The social rate of discount plays a central role in applied welfare economics, governing such decisions as the amount of public investment, interventions in private capital markets, and the size of intergenerational transfers. Ever since the social choice theory literature began to evolve into practical models of government planning, there has been a lively discussion concerning the appropriate social rate and reasons why it should or should not deviate from the private (market) rate. Kenneth Arrow was an early and frequent contributor to this literature along with many others; on the occasion of Arrow's Festschrift, I attempted to summarize a number of elements in the debate. Since that time, the subject seems to have receded somewhat from prominence, the prevailing opinion being that value judgments must ultimately be invoked and that economic theory cannot resolve such matters.

I would like to take this opportunity to reopen the subject, not because I think there is anything really new to say about the underlying value judgments, but because this is a context in which these judgments can be illuminated most starkly. I address the issue of population crowding and the appropriate way to measure its social costs.

The literature identifies one crowding externality in particular as being important to the population question: the “global commons.” To the extent that access to such common resources is essential to wellbeing, an extra person imposes external costs by crowding other people out. By way of introduction, we provide a general set-up for measuring this externality and argue that if the global commons were interpreted broadly to include all the earth's fixed factors, the associated external cost of an extra person would be quite substantial.

In most of the rest of the book, we will focus on project analysis. The framework (as developed in Chapters 6 and 7) is one in which decentralized government agencies make independent decisions on collective-goods provision in a mixed economy. The underlying status quo can be any configuration of publicly determined variables that is consistent with private-sector equilibrium. In particular, there will be no presumption of optimality in any of these choices. Any proposed change in this status quo can be thought of as defining a project. Hence, our concept of a project covers such diverse activities as a weather satellite, a pollution cleanup campaign, and a tax reform proposal. Naturally, the agencies cannot act completely independently since they are linked through the budget constraint. Further, we want agencies to take into account all relevant inter-dependencies. The principal aim of project analysis is to find ways of measuring project net benefits that correctly account for general equilibrium relationships and other interdependencies in this economic setting.

Throughout Part III we restrict attention to first-order welfare measures. We will give a precise operational meaning to “first order” in what follows, but informally, our approach amounts to introducing projects in such a way that their size is well defined and finding the best linear approximation to welfare contribution as a function of size. We develop the methodology first in a certainty model with a single jurisdiction allocating uncongestible goods for a closed economy.

In the previous two chapters, we discussed ways of integrating first-order information to get exact or approximate measures of utility (and welfare) for large changes. When the associated variables are traded in markets, we can recover the associated measures from sufficiently rich demand data. However, it is highly implausible that we can collect demand information detailed enough to perform the required numerical integrations. Moreover, since we are primarily concerned with allocating collective (hence, unmarketed) goods, market demand information alone (no matter how detailed) will not be sufficient unless we can generalize the spanning procedures of Chapter 13. This chapter discusses ways of recovering (or in most cases estimating) required information from observable data and using resulting measures to evaluate and compare alternative large projects.

We first look at methods for recovering surplus or willingness to pay for collective goods from sufficiently rich information on market demand. However, since “full information” is virtually never available, we need to look at ways of estimating or otherwise learning about utility. A standard estimating procedure involves imposing parametric restrictions on the form of utility (or demand) functions and estimating the parameters econometrically. We explain and evaluate this method in Section 16.2. Alternatively, we might try to learn about utility by designing a planning mechanism that induces agents to reveal their true surplus. Of course, we know from our discussions in Chapter 5 that the potential for solving broad classes of economic problems with a single planning mechanism is quite limited.

Much of applied welfare economics as it has developed over the past several decades involves the study and use of shadow prices. Since (as we will argue) shadow pricing means different things to different people, we start with a rather broad definition and spend some time talking about various alternative meanings of the term. Shadow pricing will refer to the study and use of first-order welfare impacts associated with changes in the levels of particular goods or groups of goods.

