microeconomics background for the study of public finance

1 INTERNET CHAPTER ONE

Microeconomics Background for the Study of Public Finance

He who has choice also has pain.

— German proverb

Certain tools of microeconomics are used throughout the text. They are briefly reviewed in this appendix. Readers who have had an introductory course in microeconomics will likely

find this review sufficient to refresh their memories. Those confronting the material for the first time may want to consult one of the standard introductory texts. 1 The subjects covered are demand and supply, consumer choice, and marginal analysis.

DEMAND AND SUPPLY The demand and supply model shows how the price and output of a commodity are determined in a competitive market. We discuss in turn the determinants of demand, supply, and their interaction.

DEMAND Which factors influence people’s decisions to consume certain goods? To make the problem concrete, let us consider the specific case of coffee. A bit of introspection suggests that the following factors affect the amount of coffee that people want to consume during a given time period:

1. Price. We expect that as the price goes up, the quantity demanded goes down. 2. Income. Changes in income modify people’s consumption opportunities. It is hard to say

a priori, however, what effect such changes have on consumption of a given good. One possibility is that as incomes go up, people use some of their additional income to purchase more coffee. On the other hand, it may be that as incomes increase, people consume less coffee, perhaps spending their money on cognac instead. We expect that changes in income affect demand one way or the other, but in some cases it is hard to predict the direction

1 See, for example, Samuelson and Nordhaus (1989).

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2 Internet Chapter One: Microeconomics Background for the Study of Public Finance

of the change. If an increase in income increases the demand (other things being the same), the good is called a normal good. If an increase in income decreases demand (other things being the same), the good is called an inferior good.

3. Prices of related goods. Suppose the price of tea goes up. If people can substitute coffee for tea, this increase in the price of tea increases the amount of coffee people wish to consume. Now suppose the price of cream goes up. If people consume coffee and cream together, this tends to decrease the amount of coffee consumed. Goods like tea and coffee are called sub-stitutes; goods like coffee and cream are called complements.

4. Tastes. The extent to which people “like” a good affects the amount they demand. Not much coffee is demanded by Mormons because their religion prohibits its consumption. Often, it is realistic to assume that consumers’ tastes stay the same over time, but this is not always the case. For example, when some scientists claimed that coffee might cause birth defects, it presumably changed the tastes of pregnant women for coffee.

We see, then, that a wide variety of things can affect demand. However, it is often useful to focus on the relationship between the quantity of a commodity demanded and its price. Suppose that we fix income, the prices of related goods, and tastes. We can imagine varying the price of coffee and seeing how the quantity demanded changes under the assumption that the other relevant variables stay at their fixed values. A demand schedule (or demand curve ) is the relation between the market price of a good and the quantity demanded of that good during a given time period, other things being the same. (Economists often use the Latin for “other things being the same,” ceteris paribus. ) A hypothetical demand schedule for coffee is represented graphically by curve D c in Fig-ure IC1.1 . The horizontal axis measures pounds of coffee per year in a particular market, and the price per pound is measured on the vertical. Thus, for example, if the price is $2.29 per pound, people are willing to consume 750 pounds; when the price is only $1.38, they are willing to consume 1,225 pounds. The downward slope of the demand schedule reflects the reasonable assumption that when the price goes up, the quantity demanded goes down. The demand curve can also be interpreted as an approximate schedule of “willingness to pay,” because it shows the maximum price that people would pay for a given quantity. For example, when people purchase 750 pounds per year, they value it at $2.29 per pound. At any price more than $2.29, they would not willingly consume 750 pounds per year. If for

some reason people were able to obtain 750 pounds at a price less than $2.29, this would in some sense be a “bargain.”

As already stressed, the demand curve is drawn on the assumption that all other variables that might affect quantity demanded do not change. What happens if one of them does? Suppose, for example, that the price of tea increases, and as a consequence, people want to buy more coffee. In Fig-ure IC1.2 , schedule D c from Figure IC1.1 (before the increase) is repro-duced. As a consequence of the increase in the price of tea, at each price of cof-fee people are willing to purchase more coffee than they did previously. In effect, then, an increase in the price of

FIGURE IC1.1 Hypothetical

Demand Curve for

Coffee

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Internet Chapter One: Microeconomics Background for the Study of Public Finance 3

tea shifts each point on D c to the right. The collection of new points is D9 c . Because D9 c shows how much people are willing to con-sume at each price ( ceteris paribus ), it is by definition the demand curve.

