The Pareto concepts often fail to justify any normative conclusions. For example, suppose that in some hypothetical economy there are ten loaves of bread, which is the sole consumption good, and everybody prefers more rather than less of it. Then every distribution of bread that exhausts the bread supply is a Pareto optimum.Footnote ⁵ Moreover, $R$ may be Pareto optimal and $S$ may be suboptimal without $R$ being a Pareto improvement over $S$. An allocation where $A$ gets seven loaves and $B$ gets three is Pareto optimal, but it is not Pareto superior to the suboptimal distribution that wastes two loaves and gives four loaves to both $A$ and $B$. As the example suggests, few economic states can be ranked in terms of Pareto superiority.

The Pareto concepts not only fail to discriminate among alternatives that appear, pretheoretically, to differ with respect to total well-being, they also have little bearing on questions of fairness, which many economists are happy to leave to others (Okun Reference Okun1975). This factoring is questionable, if for no other reason than the efficiency implications of perceptions of fairness (Hirsch Reference Hirsch1976, pp. 131–2). Welfare economists are not of much help if they can only recommend policies that are not worse for anyone.

Welfare economists in fact found a way of surpassing these limits. Nicholas Kaldor (Reference Kaldor1939) and John Hicks (Reference Hicks1939) argued in separate essays that if the winners from a new policy could in principle compensate the losers and still be better off, then, but for its distributional consequences, the new policy would be a Pareto improvement. The new policy is a potential Pareto improvement. Economists, whose self-imposed remit is limited to the assessment of efficiency, can judge the new policy to be more efficient, on the grounds that it has the capacity to satisfy everyone’s preferences better than the old policy. Whether a potential Pareto improvement is a good thing, all things considered, is a separate question, since it makes some people worse off. But that is a distributional question that economists can claim no special competence to address.

The notion of a potential Pareto improvement underlies cost–benefit analysis (Boadway Reference Boadway, Adler and Fleurbaey2016; Mishan Reference Mishan1981).Footnote ⁶ If the gains to the winners from the new policy are large enough to compensate the losers fully, then the proposed policy provides a “net benefit.” The policy with the largest net benefit is most economically efficient, in the sense of creating the greatest capacity to satisfy preferences. If, contrary to fact, compensation were paid to the losers, then the policy with the largest net benefit would be Pareto superior to the status quo. In practice, it is costly to ask people how much they would pay or how much compensation they would require, and their answers may not be truthful or accurate. But economists have devised methods of inferring willingness to pay from data on prices and quantities traded. Much of cost–benefit analysis is devoted to devising, criticizing, and improving methods of imputing costs and benefits.

Unfortunately, this understanding of potential Pareto improvements, along with the hope of separating questions of efficiency from questions of equity, cannot be defended. It turns out that it is possible for $A$ to be a potential Pareto improvement over $B$, and also for $B$ to be a potential Pareto improvement over $A$. But $A$ cannot have both a greater and a lesser capacity to satisfy preferences than $B$. Because the distribution of gains affects which policy satisfies preferences better, the separation between questions of efficiency and questions of equity cannot be sustained. The diagram in Figure 4.1, borrowed from Samuelson (Reference Samuelson1950), illustrates the problems.

Figure 4.1 Potential Pareto improvement is not asymmetric.

Each point in the plane represents a possible pair of utilities for the individuals or groups $P$ and $R$. The two curves represent the maximum levels of utility for $P$ and $R$ that the technologies $T_1$ and $T_2$ make possible. $S$ is a potential Pareto improvement over $Z$,because $P$ can compensate $R$ (that is, the social allocation moves up and to the left along the $T_1$ frontier until a Pareto improvement over $Z$, such as $S\text{’}$ is reached). However, $Z$ is also a potential Pareto improvement over $S$, because $R$ could compensate $P$ and thereby move along the economy along the $T_2$ frontier to $Z\text{’}$, which is a Pareto improvement over $S$.

