Chapter 1: Microeconomics: a Working Methodology

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Lecture Suggestions

Chapter 1: Microeconomics: A Working Methodology

For Chapter 1 we suggest you use Experiment 1 in conjunction with end-of-chapter exercise 9 as the basis for a good introductory lecture that illustrates the notions of equilibrium, Pareto-optimality, and comparative statics. In addition, by drawing out the features of some real economic problems that are captured by the experiment and the exercise, the lecture is a nice introduction to model building and experimental economics.

The experiment will take no more than five or ten minutes to conduct, if you ask students to indicate their choices by raising their hands and then record their aggregate response on the blackboard. Each student is asked to imagine that he or she is one of five students playing the following game. The game host gives each of the five students $90, with instructions to either keep the $90 or put it in an envelope. The host promises to collect the five envelopes and to create a common pool of money which will be distributed equally among the five students. For every $90 found in an envelope, the host promises to add $60 and to put it all in the common pool.

The experiment captures the essence of common property problems of the sort that are discussed throughout Chapter 1. (See especially the discussion in Section 1.2.) For example, it mimics a two-period common property fishery in which (i) each individual initially has 90 fish in a private pen; (ii) a fish returned to the open ocean "today" produces 5/3 fish "tomorrow"; (iii) a fish today is a perfect substitute for a fish tomorrow. The experiment highlights the very limited incentive that individual fishers have to permit fish to escape their nets today so they can reproduce and sustain the fishery. And it captures the essential feature of the common pool problem that arises in the extraction of oil from a reservoir by a number of independent producers under the rule of capture. The essence of the common pool problem is that a too rapid rate of extraction diminishes the total amount of oil that can be extracted form the reservoir.

In Experiment 1, a selfish student's dominant strategy is to keep the $90. That is, regardless of what the other four players do, a student maximizes his or her own payoff by keeping the $90: if the student keeps the $90 he or she is richer by $90; if the student puts the $90 in the common pool, he or she is richer by $30 (equal to (90 + 60)/5). This equilibrium is not Pareto-optimal since, if all students put $90 in the common pool instead of keeping it, there would be $750 in the common pool and all students would be richer by $150. Based on past experience with this experiment, you can expect something like 85% of students to choose the dominant strategy.

The following payoff matrix is one way to convey these results. The entries in the body of the matrix are the payoffs of a representative player. Rows correspond to the representative player's strategies—"keep" or "put"—and columns to the number of other players choosing "put".

Payoffs in the Common Property Game

In Experiment 1 students are also asked to imagine that they are in an environment in which (i) all students must choose the same action (all keep the $90, or all put the $90 in their envelopes), and (ii) the action is determined by a majority vote of the students. In this institutional environment, a selfish student's (weakly) dominant strategy is to cast a vote in favor of forcing all students to put $90 in the envelope (since each student is richer by $150 if all put $90 in the common pool, and each is richer by only $90 if, instead, each keeps $90). This comparative static exercise captures the spirit of the unitization schemes that were devised by most of the oil producing states to solve the common pool problem—these schemes, in effect, allowed a majority of the producers pumping oil form a particular reservoir to devise a unitized extraction plan for the whole reservoir.

The payoffs of a representative player in this majority rules voting game are presented in the following table. Rows correspond to the representative player's strategy—"all keep" or "all put"—and columns correspond to the number of other players who choose "all keep".

Payoffs for Majority Voting Game

Experiment 2 in conjunction with the appendix to Chapter 1, can be used to produce an additional (or an alternative) introductory lecture that focuses on model building. Experiment 2 is an imaginary game involving two players, and a host. Player One first chooses a 1, 2, 3, 4, or 5. Then, knowing Player One's choice, Player Two then chooses one of the same five integers. The host then randomly chooses one of these five integers (from a uniform probability distribution), and pays $100 to the player whose chosen integer is closest to the one randomly picked by the host. If the two chosen integers are equally close, then the host pays each player $50.

