John M. Gowdy is the Rittenhouse Teaching Professor of Humanities and Social Science in the Department of Economics at Rensselaer Polytechnic Institute. He is President of the International Society for Ecological Economics 2010-2011. Gowdy has published nine other books, including Paradise for Sale: A Parable of Nature, co-authored with Carl McDaniel.

MICROECONOMIC THEORY OLD AND NEW

A Student’s GuideBy JOHN M. GOWDY

Stanford University Press

Copyright © 2010 Board of Trustees of the Leland Stanford Junior University
All right reserved.
ISBN: 978-0-8047-5884-0

Contents

List of Figures……………………………………………………………………………ixList of Sketches…………………………………………………………………………..xiAcknowledgments……………………………………………………………………………xiiiChapter 1 The Neoclassical Theory of the Consumer…………………………………………….5Chapter 2 The Neoclassical Theory of Production………………………………………………24Chapter 3 General Equilibrium in a Barter Economy…………………………………………….42Chapter 4 Introducing Prices: Perfect Competition and Pareto Efficiency…………………………57Chapter 5 Market Failure and the Second Fundamental Theorem of Welfare Economics…………………79Chapter 6 The Theoretical Critique of Walrasian Welfare Economics………………………………101Chapter 7 The Behavioral Critique of Walrasian Welfare Economics……………………………….120Chapter 8 Cost-Benefit Analysis Old and New………………………………………………….143Chapter 9 The Future of Economic Theory and Policy……………………………………………163Index…………………………………………………………………………………….183

Chapter One

THE NEOCLASSICAL THEORY OF THE CONSUMER

Let us return to the state of nature and consider men as if … sprung out of the earth, and suddenly, like mushrooms, come to full maturity without any kind of engagement to each other.

–Thomas Hobbes, De Cive; or, The Citizen [1651], edited with an introduction by Sterling P. Lamprecht (New York: Appleton-Century-Crofts, 1949), 100

THE FOUNDATION OF UTILITY THEORY-DIRECT EXCHANGE IN A PURE BARTER ECONOMY

Imagine you are driving along a highway behind a truck loaded with merchandise. A box falls out and lands on the side of the road and you stop to take a look and examine the contents. The box is full of CDs (compact discs) of all sorts-classical music, country and western, hip-hop, jazz, Hawaiian, and blues. There is nothing in the box to indicate ownership-no invoice, no name on the box-and you did not notice the name on the truck. You are on your way to your economics class and, feeling slightly guilty about taking the box, you decide to distribute the CDs to your classmates. Suppose there are twenty people in your class and you have 500 CDs to hand out. You start handing them out randomly, not necessarily evenly-some people end up with lots of CDs and some with only two or three. So now there is a group of twenty people sitting around a table with 500 CDs randomly distributed and unevenly divided among them. This sets the stage for learning about how economists think about prices, markets, free trade, social welfare, utility, and efficiency.

The Exchange of Goods in a Pure Barter Economy

The three starting points for the analysis that follows are:

1. The number of CDs to trade (500) is fixed before trading starts. 2. The distribution of these CDs among the twenty people is given before trading starts.

3. The (musical) preferences of the twenty individuals do not change during the bargaining process.

Now the fun begins. Your economics teacher seizes the opportunity to teach the class about market exchange and devotes the class time to establishing a “market equilibrium.” Your fellow students start trading CDs-Brittney Spears for Bad Religion, Shostakovich for Metallica, or Green Day for Dale Watson. Trading goes on for most of the class as people haggle, barter, trade, and retrade to get the CDs they want. After an hour or so, things get quiet as no one is willing to make another deal. The students have done the best they can, given their different musical preferences and their initial endowment of CDs. This situation is called Pareto efficiency, an essential concept in neoclassical welfare economics.

The process of haggling and bartering in trade is what Adam Smith had in mind when he talked about the “invisible hand” of the market economy; that is, the push-and-shove, give-and-take, dynamic vitality of capitalism. Direct bartering allows for face-to-face interaction and for nonpecuniary motives such as altruism and envy, and of course old-fashioned greed. Perhaps you refuse to trade with some people because you resent the fact that they have more CDs than you do and you do not want them to be better off than they already are. Maybe you trade five CDs with someone for one CD you do not particularly want because you are trying to get a date with him or her. All these factors may affect the “well-being” you get from the CDs and they can be incorporated into your trading decisions.

Those of you who have learned the economic model of “perfect competition” (discussed in detail in Chapter 4) might recognize that some of the conditions of that model are fulfilled in this simple barter case. For example:

perfect information-everyone knows exactly how many CDs everyone else has and who the artists are

perfect resource mobility-trade can take place almost instantaneously and at negligible cost

homogeneous product-among the CDs there might be four brand-new, identical copies of Pink Floyd’s Evolution CD

This simple example illustrates some of the most basic ideas that economists dearly cling to.