This definition accords with the common view of what a shadow price stands for. Suppose we are talking about some input to a government project. Then the shadow price ought to be opportunity cost per unit of increasing this input, and the correct way to measure this opportunity cost is by the marginal welfare foregone. Ambiguity in the definition arises over the ceteris paribus assumptions. When an input level is changed, what other things are allowed to change with it? Obviously, something must change in equilibrium or else an infeasibility develops. And it would be silly to ignore this infeasibility here since the shadow price would be zero if we do.

On the other hand, issues of feasibility frequently are ignored when economists discuss shadow pricing of outputs. We ask, for example, what would an extra unit of public good be worth if we had it? (And never mind how would we get it?) Here, shadow price becomes a hypothetical construction. Having obtained such a price, we proceed by comparing it with the least cost way of actually getting an extra unit.

To this point we have espoused a rather ambitious view concerning the objectives of government planning. We sought “first-best” solutions and placed no a priori restrictions on the scope of government activity. Unfortunately, we were forced to conclude in Chapter 5 that there was little hope of finding incentive-compatible mechanisms that were both workable and comprehensive in coverage. Therefore, we will limit our objectives in most of the sequel.

The nature of our limitations involves leaving a large segment of the economy in an uncontrolled market sector and using a variety of indirect methods to allocate remaining goods in a public sector. This view of the scope of public activity is most easily justified on positive grounds: The U.S. economy has evolved into one having this mixed structure, so we want to know how well it can be expected to work. However, there is some reason to believe that the mixed economy can be given a normative justification as well. That is, such a division of responsibility in allocation may be the second-best optimal organizational form when all informational and incentive costs are accounted for correctly.

Although we cannot prove the second-best optimality of a mixed-economy structure, we can draw on material from earlier chapters to give an informal argument. We saw in Chapter 3 that market decentralization involves a considerable saving in information collection and transmission as compared to other potential allocation methods; further, such decentralization achieves a first-best allocation for the class of private goods if agents can be made to behave competitively.

We complete our analysis of the general budgeting problem in the mixed economy with a discussion of “optimal” finance. We focus on a particular constituency (which we assume must be self-sufficient) and ask how it should best collect money to finance its operations. In principle, the issues here involve both optimal pricing of publicly provided excludable goods and optimal taxation to pay for unfunded costs of providing nonexcludable goods. Although the first of these problems is not of major importance in the U.S. economy, it is worth our attention for several reasons. First, it does play an important role in budgeting for some of the European socialist democracies. Second, the “public-pricing” and “optimal-taxation” problems have strikingly similar structure so that each provides insight into the nature of the other. Finally, the public-pricing problem provides a useful transition from “optimal-planning” problems of the type discussed in Chapters 3 and 5 to the type of second-best analysis for the mixed economy that will occupy us in much of the sequel.

Optimal public pricing

We start with the budgeting problem for a very simple government, one that provides only excludable goods and has no taxing powers. “Public” activity involves producing some subset of excludable goods and selling them in such a way as to cover all costs (a constraint that follows from the lack of taxation power). Alternatively, the following model can be applied to the analysis of a government enterprise required by law to balance its budget. Although the second interpretation is more realistic, the first is useful in making comparisons with the “optimal-tax” model to follow.

To this point, our conception of the mixed economy has treated the public sector as monolithic. However, we observe a considerable degree of government decentralization in practice, and indeed, we would expect to find some such structures in a second-best organizational design for much the same reasons we argued for market decentralization of private goods earlier. Here, we will develop a model of government structure that is roughly consistent with the actual organization of the U.S. public sector. We will emphasize normative properties of this structure, drawing on earlier discussions of political decentralization and mechanism design.