Although cost–benefit analysis cannot be defended as a way of identifying which policy has the greatest capacity to satisfy preferences, it is the only practical tool for overall detailed quantitative policy evaluation.Footnote ⁷ An alternative way to justify reliance on cost–benefit information is to argue that it is a way to operationalize utilitarianism. If willingness to pay indicates preference intensities (which in turn indicate contributions to well-being), then economists can take the size of a net benefit – that is, the net gain of the winners from a policy after compensating the losers – as measuring the increase in total well-being the policy provides. The net benefit of a policy is a rough measure of the policy’s contribution to total welfare (Layard and Glaister Reference Layard and Glaister1994, pp. 1–2).

This justification for the use of cost–benefit analysis is unsatisfactory. Not only are there the problems discussed in Section 4.1 concerning whether preferences are good indicators of well-being, but willingness to pay depends on wealth as well as preference intensity. Those who own fossil fuel companies may require billions in compensation for agreeing to clean energy legislation, while those who would benefit from such legislation may be confused about its benefits to them and, owing also to their limited budgets, be willing to pay very little. The only way to forge even a tenuous link between net benefit and an increase in well-being is to assign “distributional weights” to the willingness to pay of individuals whose wealth differs. Although many welfare economists support assigning distributional weights (Fankhauser et al. Reference Fankhauser, Tol and Pearce1997), it is difficult to do, and cost–benefit analyses often do not employ distributional weights.

If economists treat cost–benefit analysis as a method for making social choices, rather than as a technique for organizing information that is relevant to making social choices, it is easy to see why many are uneasy about it. Like the other Pareto criteria, the notion of a potential Pareto improvement ignores questions of justice, and in addition it does not limit the sanctioned changes to those that make none worse off. Because there are losers as well as winners, questions of fairness are pressing. Moreover, there is a systematic bias in cost–benefit analysis against the preferences of the poor: preferences in cost–benefit analysis are weighted with dollars, and the poor have fewer of these (Baker Reference Baker1975).

4.4 Rationality and Benevolence: The Moral Authority of Economists

There are strong connections between positive economic theory and normative economic theories of rationality and of welfare. Making these explicit helps one to understand both theoretical welfare economics and some of the methodological peculiarities of positive economics.

Economists are often impatient with discussions of ethics. Concerning differences in basic values, Milton Friedman remarks that “men can ultimately only fight” (1953c, p. 5). Economists do not see themselves as moral philosophers, and they attempt to steer clear of controversial ethical commitments when doing theoretical welfare economics. Indeed, economists have sometimes supposed that welfare economics, as the investigation of the consequences of policies for preference satisfaction, is independent of all value judgments. But economists cannot limit themselves to providing technical knowledge that may be relevant to the choice and implementation of policies (§A.9.3). Moreover, as George Stigler has remarked, studying economics leads people to value private enterprise (1959). When economists address normative questions of economic welfare, they speak with an air of moral authority. They purport to know how to make society better off.

The solution to this paradox of economists denying that they make value judgments while giving policy advice lies in the following line of thought. Suppose:

1. 1. it is good to make individuals better off (which I call “minimal benevolence”);

2. 2. well-being is the satisfaction of preferences;

3. 3. it is possible to separate questions about efficiency in satisfying preferences from other normative concerns relevant to policy; and

4. 4. conclusions about satisfying preferences in a nearly perfectly competitive economy are relevant to the actual economy.

Then economists can tell policy-makers how to enhance welfare. A perfectly competitive economy serves as a moral ideal, which actual economies do not live up to, and whether society should rest content with the result, as defenders of laissez-faire would urge, or whether government has work to do to address market imperfections such as monopolies or externalities is a matter of controversy among economists. But perfect competition serves both parties as an ideal.