More generally, a change in any variable that influences the demand for a good—except its own price—shifts the demand curve. 2 (A change in a good’s own price induces a move-ment along the demand curve.)

SUPPLY Now consider the factors that determine the quantity of a commodity that firms supply to the market. We will continue using coffee as our example.

1. Price. In many cases, it is reasonable to assume that the higher the price per pound of coffee, the greater the quantity profit-maximizing firms are willing to supply.

2. Price of inputs. Coffee producers employ inputs to produce coffee—labour, land, and fertilizer. If their input costs go up, the amount of coffee that they can profitably supply at any given price goes down.

3. Conditions of production. The most important factor here is the state of technology. If there is a technological improvement in coffee production, the supply increases. Other variables also affect production conditions. For agricultural goods, weather is important. Several years ago, for example, flooding in Latin America seriously reduced the coffee crop.

As with the demand curve, it is useful to focus attention on the relationship between the quantity of a commodity supplied and its price, holding the other variables at fixed levels. The

supply schedule is the relation between mar-ket prices and the amount of a good that producers are willing to supply during a given time period, ceteris paribus.

A supply schedule for coffee is depicted as S c in Figure IC1.3 . Its upward slope reflects the assumption that the higher the price, the greater the quantity supplied, ceteris paribus.

When any variable that influences sup-ply (other than the commodity’s own price) changes, the supply schedule shifts. Sup-pose, for example, that the wage rate for coffee-bean pickers increases. This increase reduces the amount of coffee that firms are willing to supply at any given price. The supply curve therefore shifts to the left. As depicted in Figure IC1.4 , the new supply

Pounds of coffee per year

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FIGURE IC1.2 Effect of an

Increase in the

Price of Tea on the

Demand for Coffee

2 There is no need, incidentally, for D9 c to be parallel to D c . In general, this will not be the case.

FIGURE IC1.3 Hypothetical

Supply Curve for

Coffee


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curve is S9 c . More generally, when any vari-able other than the commodity’s own price changes, the supply curve shifts. (A change in the commodity’s price induces a move-ment along the supply curve.)

EQUILIBRIUM The demand and supply curves provide answers to a set of hypothetical questions: Ifthe price of coffee is $2 per pound, how much are consumers willing to purchase? If the price is $1.75 per pound, how much are firms willing to supply? Neither schedule by itself tells us the actual price and quantity. But taken together, the schedules determine price and quantity.

In Figure IC1.5 we superimpose demand schedule D c from Figure IC1.1 on supply schedule S c from Figure IC1.3 . We want to find the price and output at which there is an equilibrium —a situation that tends to be main-tained unless there is an underlying change in the system. Suppose the price is P 1 dollars per pound. At this price, the quantity demanded is Q 1 D and the quantity supplied is Q 1 S . Price P 1 cannot be maintained, because firms want to supply more coffee than consumers are willing to purchase. This excess supply tends to push the price down, as suggested by the arrows. Now consider price P 2 . At this price, the quantity of coffee demanded, Q 2 D , exceeds the quantity supplied, Q 2 S . Because there is excess demand for coffee, we expect the price to rise. Similar reasoning suggests that any price at which the quantity supplied and quantity demanded are unequal cannot be an equilibrium. In Figure IC1.5 , quantity demanded equals quantity supplied at price P e . The associated output level is Q e pounds per year. Unless some-thing else in the system changes, this price and output combination continues year after year. It is an equilibrium.

Suppose something else does change: For example, the weather turns bad, ruin-ing a considerable portion of the coffee crop. In Figure IC1.6 , D c and S c are repro-duced from Figure IC1.5 , and as before, the equilibrium price and output are P eand Q e , respectively. As a consequence of the weather change, the supply curve shifts to the left, say to S9 c . Given the new supply curve, P e is no longer the equilibrium price. Rather, equilibrium is found at the intersection of D c and S9 c , at price P9 e and output Q9 e . Note that, as one might expect, the crop disaster leads to a higher price and smaller output— P9 e . P e and Q9 e ,

Q e . More generally, a change in any vari-able that affects supply or demand creates a new equilibrium combination of price and quantity.