Trade is good. All trade is assumed to be voluntary, so why would people trade if it did not make them better off?

Restrictions on trade are bad. What if the instructor limited trades to two per person? Or collected a tax for each Radiohead CD traded? This would hinder or even prevent the achievement of Pareto efficiency.

The simple model of exchange in a barter economy is in the back of most economists’ minds as they make policy recommendations on everything from international trade to global warming. A question to keep in mind is: How closely does this face-to-face barter situation resemble a modern market economy with prices, distant markets, complex social institutions, and limited information?

A GRAPHICAL ANALYSIS OF BARTER AND TRADE

As useful as the verbal description of exchange is, it has limitations in terms of its analytical power. Economists deal with data about economic activity, and to interpret this data it is necessary to examine it in an analytical, meaning mathematical, framework. By adding a few more assumptions to the barter model we can reexamine our exchange example using graphs, then mathematics.

One of the most basic and critical tools of Walrasian analysis is the indifference curve, as depicted in Figure 1.1. The points on a particular indifference curve show all the combinations of two commodities (X and Y in Figure 1.1) that yield the same level of utility. In fact, it might be called an iso-utility curve, analogous to isothermals on a weather map. According to Figure 1.1, the consumer is just as happy with the combination of goods X and Y given by point 1 as he or she is with the combination given by point 2. The consumer is just as happy with 2X and 4Y as he or she is with 4X and 2Y.

The indifference curve in Figure 1.1 embodies a number of assumptions about human behavior. The economic analysis of consumer behavior is based on a conception of human nature defined by the assumptions of Homo economicus, or “economic man” (sometimes called the rational actor model). Economic man has well-defined preferences that are stable over time. Individual welfare (utility) is equated with the consumption of market commodities, as shown by the axes of the diagram-goods X and Y. More is preferred to less, so higher indifference curves, those farther away from the origin, represent more total utility to the consumer than ones closer to the origin. Commodities are subject to substitution, as indicated by the downward slope of the indifference curve. Indifference curves have the mathematical property of being “smooth and continuous,” meaning there are no “jumps” in utility as one commodity is substituted for another as we move along the curve.

Axioms of Consumer Choice Defining Homo economicus (economic man or the rational actor)

1. Non-satiation-More is preferred to less. A commodity bundle on a higher indifference curve is preferred to one on a lower indifference curve.

2. Transitivity-If commodity bundle A is preferred to bundle B, and bundle B is preferred to C, then bundle A is preferred to C. This implies consistency in consumer choice.

3. Preferences are stable and complete-For any pair of commodity bundles A and B, the consumer either prefers A to B, B to A, or is indifferent between the two bundles. These preferences are stable over time.

4. Diminishing marginal rates of substitution-As a consumer has more of one commodity relative to another one, he / she is willing to give up more of it for a unit of the second commodity.

5. Continuity-This is a mathematical property, meaning that any point on a line drawn between two points on an indifference curve is an interior point. As we will see later, this assumption is necessary to ensure a unique solution to any constrained maximization problem.

6. Exogenous preferences-The preferences of one consumer are unaffected by the preferences of others.

The slope of an indifference curve at a particular place along a curve, [DELTA]X/[DELTA]Y or the “rise over the run,” indicates the marginal rate of substitution (MRS) of one commodity for another. For example, as we go between points 1 and 2, the marginal rate of substitution of good Y for good X ([MRS.sub.Y for X]) is -1, [DELTA]X/[DELTA]Y = -2/2 = -1. The consumer is willing to give up 1 X to get 1 Y without changing total utility. The shape of the curves, becoming steeper or flatter as they approach the X or Y axes, indicates a diminishing marginal rate of substitution. As a consumer has more and more of good X (or good Y), he or she is willing to give up more and more of X (or Y) to get another Y (or X).

It is important to recognize the assumptions invoked in the basic model of exchange in a barter situation and those that are added as we move from a verbal to a graphical and then to a mathematical representation of exchange. Remember that this model is meant to be a plausible representation of actual human behavior. When we move to a graphical representation of utility, what assumptions are added to the three we started with in the pure barter case?

* ASSUMPTION ALERT! Critical behavioral assumptions we have added to move from a verbal to a graphical analysis of exchange:

1. The utility of one individual can be determined independently of the utility of others.

2. Utility or well-being is equated with consumption of the market goods X and Y.

3. More consumption is always preferred to less. 4. All items giving an individual “utility” are subject to substitution and trade.

FROM INDIFFERENCE CURVES TO EXCHANGE: THE EDGEWORTH BOX DIAGRAM

Armed with our model of human behavior and our goal of efficiency, we can develop a set of rules about how two people (or more than two people using mathematics) will engage in barter and trade to make themselves better off. The diagram in Figure 1.2 is called an Edgeworth box, named after the economist and mathematician Francis Edgeworth (1845-1926).

