Introduction

Professional teams, university athletic departments, event sponsors, and sports facility owners all provide something of value to sports fans and participants. Through their pricing decisions, they extract some of that value for themselves. The more that they extract, the more profit they earn at the expense of the fans and participants. As a result, pricing decisions are critical to their financial success. These pricing decisions also have important welfare consequences because they may result in allocative inefficiency. In this chapter, we examine various pricing models that have been used to extract value from the consumer. We begin with competitive pricing to provide a benchmark for comparison. We then examine various ways to exploit monopoly power: simple monopoly pricing, price discrimination, peak load pricing, bundling, two-part pricing, and pricing complements. Finally, we examine ticket scalping, which is the practice of reselling tickets at prices above the face value.

Competitive Pricing

We begin by examining the results of competitive pricing. Suppose that the demand for tickets to a basketball game is represented by D in Figure 5.1. The marginal cost of each additional spectator is low and we assume that it is constant. When marginal cost is constant, average cost is also constant and equal to marginal cost. The constant marginal and average cost are shown as MC = AC in Figure 5.1. Now, in competitive markets, price is driven to marginal cost by competing sellers. If the organizer of the basketball game were to price at the competitive level, price would be P1, which is equal to MC, and the number of spectators would be Q1.

Introduction

Major sports events undeniably bring with them large crowds of fans and media. The Super Bowl, Major League Baseball's (MLB's) All-Star Game, the Masters Golf Tournament, and big home football games in College Station, Auburn, Tallahassee, and Clemson all attract hordes of people and an apparent burst of economic activity. Thousands of people flock to these events, and they spend plenty of money in the local area. In addition to their spending at the event (tickets, concessions, and souvenirs), these fans spend substantial sums at local hotels and motels, car rental agencies, bars and restaurants, gas stations, T-shirt shops, and so on. This first round of spending provides income to residents in the local community, which results in subsequent rounds of spending. There is a multiplied effect of the initial spending, which is the economic impact of the sports event. Sports leagues and organizations often grossly exaggerate this economic impact for their own purposes. The National Football League (NFL), for example, claims that the impact of the Super Bowl is hundreds of millions of dollars. As we will see, however, such claims are dubious.

In this chapter, we examine the fundamentals of economic impact analysis. We begin with a simple multiplier model and explain why the impact of an event is not as large as some leagues and organizations would have us believe. We also review and evaluate some empirical studies that have been conducted to test the reliability of some claimed impacts.

Overview

Thermodynamics is unquestionably the most powerful and most elegant of the engineering sciences. Its power arises from the fact that it can be applied to any discipline, technology, application, or process. The origins of thermodynamics can be traced to the development of the steam engine in the 1700's, and thermodynamic principles do govern the performance of these types of machines. However, the power of thermodynamics lies in its generality. Thermodynamics is used to understand the energy exchanges accompanying a wide range of mechanical, chemical, and biological processes that bear little resemblance to the engines that gave birth to the discipline. Thermodynamics has even been used to study the energy exchanges that are involved in nuclear phenomena and it has been helpful in identifying sub-atomic particles. The elegance of thermodynamics is the simplicity of its basic postulates. There are two primary ‘laws’ of thermodynamics, the First Law and the Second Law, and they always apply with no exceptions. No other engineering science achieves such a broad range of applicability based on such a simple set of postulates.

So, what is thermodynamics? We can begin to answer this question by dissecting the word into its roots: ‘thermo’ and ‘dynamics’. The term ‘thermo’ originates from a Greek word meaning warm or hot, which is related to temperature. This suggests a concept that is related to temperature and referred to as heat. The concept of heat will receive much attention in this text. ‘Dynamics’ suggests motion or movement. Thus the term ‘thermodynamics’ may be loosely interpreted as ‘heat motion’. This interpretation of the word reflects the origins of the science. Thermodynamics was developed in order to explain how heat, usually generated from combusting a fuel, can be provided to a machine in order to generate mechanical power or ‘motion’. However, as noted above, thermodynamics has since matured into a more general science that can be applied to a wide range of situations, including those for which heat is not involved at all. The term thermodynamics is sometimes criticized because the science of thermodynamics is ordinarily limited to systems that are in equilibrium. Systems in equilibrium are not ‘dynamic’. This fact has prompted some to suggest that the science would be better named ‘thermostatics’ (Tribus, 1961).

Combustion is the reaction of a fuel with oxygen. It is a subset of the more general subject of chemical equilibrium, which is considered in Chapter 14. Combustion is treated as a separate topic because combustion reactions tend to progress until the fuel is completely consumed. Combustion of various hydrocarbon fuels is the major source of useful energy (i.e., exergy) for transportation, electrical generation, space conditioning, water heating, and industrial processes.