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FIGURE IC1.4 Effect of an

Increase in the

Wages of Coffee

Pickers on the

Supply of Coffee

FIGURE IC1.5 Equilibrium in the

Coffee Market


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SUPPLY AND DEMAND FOR INPUTS Supply and demand can be used not only to investigate the markets for consump-tion goods but also the markets for inputsinto the production process. (Inputs are sometimes referred to as factors of pro-duction. ) For example, we could label the horizontal axis in Figure IC1.5 “number of hours worked per year” and the vertical axis “wage rate per hour.” Then the sched-ules would represent the supply and demand for labour, and the market would determine wages and employment. Simi-larly, supply and demand analysis can be applied to the markets for capital and for land.

MEASURING THE SHAPES OF SUPPLY AND DEMAND CURVES Clearly, the market price and output for a given item depend substantially on the shapes of its demand and supply curves. Conventionally, the shape of the demand curve is measured by the price elasticity of demand: the absolute value of the percentage change in quantity demanded divided by the percentage change in price. 3 If a 10 percent increase in price leads to a 2 percent decrease in quantity demanded, the price elasticity of demand is 0.2. An important special case is when the quantity demanded does not change at all with a price increase. Then the demand curve is vertical and elasticity is zero. At the other extreme, when the demand curve is hori-zontal, then even a small change in price leads to a huge change in quantity demanded. By convention, this is referred to as an infinitely elastic demand curve. Similarly, the price elastic-ity of supply is defined as the percentage change in quantity supplied divided by the percentage change in price.

THEORY OF CHOICE The fundamental problem of economics is that resources available to people are limited relative to their wants. The theory of choice shows how people make sensible decisions in the presence of such scarcity. In this section we develop a graphical representation of consumer tastes and show how these tastes can best be gratified in the presence of a limited budget.

TASTES We assume that an individual derives satisfaction from the consumption of commodities. 4 Econ-omists use the slightly archaic word utility as a synonym for satisfaction. Consider Oscar who consumes only two commodities, marshmallows and donuts. (Using mathematical methods, all the results for the two-good case can be shown to apply to situations in which there are many commodities.) Assume further that for all feasible quantities of marshmallows and donuts, Oscar

FIGURE IC1.6 Effect of Bad

Weather on the

Coffee Market


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3 The elasticity need not be constant all along the demand curve. 4 In this context, the notion of commodities should be interpreted very broadly. It includes not only items such as food, cars, and compact disk players, but also less tangible things like leisure time, clean air, and so forth.


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is never satiated—more consump-tion of either commodity always produces some increase in his util-ity. Economists believe that under most circumstances, this assump-tion is pretty realistic.

In Figure IC1.7 , the horizontal axis measures the number of donuts consumed each day, and the vertical axis shows daily marshmallow con-sumption. Thus, each point in the quadrant represents some bundle of marshmallows and donuts. For example, point a . represents a bun-dle with seven marshmallows and five donuts.

Because Oscar’s utility depends only on his consumption of marsh-

mallows and donuts, we can also associate with each point in the quadrant a certain level of utility. For example, if seven marshmallows and five donuts create 100 “utils” of happiness, then point a is associated with 100 “utils.” Some commodity bundles create more utility than point a, and others less. Consider point b in Figure IC1.7 , which has both more marshmallows and donuts than point a . Since satiation is ruled out, b must yield higher utility than a . Bundle f has more donuts than a and no fewer marsh-mallows, and is also preferred to a . Indeed, any point to the northeast of a is preferred to a . The same reasoning suggests that bundle a is preferred to bundle g, because the latter has fewer marshmallows and donuts than the former. Point h is also less desirable than a, because although it has the same number of marshmallows as a, it has fewer donuts. Point a is preferred to any point southwest of it.

We have identified some bundles that yield more utility than a, and some that yield less. Can we find some bundles that produce just the same amount of utility as point a ? Presumably there are such bundles, but we need more information about the individual to find out which they are. Consider Figure IC1.8 , where point a from Figure IC1.7 is reproduced. Imagine that

we pose the following question to Oscar: “You are now consuming seven marshmal-lows and five donuts. If I take away one of your donuts, how many marshmallows do I need to give you to make you just as sat-isfied as you were initially?” Suppose that after thinking a while, Oscar (honestly) answers that he would require two more marshmallows. Then by definition, the bundle consisting of four donuts and nine marshmallows yields the same amount of utility as a . This bundle is denoted i in Fig-ure IC1.8 .

We could find another bundle of equal utility by asking: “Starting again at point a,suppose I take away one marshmallow. How many more donuts must I give you to keep you as well off as you originally

7f

These bundles arepreffered to bundle a

These bundles are lessdesirable than bundle a

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FIGURE IC1.7 Ranking

Alternative

Bundles

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FIGURE IC1.8 Derivation of an

Indifference Curve


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were?” Assume the answer is two donuts. Then the bundle with six marshmallows and seven donuts, denoted j in Figure IC1.8 , must also yield the same amount of utility as bundle a .