If players are assumed to maximize expected payoff, then it is easy to see that the equilibrium of the game is for both to choose the integer 3. The logic of the exercise is quite interesting because it illustrates how to take a rational approach to sequential decision making. To make a rational choice, Player One must anticipate Player Two's choice. Player One will reason as follows. If I choose 1 (respectively, 5), then Player Two will rationally choose 2 (respectively 4), because by doing so Player Two maximizes his or her expected payoff. Therefore, if I choose 1, my expected payoff is $20. If I choose 2 or 4, then Player Two will rationally choose 3, and my expected payoff will be $40. If I choose 3, then Player Two will rationally choose 3, and my expected payoff will be $50. Therefore, to maximize my expected payoff, I will choose 3. In equilibrium, Player Two also chooses 3.

Chapter 2: A Theory of Preferences

For Chapter 2, we have two suggested lectures: one concerning the rudiments of the economist's theory of preferences and the other concerning the way in which economists use the theory of preferences to attack various problems.

Using experiment 2 in conjunction with the material in Section 2.1 is an effective way to show why economists need a theory of preferences and to introduce the rudiments of the standard theory of preferences. In the experiment, students are asked make a number of binary comparisons regarding a one-week, all-expenses-paid vacation in a variety of cities. For example, would the student prefer Aspen to London, London to Aspen, or are they indifferent between these destinations. The experiment is structured so that students have the opportunity to display preferences that violate both the two-term and three-term consistency assumptions. In a group of 50 students, one usually finds one or two students whose preference statements violate the three-term consistency (transitivity) assumption and once in a while a student's preference statements violate the two-term consistency (reflexivity) assumption. The experiment serves three purposes. (i) It illustrates the need for a theory of preferences—a theory of choice cannot easily be built without a theory of preferences. (ii) With a little massaging, it suggests all three of the fundamental axioms of the standard theory of choice (discussed in detail in Section 2.1). (iii) It alerts the student to the fact that real preferences will sometimes be inconsistent with the theory.

It is very important—but not very easy—to convey to students just how flexible, powerful, and pervasive the theory of preferences is in economics. The chapter contains a number of examples that demonstrate the general applicability of ideas such as maximization, substitution, and diminishing marginal rates of substitution. To motivate the student it is often useful to ask the class “What type of behavior would be inconsistent with, say, substitution.” Students invariably say things like “I would never trade off my life or my friend’s life for anything.” Once this has been stated you can start to probe the student’s behavior. Have the ever sped in a car, consumed too much alcohol, or accepted a dangerous job for more money. Students will usually admit that their own behavior does not conform to their assertions. In the book we look at a number of specific applications that address the basic assumptions of preferences and give students some feeling for the way in which economists use the theory of preferences. Many of the Exercises try to get students more directly into the act as well. A lecture based on theses applications and end-of-chapter exercises will give students an appreciation of the central role of preferences in economics.

Chapter 3: Demand Theory

One of the key ideas in this chapter is that—given an individual's preferences, and the hypothesis that the individual is a utility-maximizer—that individual's behavior can be described by finding his or her demand functions—the functions that tell us what quantities the individual will demand, given any values of the exogenous variables ( p1, p2, and M). The more general idea is that the endogenous variables in a problem (in this case quantities demanded consumption goods) are determined by the exogenous variables (in this case prices and income). Because this idea occurs in all maximizing (or minimizing) models, it is worth exploring in some detail. In these notes we examine four tractable utility functions: perfect substitutes, perfect complements, hierarchical preferences, and Cobb-Douglas preferences. We first examine the intuition behind the utility functions themselves—what sort of preferences do they capture or approximate? We then derive the associated demand functions, and provide an intuitive understanding of just how the prescribed behavior does, in fact, solve the utility maximizing problem.

Of course, these four utility functions and their associated demand functions can be used in a number of other contexts as well—for example, to illustrate the no-money-illusion properties of demand functions. You can also produce a number of useful problems by looking at variations of these functional forms.