Figure 1.2 is actually two indifference curve diagrams put together, one for consumer A and one for consumer B. The origin for consumer A is at the lower left-hand corner so that his utility increases steadily as we move up and to the right in the Edgeworth box (because he has more of goods A and B). The origin for consumer B is at the upper right-hand corner so that her utility increases as we move down and to the left in the Edgeworth box. Any point inside the Edgeworth box shows the distribution of the two goods among the two consumers.

Notice that if we move from point 1 to point 2, the utility for both consumers increases. Consumer A moves from indifference curve [I.sub.A1] to the higher indifference curve [I.sub.A2] and consumer B moves from indifference curve [I.sub.B1] to the higher indifference curve (farther from the origin for B) [I.sub.B2]. At point 2 both consumers have been made better off by trading. A movement from point 1 to point 2 in Figure 1.2 is a graphical representation of a voluntary trade of one CD for another in the barter example we began with.

Notice that at point 2 no further trading can take place without making one of the consumers worse off. If we move away from point 2 to anywhere else on indifference curve [I.sub.A2], consumer B moves to an indifference curve with less utility. If we move from point 2 to any other point on indifference curve [I.sub.B2], consumer A is on a lower indifference curve with less total utility. Point 2 is a Pareto-efficient point. Now looking at the indifference curves for the two consumers at point 2 we can see something very important. The indifference curves are just tangent to one another, indicating that their slopes (their marginal rates of substitution of X for Y) are the same.

* ASSUMPTION ALERT!

1. This is a model of the static exchange of a fixed amount of goods among consumers with stable preferences, and each consumer has (implicitly) perfect information about the characteristics of the goods and the preferences of the other consumer.

2. The particular Pareto-efficient outcome depends on the initial distribution of the goods among the two consumers. Look at Figure 1.2 and convince yourself that a different initial distribution of X and Y will result in a different Pareto-efficient distribution.

ONE MORE THING BEFORE MOVING ON-THE MANY PARETO EFFICIENCIES

For any particular initial distribution of goods X and Y among consumers A and B, there will be only one Pareto-efficient outcome of trade. Each different initial distribution of X and Y will yield a different Pareto-efficient outcome. A line connecting all the Pareto points in an Edgeworth box is called a contract curve, and such a curve is shown in Figure 1.3. We will return to the contract curve later when we discuss the notion of a social welfare function. Given the preferences of the two consumers A and B, for the two goods X and Y, as depicted by the shapes of the indifference curves, the contract curve shows the Pareto-efficient allocations of the two goods for all possible initial distributions of the two goods between the two consumers.

Figure 1.3 illustrates a very important concept lying at the base of Walrasian economic policy. By altering the initial distribution of goods X and Y (this is called a lump-sum transfer), any particular Pareto-efficient outcome can be reached. This has important implications for economic policy. In this framework the ideal policy to correct inequality, for example, is to let the political process set the parameters (the initial distribution of goods) and let the “market” determine the final outcome. This preserves the efficiency of the trading process.

THE MATHEMATICAL INTERPRETATION OF UTILITY

Mathematically, the indifference curve may be stated as a utility function of the form:

(1.1) [U.sub.A] = f(X,Y)

The utility of consumer A is a function of (depends on) the amounts of commodities X and Y consumed. Much of Walrasian analysis uses the mathematics of constrained optimization. This mathematics is very simple but it can be intimidating to the uninitiated. Most of the mathematics in economics deals with marginal change, which is expressed by the concept of the derivative. For example, the change in utility of consumer A that results from a change in the amount of good X is expressed as dU / dX (or using the Greek letter delta, [DELTA]U / [DELTA]X or [partial derivative]U / [partial derivative]X). It shows the effect of a small change in the amount of good X on total utility with the amounts of all other goods possessed by consumer A held constant. This is called the marginal utility of X. Likewise, dU / dY is the marginal utility of good Y.

Referring to equation (1.1), we can perform a mathematical operation called total differentiation to examine the change in utility resulting from changes in the amounts of goods X and Y.

(1.2) dU = (dU / dX) [DELTA]X + (dU / dY) [DELTA]Y

The change in total utility in the simple two-good economy is equal to the marginal utility of X, that is, how a one-unit change in X (or dX) changes the utility of the consumer (or dU), multiplied by the actual unit change in X (or [DELTA]X) plus the marginal utility of Y multiplied by the actual unit change in Y. For example, if the marginal utility of X is 2 “utils” and the marginal utility of Y is 3 “utils,” and we give the consumer 2 more X’s and 3 more Y’s, the consumer’s utility goes up by 2 2 + 3 3 = 13 utils.

By definition, utility does not change along an indifference curve, so dU=0. Thus we can rewrite equation (1.2) as:

(1.3) (dU / dX) [DELTA]X = -(dU / dY) [DELTA]Y or

(1.4) (dX / dY) = -(dU / dY) / (dU / dX) = -([MU.sub.Y] / [MU.sub.X]) = [MRS.sub.Y for X]

(Continues…)

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