We could go on like this indefinitely—start at point a, take away various amounts of one commodity, find out the amount of the other commodity required for compen-sation, and record the results on Figure IC1.8 . The outcome is curve U 0 U 0 , which shows all points that yield the same amount of utility. U 0 U 0 is referred to as an indiffer-ence curve, because it shows all consump-tion bundles among which the individual is indifferent.

By definition, the slope of a curve is the change in the value of the variable measured

on the vertical axis divided by the change in the variable measured on the horizontal—the “rise over the run.” The slope of an indifference curve has an important economic interpretation. It shows the rate at which the individual is willing to trade one good for another. For example, in Figure IC1.9 , around point i, the slope of the indifference curve is m/n . But by definition of an indifference curve, n is just the amount of donuts that Oscar is willing to substitute for sacrificing m marshmallows. For this reason, the absolute value of the slope of the indifference curve is often referred to as the marginal rate of substitution of donuts for marshmallows. 5

This is abbreviated MRS dm . As drawn in Figure IC1.9 , the marginal rate of substitution declines as we move down along the indifference curve. For example, around point ii, MRS dm is p/q, which is clearly smaller than m/n . This makes intuitive sense. Around point i, Oscar has a lot of marshmallows relative to

donuts and is therefore willing to give up quite a few marshmallows in return for an additional donut—hence a higher MRS dm . On the other hand, around point ii, Oscar has a lot of donuts relative to marshmallows, so he is unwilling to sacrifice a lot of marsh-mallows in return for yet another donut. The decline of MRS dm as we move down along the indifference curve is called a diminishing marginal rate of substitution.

Recall that our construction of indiffer-ence curve U 0 U 0 was based on bundle a as a starting point. But point a was chosen arbi-trarily, and we could just as well have started at any other point in the quadrant. In Figure IC1.10 , if we start with point b and proceed in the same way, we generate indifference curve U 1 U 1 . Or starting at point k we generate

5 As noted later, marginal means additional or incremental . The indifference curve’s slope shows the marginal rate of substitution because it indicates the rate at which the individual would be willing to substitute marshmal-lows for an additional donut.

FIGURE IC1.9 An Indifference

Curve with a

Diminishing

Marginal Rate of

Substitution

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FIGURE IC1.10 An Indifference

Map

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indifference curve U 2 U 2 . Note that any point on U 2 U 2 represents a higher level of utility than any point on U 1 U 1 , which in turn is preferred to any point on U 0 U 0 . If Oscar is interested in maximizing his util-ity, he tries to reach the highest indifference curve that he can.

The entire collection of indifference curves is referred to as the indifference map. The indifference map tells us every-thing there is to know about the individ-ual’s preferences.

BUDGET CONSTRAINT Basic setup. Suppose that marshmallows ( M ) cost 3 cents apiece, donuts ( D ) cost

6 cents, and Oscar’s weekly income is 60 cents. What options does Oscar have? Whatever amounts he purchases must satisfy the equation

3 3 M 1 6 3 D 5 60. ( IC1.1 )

In words, expenditures on marshmallows (3 3 M ) plus expenditures on donuts (6 3 D ) must equal income (60). 6 Thus, for example, if M 5 10, then to satisfy Equation (IC1.1) , D must equal 5 (3 3 10 1 6 3 5 5 60). Alternatively, if M 5 8, then D must equal 6 (3 3 8 1 6 36 5 60). Let us represent Equation (IC1.1) graphically. The usual way is to graph a number of points that satisfy the equation. This is straightforward once we recall from basic algebra that (IC1.1) is just the equation of a straight line. Given two points on the line, the rest of the line is deter-mined by connecting them. In Figure IC1.11 , point r represents 10 marshmallows and 5 donuts, and point s represents 8 marshmallows and 6 donuts. Therefore, the line associated with Equa-tion (IC1.1) is LN, which passes through these points. By construction, any combination of marshmallows and donuts that lies along LN satisfies Equation (IC1.1) . Line LN is known as the budget constraint or the budget line. Any point on or below LN (the shaded area) is fea-sible because it involves an expenditure less than or equal to income. Any point above LN is impossible because it involves an expenditure greater than income. Two aspects of line LN are worth noting. First, the horizontal and vertical intercepts of the line have economic interpretations. By definition, the vertical intercept is the point associated with D 5 0. At this point, Oscar spends all his 60 cents on marshmallows, buying 20 (5 60 4 3) of them. Hence, distance OL is 20. Similarly, at point N, Oscar consumes zero marshmallows, but can afford a binge consisting of 10 (5 60 4 6) donuts. Distance ON is therefore 10. In short, the vertical and horizontal intercepts represent bundles in which Oscar consumes only one of the commodities. The slope also has an economic interpretation. To calculate the slope, recall that the “rise” (OL) is 20 and the “run” (ON) is 10, so the slope (in absolute value) is 2. Note that 2 is the ratio of the price of donuts (6 cents) to the price of marshmallows (3 cents). This is no accident. The absolute value of the slope of the budget line indicates the rate at which the market permits an individual to substitute marshmallows for donuts. Because the price of donuts is twice the price of marshmallows, Oscar can trade two marshmallows for each donut.