Perfect substitutes:is, perhaps, the easiest case. Here we suggest that you use the example of Anna's preferences for salmon and trout, which is developed in the textbook. The utility function is U(x1,x2) = x1 + x2, where x1 is pounds of trout and x2 is pounds of salmon. In contrast to the development in the textbook, we suggest that you use a graphic approach. First, draw the indifference map, and then explain that the slope of an indifference curve is -1 (and therefore MRS is 1) because Anna is always willing to swap one more pound of salmon for one less pound of trout. Then suppose p1 is less than p2 and add the budget line to the figure, observing that the budget line is flatter than the indifference curves. Then, solve the utility maximizing problem by picking the bundle on the budget line that lies on the highest indifference curve, and record the result algebraically:

If p1p2, then x1* = M/p1 and x2* = 0.

Next, suppose that p2 is less than p1 and repeat the exercise to get the following.

If p2p1, then x2* = M/p2 and x1 = 0.

Next, suppose the prices are equal and show that any bundle on the budget line solves the utility maximizing problem because the budget line is coincident with an indifference curve. Finally, provide an intuitive explanation of why the behavior prescribed by these demand functions solves Amy's utility-maximizing problem. Because a pound of salmon is a perfect substitute for a pound of trout, Amy spends all of her budget for fish on (1) trout, if trout is cheaper than salmon, and (2) salmon, if salmon is cheaper than trout. You may want to provide more examples of cases in which this formulation of preferences is appropriate. For example, the fact that some undergraduates always buy the cheapest available brand of beer is consistent with this case of perfect substitutes.

Perfect complements:is perhaps the next-easiest case. In-chapter Problem 3.4 examines this case. We suggest that you interpret x1 and x2 as the number of right and left shoes, and explain why this mathematical formulation is a sensible description of preferences for right and left shoes. Again we suggest that you solve the problem graphically by first drawing a number of indifference curves and then drawing the budget line. Then write out the algebraic description of the solution, and give an intuitive explanation of why the prescribed behavior solves the utility maximizing problem. Finally, you might want to observe that this simple theory answers the question: Why are shoes sold in pairs? Alternatively, why are the two resins used to make epoxy glue packaged together and sold as one unit?

Hierarchical preferences:provide the third, but more difficult case: U(F,T) is F if F 100 and is T if F > 100, where F is pounds of food and T is yards of textiles. It is first useful to give an intuitive explanation of these preferences in terms of a hierarchy of needs. Here, too, we suggest that you develop a graphic solution. First, draw the indifference map. Then assume that 100pFM (the person does not have enough money to buy 100 pounds of food), draw the budget line, and solve the utility-maximizing problem graphically. It is worthwhile to observe what happens to the solution as pT changes (nothing), as M decreases or pF increases (the person continues to spend all his or her income if food.. Next, record the result algebraically:

If 100pFM, then F* = M/pF and T* = O.

Next, assume that 100pFM, and construct the appropriate graphic solution. Let pFor pTdecrease, or M increase and observe that consumption of food does not change, while consumption of textiles increases. Record results algebraically:

If 100pFM, then F* = 100 and T* = (M - lOOpF)/pF.

Finally, provide an intuitive explanation of why this behavior solves the utility maximizing problem.

Cobb-Douglas preferences: are the last case. It is worth developing this case—not so much for its intuitive appeal—but because the solution to the utility-maximizing problem is an interior solution. The problem is, of course, to get an expression for MRS. The following Cobb-Douglas utility function is one case for which MRS can be derived without resorting to calculus:

U(x1,x2) = x1x2

To derive MRS you should use a diagram analogous to Figure 2.5 in conjunction with the following algebraic argument. Suppose the individual initially has bundle (xl,X2) and let u denote the corresponding utility number; that is, u = xlx2. Now ask what increase x in quantity of good 2 will substitute for decrease x1 quantity of good 1. Since the original bundle (x1,x2) is associated with utility number u, so, too, is the bundle