This shared commitment to the ideal of perfect competition explains why economists are so concerned with the analysis of market failures. (Why should they matter if market successes are not a good thing?) The fact that this commitment appears to presuppose nothing more controversial than minimal benevolence explains how economists can feel that they possess moral authority without troubling with moral reflection. The theoretical commitment to equilibrium theory and nothing more sets off an economic domain within social life (see §7.4 and §13.7) and apparently permits definite moral conclusions (other things being equal) that rely on only the least controversial of moral premises. With one big step into the theoretical world of equilibrium theory, rationality, morality, and the “facts” of economic choice become tightly interlinked. These linkages not only explain the attractions of welfare economics, but they go a long way toward explaining the pervasive commitment to equilibrium theory among contemporary economists.

4.5 Conclusions and Alternatives

Mainstream normative economics, the subject of this chapter, dominates the appraisal of economic policies. However, before closing this discussion of normative economics, a few words should be said about alternatives and competitors. Two of these are especially notable. One, defended most prominently by Amartya Sen, proposes to reorient normative economics from its fixation on welfare to a concern with capabilities, which are sets of possible ways to function (Nussbaum and Sen Reference Nussbaum and Sen1993; Nussbaum Reference Nussbaum2000). For example, literacy is a capability which enables the functions of reading books or writing tweets. Sen’s proposal is attractive, but he provides no general method to rank different capabilities or functionings unless one fully encompasses another. This means that there is no optimal way to enhance capabilities. However, on the one hand, one may doubt whether the calculations of net benefit economists make to determine which policies are optimal with respect to welfare are well founded, and, on the other hand, it is possible to define rough and ready indicators of levels of capability such as the human development index, which depends on life expectancy, education, and income.Footnote ⁸

The other alternative that should be mentioned retains the mainstream economists’ focus on welfare. However, it identifies welfare with subjective feelings or attitudes rather than preference satisfaction.Footnote ⁹ This view of welfare is questionable, because many things contribute to a good life in addition to feelings. Moreover, as the following comments from Adam Smith’s Theory of Moral Sentiments dramatize, feelings are sometimes very poor indicators of well-being:

If living well consists in being in a good mood, then life is going great for Smith’s “poor wretch.”

This chapter’s excursion into welfare economics reinforces the methodological point that equilibrium theory is central to the theoretical perspectives, problems, and projects of contemporary mainstream economists. Equilibrium theory determines the most fundamental questions to be addressed, and it constrains the techniques employed to answer them. Without an appreciation of the vision inherent in equilibrium theory, welfare economics would be deeply puzzling. With such an appreciation, one can see it as a clever attempt to address a set of pressing practical problems with a conceptual apparatus that is unfortunately not up to the task.

But how then is one to understand this commitment to equilibrium theory? What general sense can one make of neoclassical theorizing? We need to probe more deeply. Before doing so, something needs to be said about macroeconomics, the other central branch of mainstream economics.

Macroeconomic models of economic growth and fluctuations and of the interactions between “real” and monetary phenomena are too complicated and controversial to be surveyed competently in a single chapter. The objective here is instead to highlight some of the philosophical questions that macroeconomic models raise and to relate them to equilibrium theory. Consequently, this chapter only scratches the surface of elementary macroeconomics. Section 5.1 discusses how growth theory is linked to equilibrium theory. Section 5.2 considers how growth theory can be adapted to address questions about economic fluctuations, including recessions. Section 5.3 focuses on a simple influential Keynesian model of economic fluctuations. Section 5.4 discusses a specific relationship between employment and the rate of inflation that highlights methodological issues concerning causal inference and microfoundations that led many economists to reject Keynesian economics. Section 5.5 develops these methodological issues further, highlighting the role of identities in macroeconomics. Section 5.6 concludes.

5.1 Equilibrium Theory and Models of Economic Growth

General equilibrium models encompass the entire economy and should form the basis for an understanding of economic growth, the ups and downs to which competitive economies are subject, and how the “real” circulation of goods and services interacts with monetary policy and the financial sector. A fully disaggregated account of the economy is out of the question. The detailed causal interactions of thousands of firms and millions of households are too complicated. Even if economists knew all the relevant mechanisms, it is impossible to gather the data needed to draw detailed inferences from a perfected economic theory. In addition, as discussed in Section 3.7, the Sonnenschein, Mantel, and Debreu results show that few inferences can be made concerning overall economic outcomes from axioms governing the choices of individual consumers and entrepreneurs.