6 If Oscar is a utility maximizer, he will not throw away any of his income.

FIGURE IC1.11 Budget Constraint

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To generalize this discussion, suppose that the price per marshmallow is P m , the price per donut is P d, and income is I. Then in analogy to Equation (IC1.1) , the budget constraint is

PmM 1 PdD 5 I. ( IC1.2)

If M is measured on the vertical axis and D on the horizontal, the vertical intercept is I/P m and the horizontal intercept is I/P d . The slope of the budget constraint, in absolute value, is P d/ P m . A common mistake is to assume that because M is measured on the vertical axis, the absolute value of the slope of the budget constraint is P m /P d. To see that this is wrong just divide the rise (I/P m ) by the run ( I / P d ): ( I / P m ) 4 ( I / P d ) 5 P d / P m . Intuitively, P d must be in the numerator because its ratio to P m shows the rate at which the market permits one to trade M for D.

Changes in prices and income. The budget line shows Oscar’s consumption opportunities given his current income and the prevailing prices. What if any of these change? Return to the case where P m 5 3, P d 5 6, and I 5 60. The associated budget line, 3 M 1 6 D 5 60, is drawn as LN in Figure IC1.12 . Now suppose that Oscar’s income falls to 30. Substituting into Equation (IC1.2) ,

the new budget line is described by 3 M 1 6 D 5 30. To graph this equation, note that the vertical intercept is 10 and the horizon-tal intercept is 5. Denoting these two points in Figure IC1.12 as R and S, respectively, and recalling that two points determine a line, we find that the new budget con-straint is RS. The slope of RS in absolute value is 2, just like that of LN. This is because the relative prices of donuts and marshmallows have not changed. When income changes but relative prices do not, a parallel shift in the budget line is induced. If income decreases, the constraint shifts in; if income increases, it shifts out.

Return again to the original con-straint, 3 M 1 6 D 5 60, which is repro-duced in Figure IC1.13 as LN. Suppose that the price of D increases to 12, but everything else stays the same. Then by Equation (IC1.2) , the relevant budget con-straint is 3 M 1 12 D 5 60. To graph this new constraint, we begin by noting that it has a vertical intercept of 20, which is the same as that of LN. Because the price of M has stayed the same, if Oscar spends all his money only on M, then he can buy just as much as he did before. The horizontal intercept, how-ever, is changed. It is now at five donuts (5 60 4 12), a point denoted T in Figure IC1.13 . The new budget con-straint is then LT. The slope of LT in abso-lute value is 4 (5 20 4 5), reflecting the fact that the market now allows each indi-vidual to trade four marshmallows per donut.

FIGURE IC1.12 Effect on the

Budget Constraint

of a Decrease in

Income

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FIGURE IC1.13 Effect on the

Budget Constraint

of a Change in

Relative Prices

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More generally, when the price of one commodity changes and other things stay the same, the budget line pivots along the axis of the good whose price changes. If the price goes up, the line pivots in; if the price goes down, the line pivots out.

EQUILIBRIUM The indifference map shows what Oscar wants to do; the budget constraint shows what he can do. To find out what Oscar actually does, they must be put together.