One possible approach to public-sector design would be to mimic closely the structure of market decentralization. That is, we could divide up responsibilities into a large collection of fully autonomous agencies, each of which would be responsible for the allocation of a narrow range of collective goods. Autonomy would be achieved by having each individual agency elicit information on preferences and assess separate taxes and/or user charges. To the extent that “true” information is learned, it can be used to organize finance according to the so-called benefits principle – household payments for the collective goods and services would be directly related to benefits received.

This mode of organization has many desirable features. First and foremost, it eliminates entirely the need for centralized information gathering and the associated cost of bureaucracy needed to administer and coordinate activities. Further, to the extent that the finance tax can be made a charge for services rendered, it will act like a price that will induce the relevant clientele to reveal their preferences.

We found, in the previous chapter, that methods of political decision making are severely limited in their applicability. Tractability requires that the number of alternatives considered by any one political agency be relatively small. However, when we prune the set of alternatives either directly or through political decentralization, biases are likely to emerge in the resulting choices.

Of course, the market offers an alternative method of allocation and one that appears to require little in the way of administrative and/or coordination costs. Indeed, several of the troublesome examples in Chapter 2 appeared to yield to “market-type” solutions. Market decentralization through the “invisible hand” has at least as many information-conserving benefits as does political decentralization, but does it have any corresponding costs?

Much of the controversy in political economy during the past century has centered on whether we should allow the invisible hand to allocate resources. Many of the proponents of market decentralization have based their argument on the so-called two theorems of welfare economics, the one saying that a competitive equilibrium is Pareto efficient and the other saying that every Pareto-efficient allocation can be supported as a competitive equilibrium with an appropriate distribution of income. When the hypotheses of these theorems hold, market decentralization involves no costs. The opposition has challenged both the assumptions underlying competitive behavior and the supposition that income distribution will be made “appropriate.” Although some of their arguments are quite telling, this group has been noticeably on the defensive.

Up to now, our project analysis has been conducted in a first-order framework without much discussion of limitations of the approach. Part IV of this book addresses these limitations and develops more general procedures for project analysis when first order is inadequate. Unfortunately, as we shall see, the new methods are much more difficult to implement from a practical point of view. For this reason it is desirable to make the most use we can of the first-order approach.

Assuming that there are no significant indivisibilities, it is always possible to construct general decision-making procedures on the basis of the first-order approach. Each large project (or combination of large projects) can be constructed from a sequence of small projects, and these can be evaluated iteratively using the methods of Part III. To make this procedure operational, we need a rule for deciding the sequence by which projects are introduced. Many rules are possible, but for now let us suppose that they are introduced in order of their “efficiency”; that is, we implement the project with the highest dW/dα first, recompute a status quo, look for the next best project, and iterate. Of course, we stop when there are no more projects that generate a positive increment in welfare.

Iterative planning methods of this type have a long history in the literature. They are known to generate overall optimal performance as long as the economic environment is convex. But they work badly when there are significant elements of increasing returns to scale or other nonconvexities.

Any book on normative economics ought to begin with some discussion of social objectives. Since the meat of this book involves practical methods for evaluating such objectives, and since the extant literature on social choice theory is voluminous, we choose not to spend a great deal of time on the subject here. However, a short discussion of our basic philosophy is in order.

Fundamental to our approach is the implicit acceptance of “consumer sovereignty.” Operationally, this principle means that only measures of individual preference affect social choice. We reject the paternalist view that government knows better than its citizens what is good for them. Having taken this position, it remains to decide how to measure individual preference and how to reconcile differences among these individual preferences.

We also accept the classical view of economic person as utility maximizer. If we think of preference as revealed by choice, the underlying choice functions must be consistent. Although violations of this principle of rationality can be found in the experimental literature, they seem to be exceptions rather than the rule, at least in a certainty context. Assumptions of rationality in an uncertainty context generate more serious objections, which we will comment on later. Unfortunately, we would not make much progress in this book if we tried to drop all principles of rationality unless we also dropped consumer sovereignty; the planner will have a hard time keeping hands off consumer preferences when they are inconsistent.