Theories of the growth and of the hiccups of actual monetized economies with their “real” and financial interactions are, of necessity, aggregative, and the properties of the aggregates in macroeconomic models cannot be derived from the generalizations of equilibrium theory. When economic outcomes are depicted as the results of the rational choices of a single representative agent, the aggregation is disguised, but the representative agent is no less an aggregate than is the bond market.

Partly because it is aggregative without fully specified microfoundations, macroeconomics is a realm of uncertainty and approximation. Aggregative models need not be like this. They can sometimes be highly precise, as is the case in statistical mechanics. But the subject matter of economics is unlike the subject matter of statistical mechanics. Although there are many economic actors, their numbers pale beside the number of gas molecules in a small balloon. Moreover, unlike molecules, the behavior of economic agents is not uniform, and some individuals or groups of economic agents may, by themselves, have significant influence on economic outcomes. Generalizations about the behavior of individual markets for nonfinancial goods and services often break down when applied to financial markets or labor markets. The fact that one person’s spending is another’s income, which means little in the context of markets for shoes or breakfast cereal, matters crucially when one is looking at an economy as a whole. When Margaret decides to cut down on her lattes and save for a vacation, her savings increase. When everyone does so, the economy slumps, individuals such as Margaret lose their jobs, and savings, which depend on incomes as well as the desire to consume one’s income, diminish rather than increase. If Herbert goes into debt and then dies, his debts must be repaid out of his estate, and he has to that extent impoverished his descendants. If, in contrast, a government goes into debt by borrowing from its own citizens, the debt its borrowing imposes on some is balanced by the repayments it promises to others. Individuals and households are poor models for whole economies.

Although theories of economic fluctuations – booms and busts – are especially pressing, it is convenient to begin, as modern macro texts typically do, with theories of economic growth. For the moment, let us set aside the role of government. In that case, economic growth occurs just in case the goods and services that firms produce and sell to consumers increase. This additional output requires either an increase in the inputs or an improvement in the processes that transform inputs into outputs. Unlike a description of the production and exchange of some single commodity or service, such as wheat or aluminum, there is no sensible way to measure the quantity of the economy’s inputs or outputs in some scalar physical unit. When manufacturers of all sorts update their technology – installing robots in their factories, replacing mechanical with computer controls, or varying the kinds of inputs they employ – it is meaningless to ask whether they are using more or fewer inputs. Economists instead measure the size of an economy and the extent to which it grows or shrinks by the value of its output, not by tons of steel or bushels of wheat. However, the value of outputs or inputs depends on prices as well as the quantities. To have a measure of “real” as opposed to “nominal” economic growth, economists must make adjustments for inflation or deflation.

Although models of economic performance and growth are aggregative, they differ widely in the extent and kind of aggregation they involve. At one extreme, economists construct models that specify relationships between dozens or even hundreds of sectors so that, for example, the outputs of the steel industry equal the steel inputs into construction, consumer durables, and vehicles. Although less aggregative than other models, these input–output models are not, and are not intended to be, fully disaggregated. They might, for example, contain a market for a single commodity such as steel or wheat, when in fact there are many grades of both. Although useful for economic forecasting, models of this sort are not suited to explain economic growth or fluctuations.

The general equilibrium models employed to theorize about growth and fluctuation abstract from the heterogeneity of firms and consumers. In that regard, they are much simpler, but in other ways they are difficult to grasp. For example, economists often begin their accounts of economic growth with the Solow growth model. Its fundamental relation is the following aggregate production function:

$Y(t)=F\left[K(t),A(t)\times L(t)\right]$

$Y(t)$, output at time $t$, depends upon $K(t)$, the capital stock at time $t$, $L(t)$, the labor stock available at $t$, and $A(t)$, the technological “know-how” at $t$ that directs the combination of labor and capital to produce output. $A(t)$ is a catch-all for all the factors other than the quantities of capital and labor that affect output, including human capital and technology. In this equation, technology is modeled as enhancing labor inputs, but this is not an essential feature of this style of growth theory. $K(t)$ includes land and natural resources. $Y(t)$, $K(t)$, $A(t)$, and $L(t)$ are all aggregates. Even in relatively simple economies, there is a mind-boggling heterogeneity among actual outputs, actual inputs (both labor and nonlabor), and all the nitty-gritty knowledge and other background factors required to transform inputs into outputs. In simple applications, economists assume that $A(t)$ is increasing over time at a constant rate. Economists can then focus on the growth of capital per capita as a cause of per capita growth in output.