In Figure IC1.14 , we superimpose the indifference map from Figure IC1.10 onto budget line LN from Figure IC1.11 . The problem is to find the combination of

M and D that maximizes Oscar’s utility subject to the constraint that he cannot spend more than his income. Consider first bundle i on U 2 U 2 . This bundle is ruled out, because it is above LN. Oscar might like to be on indifference curve U 2 U 2 , but he simply cannot afford it. Next consider point ii, which is certainly feasible, because it lies below the budget constraint. But it cannot be optimal, because Oscar is not spending his whole income. In effect, at bundle ii, he just throws away money that could have been spent on more marshmallows and/or donuts. What about point iii ? It is feasible, and Oscar is not throwing away any income. Yet he can still do better in the sense of putting himself on a higher indifference curve. Consider point E 1 , where Oscar consumes D 1 donuts and M 1 marshmallows. Because it lies on LN, it is feasible. Moreover, it is more desirable than bundle iii, because E 1 lies on U 1 U 1, which is above U 0 U 0 .Indeed, no point on LN touches an indifference curve that is higher than U 1 U 1 . Therefore, the bundle consisting of M 1 and D 1 maximizes Oscar’s utility subject to budget constraint LN. E 1is an equilibrium because unless something else in the system changes, Oscar will continue to consume M 1 marshmallows and D 1 donuts day after day. Note that at the equilibrium, indifference curve U 1 U 1 just barely touches the budget line. Intuitively, this is because Oscar is trying to achieve the very highest indifference curve he can while still keeping on LN. In more technical language, line LN is tangent to curve U 1 U 1 at point E 1 . This means that at point E 1 the slope of U 1 U 1 is equal to the slope of LN . This observation suggests an equation to characterize the point of utility maximization. Recall that by definition, the slope of the indifference curve (in absolute value) is the marginal rate of substitution of donuts for marshmallows, MRS dm . The slope of the budget line (in abso-lute value) is P d /P m . But we just showed that at equilibrium, the two slopes are equal, or

MRSdm 5 Pd /Pm. (IC1.3)

Equation (IC1.3) is a necessary condition for utility maximization. 7 That is, if the consump-tion bundle is not consistent with Equation (IC1.3) , then Oscar could do better by reallocating his income between the two commodities. Intuitively, MRS dm is the rate at which Oscar is willing to trade M for D, while P d / P m is the rate at which the market allows Oscar to trade M for D . At equilibrium, these two rates must be equal.

FIGURE IC1.14 Utility

Maximization

Subject to a

Budget Constraint

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7 The equation holds only if some of each commodity is consumed. If the consumption of some commodity is zero, then Equation (IC1.3) need not be satisfied.


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Now let us suppose that the price of marsh-mallows falls by some amount. Figure IC1.15 reproduces the equilibrium point E 1 from Fig-ure IC1.14 . As we showed earlier, when a price changes (ceteris paribus) the budget line pivots along the axis of the good whose price has changed. Because P m falls, the budget line LNpivots around N to a point that is higher on the vertical axis. The new budget line is VN . Given that Oscar now faces budget line VN, E 1 is no longer an equilibrium. The fall in P m creates new opportunities for Oscar, and utility maxi-mization requires that he take advantage of them. Specifically, subject to budget line VN , Oscar maximizes utility at point E 2 , where he consumes M 2 marshmallows and D 2 donuts.

At the new equilibrium, the amounts of both D and M increase relative to the amounts consumed at the old equilibrium (D 2 . D 1 and M 2 . M 1 ) . In effect, the price decrease in marshmallows allows Oscar to purchase more marshmallows and still have money left to purchase more donuts. While this is common, it need not always be the case. The change depends on the tastes of the particular indi-vidual. Suppose that Bert faces exactly the same prices as Oscar and also has the same income. Bert’s indifference map and budget constraints are depicted in Figure IC1.16 . For Bert, donut consumption is totally unchanged by the decrease in the price of marshmallows. On the other hand, Ernie’s preferences, depicted in Figure IC1.17 , are such that a fall in P m leaves the amount of marshmallows the same, and only the amount of donuts increases. Thus, without information about the individ-

ual’s indifference map, we cannot predict just how he or she will respond to a change in relative prices.

More generally, a change in prices and/or income changes the position of the budget con-straint. The individual then reoptimizes —finds the point that maximizes utility subject to the new budget constraint. This usually involves the selection of a new commodity bundle, but without information on the individual’s tastes, one cannot know for sure exactly what the new bundle looks like. We do know, however, that as long as the individual is a utility maximizer, the new bundle satisfies the condition that the price ratio equal the marginal rate of substitution.