Introduction to Combustion

Table 13-1 summarizes the sources of the energy that are consumed in the United States. The nation consumes about 102 quads (1.02 × 1017 Btu or 1.08 × 1011 GJ) of useful energy each year, which represents about 25% of the world energy consumption. The majority of this energy is provided by combustion. There are two major concerns with this current situation. First, nearly all combustible fuels contain carbon, which results in the generation of carbon dioxide during combustion, as shown in this chapter. Combustion in the U.S. alone resulted in the production of 5,990 million metric tons (5.9 × 1012 kg) of carbon dioxide in 2007 according to the U.S. Department of Energy (2009). Carbon dioxide in the atmosphere absorbs a portion of the thermal energy that is re-radiated from the earth and thereby contributes to global warming. Second, reserves of petroleum and natural gas, which account for over 60% of our useful energy supply, are finite. Although the extent of these reserves is a subject of debate, it is likely that they will become depleted in less than 50 years at the present rate of use. There are hundreds of years of coal reserves, but coal generates more carbon dioxide per unit energy than natural gas and coal also produces other contaminants when combusted. The sustainability of our energy supply and the associated problem of global warming are perhaps the most serious problems that the human race has ever faced.

The specific internal energy, enthalpy and entropy at 1 atm pressure for common combustion gases are provided as a function of temperature in the following tables.

1. Table F-1: Ideal gas properties of CO2

2. Table F-2: Ideal gas properties of CO

3. Table F-3: Ideal gas properties of O2

4. Table F-4: Ideal gas properties of N2

5. Table F-5: Ideal gas properties of H2O

The data in these tables were obtained from EES. The reference state for specific enthalpy is based on the enthalpy of formation relative to the elements at 25°C. The reference state for specific entropy is based on the Third Law of Thermodynamics. The reference values are from:

1. Bonnie J. McBride, Michael J. Zehe, and Sanford Gordon

2. “NASA Glenn Coefficients for CalculatingThermodynamic Properties of Individual Species”

3. NASA/TP-2002-211556, Sept. 2002

4. http://www.lerc.nasa.gov/WWW/CEAWeb/

Note that these tables can be printed from the website associated with this text, www.cambridge.org/kleinandnellis, for use during closed book examinations.

As noted in Chapter 1, there are two very different methods to describe a thermodynamic system corresponding to the microscopic approach and the macroscopic approach. So far, only the macroscopic (or classical) approach has been used in this book. The macroscopic approach is based on empirical laws and it describes the equilibrium state of a system in terms of a relatively small number of properties such as temperature, pressure, internal energy, and entropy. The macroscopic approach can be applied to any system and it is mathematically much simpler than the microscopic approach. At no point in the development of the First or Second Laws is it necessary to know that matter consists of individual particles (molecules).

The disadvantage of the macroscopic approach to thermodynamics is that it does not provide any physical insight into the First and Second Laws upon which it is based. More importantly, classical thermodynamics does not provide any means to directly calculate the thermodynamic properties that are needed to apply the First and Second Laws. For example, we know that the specific heat capacities, cP and cv , are needed to evaluate specific enthalpy and specific internal energy. Macroscopic thermodynamics shows us that cP and cv are related (e.g., cP – cv = R for an ideal gas) and it can also explain how these specific heat capacities vary with pressure at a given temperature, as discussed in Chapter 10. However, macroscopic thermodynamics offers no information on how cP and cv vary with temperature at constant pressure. Indeed, it is even difficult to understand what the property temperature refers to using only concepts from macroscopic thermodynamics. Statistical thermodynamics takes a microscopic approach in an attempt to advance our knowledge in these areas.

This extended section can be found online at www.cambridge.org/kleinandnellis. The mathematical description of many interesting problems in thermodynamics and other areas of engineering involves ordinary differential equations (ODEs). In some cases, the ordinary differential equations are sufficiently simple that an analytical solution can be derived. However, in most cases this is not possible and therefore numerical solutions to the ODEs is required. This appendix provides an introduction to numerical techniques and a discussion of the use of the Integral command in EES.

Thermodynamics is a mature science. Many excellent engineering textbooks have been written on the subject, which leads to the question: Why yet another textbook on classical thermodynamics? There is a simple answer to this question: this book is different. The objective of this book is to provide engineers with the concepts, tools, and experience needed to solve practical real-world energy problems. With this in mind, the focus of this effort has been to integrate a computer tool with thermodynamic concepts in order to allow engineering students and practicing engineers to tackle problems that they would otherwise not be able to solve.

It is generally acknowledged that students need to solve problems in order to integrate concepts and skills. The effort required to solve a thermodynamics problem can be broken into two parts. First, it is necessary to identify the fundamental relationships that describe the problem. The set of equations that leads to a useful solution to a problem results from application of appropriate balances and rate relations, simplified with justified assumptions. Identifying the necessary equations is the conceptual part of the problem, and no computer program can provide this capability in general. Proper application of the First and Second Laws of Thermodynamics is at the heart of this process. The ability to identify the appropriate equations does not come easily to most thermodynamics students. This is an area in which problem-solving experience is helpful. A distinguishing feature of this textbook is that it presents detailed examples and discussion that explain how to apply thermodynamics concepts identify a set of equations that will provide solutions to non-trivial problems.