The Solow growth model omits any direct influence of government policy. This is not to deny that government has a huge role in determining growth. It is merely a first step in modeling the complexities in growth. It assumes that the aggregate production function shows constant returns to scale and diminishing returns to individual inputs, just like the production functions for specific outputs. These are substantive assumptions that are not implied by the generalizations of equilibrium theory. If, for example, there are gains from greater specialization in larger economies, then there should be increasing rather than constant returns to scale.

Despite its simplicity, the Solow growth model suggests some strong conclusions concerning economic growth. In particular, it is possible to explain only a small portion of economic growth by the increase in labor or capital inputs. Given the limits of the model, that means the main driver of economic growth has been $A(t)$ – that is, developments in technology, knowledge, and other background factors. This is an empirical finding, not an economic law. Moreover, the development of technology depends on investments. As Solow notes (1957, p. 316), “[o]f course this is not meant to suggest that the observed rate of technical progress would have persisted even if the rate of investment had been much smaller or had fallen to zero. Obviously much, perhaps nearly all, innovation must be embodied in new plant and equipment to be realized at all.”

5.2 Equilibrium and Booms and Busts

By itself, this growth model is not intended as an account of the overall functioning of an economy. It says nothing about how the choices of individuals concerning consumption and the willingness to work and invest depend upon and influence the size or rate of change of the variables in the model. To address economic fluctuations, the Solow model needs to be supplemented or replaced. The simplest account, which goes back nearly a century to work by Frank Ramsey, abstracts from financial markets and assumes fully competitive conditions. The economy is populated by firms and households. Firms are all the same. Each has the production function from the Solow model. Firms rent identical capital goods from their owners, and they hire labor of uniform productivity from households. Firms take technology, $A(t)$, as given. It grows at a constant rate, which does not depend on anything in the model. Under competitive conditions, the prices of the inputs of firms and their outputs are also given. Firms adjust their use of capital and labor to maximize profits.

To avoid dealing with relations among different generations, the Ramsey model assumes that households are identical and infinitely long lasting. Households grow in size at a constant rate, and each household member supplies the same amount of undifferentiated labor. Households begin with equal shares of the economy’s capital, and they rent the capital they own to firms. Households save some of the income they receive from the labor and capital they supply to firms, and they consume the rest. They adjust their consumption in order to maximize the lifetime utility of their members – that is, each household allocates its earnings between consumption and savings in order to achieve the consumption stream it most prefers.

Growth is steady, although it may be shifted by changes in $A(t)$ or by factors that lead consumers to change the allocation of their income between savings and consumption. Unless there are “shocks,” the (fictional) history of such an economy is a dull story of smooth expansion. Indeed, there is a venerable argument that purports to show that it is impossible for economies to experience recessions, where goods pile up unsold in warehouses, investment is unprofitable, and large numbers of people are unemployed.

It is clearly possible for there to be an excess supply of any particular commodity or service, but if one thinks of exchange in terms of barter, then the notion that people could collectively seek to sell more than they are willing to buy makes no sense. John Stuart Mill (Reference Mill1836b, p. 69) explains this conclusion as follows:

However, recessions are not just a mirage. How are they possible? Mill answers that money is the culprit:

In Mill’s view, a desire for liquidity (cash on hand) – whether justified or not – can lead to the hoarding of money and create a disequilibrium, albeit one that cannot last. The excess supply of everything other than money means that prices (and wages) drop. With that drop, the purchasing power of money increases, and people need less of it to cover contingencies. The hoarding is thus self-correcting, even though its short-lived economic consequences may be painful.