DERIVATION OF DEMAND CURVES There is a simple connection between the theory of consumer choice and individual demand curves. Recall from Figure IC1.15 that at the original price of marshmallows—call it P m1 —Oscar consumed M 1 marshmallows. When the price fell to P m

2 , Oscar increased his marsh-mallow consumption to M 2 . This pair of points may be plotted as in Figure IC1.18 .

FIGURE IC1.15 Effect on

Equilibrium of a

Change in Relative

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FIGURE IC1.16 Change in Relative

Prices with No

Effect on Donut

Consumption


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Repeating this experiment for various prices of marshmallows, we find the quantity of marshmallows demanded at each price, holding fixed money income, the price of donuts, and tastes. By definition, this is the demand curve for marshmallows, shown as D m in Figure IC1.18 . Thus, we see how the demand curve is derived from the underlying indifference map.

SUBSTITUTION AND INCOME EFFECTS Figure IC1.19 depicts the situation of Grover, who initially faces budget constraint WN, and maximizes utility at point E 1 on indifference curve i, where he consumes D 1 donuts. Sup-pose now that the price of donuts increases.

Grover’s budget constraint pivots from WN to WZ, and at the new equilibrium, point E 2 on indifference curve ii, he consumes D 2 donuts. Just for hypothetical purposes, suppose that at the new equilibrium E 2 , the price of donuts falls back to its initial level, but that simultaneously, Grover’s income is adjusted so that he is kept on indifference curve ii . If this hypothetical adjustment were made, what budget constraint would Grover face? Suppose we call this budget constraint XY . We know that XY must satisfy two conditions:

• Because Grover is kept on indifference curve ii, XY must be tangent to indifference curve ii. • The slope (in absolute value) must be equal to the ratio of the original price of donuts to

the price of marshmallows. This is because of the stipulation that the price of donuts is at its original value. Recall, however, that the slope of WN is the ratio of the original price of donuts to the price of marshmallows. Hence, XY must have the same slope as WN; that is, it must be parallel to WN.

In Figure IC1.19 , XY is drawn to sat-isfy these two conditions—the line is parallel to WN and is tangent to indif-ference curve ii. If Grover were con-fronted with constraint XY, he would maximize utility at point E c, where his consumption of donuts is D c.

Why should this hypothetical budget line be of any interest? Because drawing line XY helps us break down the effect of the change in the price of donuts into two components, the first from E 1 to E c , and the second from E c to E 2 .

1. The movement from E 1 to E c is generated by the parallel shift of WN down to XY. But recall from Figure IC1.12 that such parallel

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D2

M1 = M2E2E1

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FIGURE IC1.17 Change in Relative

Prices with No

Effect on

Marshmallow

Consumption

Pric

e pe

r mar

shm

allo

w (P

m)

Marshmallows per day

O M1 M2

Pm1

Pm2

Dm

FIGURE IC1.18 Demand Curve for

Marshmallows

Derived from an

Indifference Map


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movements are associated with changes in income, holding rela-tive prices constant. Hence, the movement from E 1 to E c is in effect due to a change in income, and is called the income effect of the price change.

2. The movement from E c to E 2 is a consequence purely of the change in the relative price of donuts to marsh-mallows. This movement shows that Grover substitutes marshmallows for donuts when donuts become more expensive. Hence, the movement from E c to E 2 is called the substitu-tion effect. Since the movement from E c to E 2 involves compensating income (in the sense of changing income to stay on the same indif-ference curve), the movement from

E c to E 2 is sometimes called the compensated response to a change in price. If we wish to keep utility at the level represented by indifference curve ii, we measure the substitution effect by moving along ii. If, alternatively, we had wanted to keep utility at the level enjoyed along indifference curve i, we could have measured the substitution effect along indifference curve iinstead. In any case, the compensated response to a price change shows how the price change affects quantity demanded when income is simultaneously altered so that the level of utility is unchanged.

Intuitively, when the price of donuts increases two things happen:

• The increase in price reduces the individual’s real income—his or her ability to afford com-modities. When income goes down, the quantity purchased generally changes, even without any change in relative prices. This is the income effect.

• The increase in the price of donuts makes donuts less attractive relative to marshmallows, inducing the substitution effect.

Any change in prices can be broken down into an income effect and a substitution effect. We could repeat the exercise depicted in Figure IC1.19 for any change in the price of marshmallows. Suppose that for each price, we find the compensated quantity of donuts demanded and make a plot with price on the vertical axis and donuts on the horizontal. This plot is called the compensated demand curve for donuts. Note that the ordinary demand curve discussed at the beginning of this appendix shows how quantity demanded varies with price, holding I fixed, where I is income measured in dollars. In contrast, the compensated demand curve shows how quantity demanded varies with price, holding the level of utility fixed.