(x1 - x1,x2 + x2); that is,

(x1 - x1(x2 + x2) = u

In other words,

(x1 - x1(x2 +x2) = x1x2

Solving this expression for x2, we get

x2 = x2 x1/(x1 - x)

Now, to get MRS, form the ratio x2/x1 and let x1 approach 0

MRS = x2/x1

Then use this expression for MRS in conjunction with the characterization of an interior solution to get the demand functions:

x* = M/2p1 and x2* = M/2p2

Finally, provide an intuitive interpretation of these demand functions: the individual spends half of his or her income on good 1 and half on good 2. You may also want to, as it were, "wave your hand," to generalize this result. If the utility function is

U(x1,x2) = (x1)a((x1)1 - a, then to maximize utility spend a% of income on good 1 and

(1 - a)% on good 2.

Once students have grasped that demand functions are the result of utility maximizing behavior, another lecture can be spent on the subject of elasticity and how to describe various demand curves.

Chapter 4: More Demand Theory

The focus on Chapter 3 was on deriving demand functions from utility functions and showing how each individual assumption made about preferences has implications for demand functions. For example, the application based on advertising, shows how demand functions reflect the cost minimizing choices made by consumers. Chapter 4 considers more advanced topics in demand, and more applications. Several lectures can follow from Chapter 4.

Once students have understood the technique of moving from indifference curves to demand curves, they usually begin to ask questions that they feel are inconsistent with the notion of downward sloping demands. For example, “why do expensive perfumes sell better than cheap perfumes” or “why do people continue to buy stocks when the price increases.” Most of these questions revolve around confusions over relative prices, the nature of the good, and the concept of real income. The first section of the chapter is devoted to dealing with these issues.

Discussing potential objections to the law of demand naturally leads to a discussion of income and substitution effects caused by a price change. The most difficult aspect here is to convince students that there is a change in real income even though nominal income remains constant. A useful exercise is to go through the graphs in the text, and after each one, have the students do the same procedure by in terms of either an opposite movement in price or in terms of good 2. For example, in the text the income and substitution effect are done for a fall in the price of good 1. Simply have the class conduct the thought experiment in terms of a rise in the price of good 1.

Once you have covered the consumer surplus techniques you can use them to draw together three pieces of analysis from Chapter 3 and 4: the pricing problem for a nonprofit dining club, the Polaroid pricing dilemma, and the demonstration that a lump-sum tax is preferred to an excise tax that raises equal revenue. In order to use consumer surplus techniques, we suppose there are no income effects on the demand for the good in question (meals in the club, the number of Polaroid snapshots, the good on which an excise tax is imposed).

Consider Exercise 20 from Chapter 3 where a private, nonprofit dining club (in which all members have the same preferences) that produces meals at a constant marginal cost of $50 per meal, has a fixed overhead cost equal to $1,000 per member per year. We want to show the student that in order to maximize welfare of the representative club member, the club will choose what we can call a membership fee scheme (charge its members an annual membership fee of $1,000 and sell meals at their $50 marginal cost) in preference to what we can call a mark-up scheme (charge a price greater than $50 such that profit per member is $1,000 per year). The representative member's demand curve is the curve CDF in Figure L1. Distance 0A is equal to the $50 marginal cost. By construction, the shaded area is equal to $1,000. Hence, under the mark-up scheme, the club would sell meals at a price equal to distance OB, and each member would buy x' meals. Notice that the annual value of club membership under the mark-up scheme is the area of triangle BCD. In contrast, the value to the club member of the right to buy meals at the $50 marginal cost is the area of triangle ACF. Once the $1,000 annual membership fee is subtracted from this area, we see that the annual value of club membership under the membership fee scheme is the sum of areas BCD and DEF. In other words, relative to the mark-up scheme, the benefit to the club member of the membership fee scheme is the area of triangle DEF.