Although John Maynard Keynes and his followers were not responding to growth models like those roughly sketched earlier, they were convinced, unlike Mill, that an account of fluctuations required modifying both the generalizations of equilibrium theory and the simplifications equilibrium models rely on, such as perfect competition, complete knowledge, and so forth. Moreover, unlike Mill, Keynes did not believe that recessions were necessarily short-lived and self-healing. Keynes believed that without a shot in the arm from government policy recessions could drag on for long periods. As people attempt to save, demand for commodities and labor diminishes, which in turn diminishes the earnings of firms and lessens demand for labor. Firms have less to invest and banks are unwilling to make loans to firms with poor prospects. Workers have less to spend. Demand diminishes further. If wages and prices can drop enough, the mechanism described earlier can kick in – with deflation the purchasing power of savings increases, and people do not attempt to save as much. Investments will again be profitable, and the economy can claw its way out of the chasm. But wages in particular are “sticky.” Workers vigorously oppose reductions in their wages, often making it impossible for firms to lower wages without suffering heavy costs in lessened productivity from a disgruntled labor force. Moreover, at the same time that deflation increases the purchasing power of savings, lower wages diminish savings and increase the burden of debtors, who are less affluent than creditors and more inclined to consume additional income. Keynesians believe that government can and should arrest the downward spiral and help to restore economic prosperity by increasing the money supply and by deficit spending that will directly increase demand.

Some of Keynes’ views are now widely challenged. In the last few decades of the twentieth century, a number of theorists demonstrated that it is possible to construct a model of an economy in perfectly competitive equilibrium that nevertheless shows fluctuations in output and employment like those in booms and busts.Footnote ² What if, instead of constant growth in $A(t)$ – technology, knowledge, institutions, etc. – there are significant shocks that affect the ability to transform capital and labor into output? There might also be large shifts in taxation and government spending that could shift the balance of income between consumption and savings. To make this way of accounting for fluctuations feasible, it is necessary to relax the assumptions that labor supply is fixed and that household preferences depend only on lifetime consumption and not at all on whether household members are working. But these are presumably welcome steps toward somewhat greater realism. Because this way of accounting for economic fluctuations relies on real – that is, nonmonetary – factors, theories of this sort are called “real business cycle theories.”

Although many economists hope to be able to explain economic fluctuations and to understand how best to avoid and cure them, while maintaining their commitment to equilibrium theory, including the view that economies are always at or near general competitive equilibrium, few accept the implication of real business cycle models that monetary policy and financial institutions play no part in recessions and that monetary and fiscal policies cannot help to mitigate recessions. Indeed, Long and Plosser themselves argue for a much more modest interpretation of their model:

In fact, there is little doubt that the financial sector played a major role in the monster recession that gripped most of the world in 2009, or that the actions of the Federal Reserve instigated the severe recession of 1982.

Real business cycle models and contemporary “new Keynesian” models represent the most recent iterations in a “new classical” research program initiated in the 1970s, especially in the work of Robert Lucas. Previous to Lucas, most economists regarded recessions as malfunctions of market economies. In recessions, large numbers of workers are unemployed, bankruptcies of both individuals and firms are rampant, and warehouses burst with unsellable inventories. If that’s an equilibrium, what would a disequilibrium look like? But science aims to discover the inner workings of things, not to describe their outward manifestations. Physics and chemistry tell us that solids are largely empty space inhabited by weird part-wave part-particle inhabitants. If science can spin yarns this bizarre, then might it not be the case that, as Robert Lucas claims, the many who are unemployed during a recession have rationally calculated that they are better off continuing to search for more attractive employment than accepting what the labor market offers them? Once one recognizes that people’s choices are governed by their expectations concerning the future as well as by their present circumstances, the prospects for describing outcomes as equilibria expand immensely. Choices that make agents worse off today and that hence seem to indict their rationality or cast into doubt other generalizations of equilibrium theory may be intertemporally optimal. If the expectations of individuals are “rational” both in the sense of conforming to the axioms of the theory of probability and in the tendentious sense of matching the predictions of mainstream economics, then it might be possible to trace disappointing economic outcomes to the vagaries of nature, such as crop failures, or to the deprecations of government in the form of wars, waste, and harmful policies. The disappointing outcomes that result, like the massive unemployment during the Covid-19 pandemic, can all be optimal, given the circumstances. Just as losses at cards may be due to having been dealt bad hands rather than to bad play, so mediocre economic outcomes may be due to the bad hands that technology or nature has dealt the economy. For those committed to equilibrium theory, and especially to the view that competitive markets will achieve an efficient equilibrium, such an approach is attractive. On such a view, only unexpected shocks and surprises can – albeit temporarily – create a disequilibrium. Section 5.4 presents an example that helps to clarify this abstract characterization of the program of “new classical” economists.