MARGINAL ANALYSIS IN ECONOMICS In economics, the word marginal usually means additional or incremental . Suppose, for example, the annual total benefit per citizen of a 50-kilometre road is $42, and the annual total benefit of a 51-kilometre road is $43.50. Then the marginal benefit of the 51st kilometre is $1.50 ($43.50 − $42.00). Similarly, if the annual total cost per person of maintaining a 50-kilometre

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Substitutioneffect

Incomeeffect

O D2 D1

M1

M2

Dc

McEc

W

Z

X

Y N

E2

E1

iii

FIGURE IC1.19 Substitution and

Income Effects of

a Price Change


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road is $38, and the total cost of a 51-kilometre road is $40, then the marginal cost of the 51st kilometre is $2. Economists focus a lot of attention on marginal quantities because they usually convey the information required for rational decision making. Suppose that the government is trying to decide whether to construct the 51st kilometre. The key question is whether the marginal ben-efit is at least as great as the marginal cost. In our example, the marginal cost is $2 while the marginal benefit is only $1.50. Does it make sense to spend $2 to create $1.50 worth of benefits? The answer is no, and the extra kilometre should not be built. Note that basing the decision on total benefits and costs would have led to the wrong answer. The total cost per person of the 51-kilometre road ($40) is less than the total benefit ($43.50). Still, it is not sensible to build the 51st kilometre. An activity should be pursued only if its marginal benefit is at least as large as its marginal cost. 8 Another example of marginal analysis: Farmer McGregor has two fields. The first is planted in wheat and the second in corn. McGregor has seven tons of fertilizer to distribute between the two fields and wants to allocate the fertilizer so that his total profits are as high as possible. The relationship between the amount of fertilizer and total profitability for each crop is depicted in Table IC1.1 . Thus, for example, if six tons of fertilizer were devoted to wheat and one ton to corn, total profits would be $503 (5 $178 1 $325). To find the optimal allocation of fertilizer between the fields, it is useful to compute the marginal contribution to profits made by each ton of fertilizer. The first ton in the wheat field increases profits from $0 to $100, so the marginal contribution is $100. The second ton increases profits from $100 to $150, so its marginal contribution is $50. The complete set of computations for both crops is recorded in Table IC1.2 .

8 If the marginal cost of an action just equals its marginal benefit, one is indifferent between taking the action and not taking it.

TABLE IC1.1 Total Profit

Tons of Fertilizer Wheat Corn 0 $ 0 $ 0 1 100 325 2 150 385 3 170 415 4 175 435 5 177 441 6 178 444

TABLE IC1.2 Marginal Profit

Tons of Fertilizer Wheat Corn 1 $100 $325 2 50 60 3 20 30 4 5 20 5 2 6 6 1 3


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Suppose that McGregor puts two tons of fertilizer on the wheat field and five tons on the corn field. Is this a profit-maximizing allocation? To answer this question, we must determine whether any other allocation would lead to higher total profits. Suppose that one ton of fertil-izer were removed from the corn field and devoted instead to wheat. As a consequence of removing the fertilizer from the corn field, profits from corn would go down by $6. But at the same time, profits from the wheat field would increase by $20 (the marginal profit associated with the third ton of fertilizer in the wheat field). Farmer McGregor would therefore be $14 richer on balance. Clearly, it is not sensible for McGregor to put two tons of fertilizer on the wheat field and five tons on the corn, because he can do better (by $14) with three tons devoted to wheat and four to corn. Is this latter allocation optimal? To answer, note that at this allocation, the marginal profit of fertilizer in each field is equal to $20. When the marginal profitability of fertilizer is the same in each field, there is no way that fertilizer can be reallocated between fields to increase total profit. In other words, total profits are maximized when the marginal profit in each field is the same. Readers who are skeptical of this result should try to find an allocation of the seven tons of fertilizer such that the total profit is higher than the $605 ($170 1 $435) associated with the allocation at which the marginal profits are equal. In general, if resources are being distributed across several activities, maximization of total returns requires that marginal returns in each activity be equal. 9

9 More precisely, this result requires that the marginal returns be diminishing, as they are in Table IC1.2 . In most applications, this is a reasonable assumption.


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microeconomics background for the study of public finance

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