DSGE modeling was developed by the new classical economists, and it was initially associated with models that undermine the case for monetary and fiscal policies to mitigate recessions, such as those developed by real business cycle theorists. Yet these modeling techniques have a much wider application, and contemporary new Keynesian theorists have been able to formulate DSGE models that capture many of Keynes’ insights and defend the efficacy of monetary and fiscal policies to address recessions.

5.3 Simplified Keynesian Theory: IS-MP

One very simple Keynesian model of the aggregate workings of an economy, depicted in the diagram in Figure 5.1, is adapted from John Hicks.Footnote ³

Figure 5.1 IS-MP.

The MP (monetary policy) curve is easy to explain and captures a causal relationship, albeit one that depends on institutional facts concerning central bank policy. When the economy heats up, central banks raise the interest rate to prevent inflation and discourage unsustainable overinvestment. When the economy slows down, central banks lower the interest rate to encourage investment and spur output. The MP curve representing the relationship between output and the rate of interest is thus upward sloping.

The IS curve consists of those combinations of output and interest rate where investment equals savings. (Thus the “I” and the “S.”) Investment declines when the interest rate rises. Setting aside the effects of government, $S=Y-C$, where $S$ is savings, $Y$ is output, and $C$ is consumption. Consumption in turn is $b\times Y$, where $b$ is the marginal propensity to consume out of income, which Keynes assumes is less than one. So $S=(1-b)\times \text{Y}$. If investment, equals savings, $I=(1-b)\times Y$. So if investment declines, $(1-b)\times \text{Y}$ declines, which means that either the marginal propensity to consume increases or output decreases. The marginal propensity to consume is typically treated as a constant, and, if anything, it is likely to fall when interest rates (and thus the return on savings) increase. Thus, an increase in interest rates implies a decrease in output and a downward-sloping IS curve. Both output and the rate of interest depend on and influence supply and demand for investment, savings, or “loanable funds.” Unlike a demand curve, the IS curve does not represent any direct causal dependence of output on the rate of interest that combines with an independent MP relationship.

Although investment depends on the interest rate, this dependence cannot be regarded as a mechanism that is separable from a variety of other mechanisms. Of course, microeconomic supply and demand curves also shift with changes in the values of other variables, such as income and the prices of substitutes and complements. However, unlike in microeconomics, variables that investment depends on other than the rate of interest are not causally independent of the rate of interest.

Figure 5.2 may help to clarify the causal complications in the IS relationship and in IS-LM or IS-MP analysis.

Figure 5.2 IS-LM causal complexities.

Figure 5.2a depicts demand for $x$, $d^x$ as causally depending on $p_x$ (the price of $x$), $p_c$ (the price of complements), $p_s$ (the price of substitutes), $Y$ (income), and $T$ (tastes), and it supposes (as a first approximation) that there are no causal relations among $p_x$, $p_c$, $p_s$, $Y$, and $T$. Although there may sometimes be causal dependencies among the separate causes of $d^x$, it is perfectly reasonable to consider how $d^x$ depends on each of these factors, holding the others constant.