The Theory of Consumer Choice This chapter covers topics considered advanced for the typical principles course: budget constraints, indifference curves, household optimization, and the income and substitution effects of price changes. Most students find it more difficult than average. The first half of the chapter develops the theory. The second half applies the theory to three consumer choice problems: 1) Giffen goods and positively-sloped demand curves 2) The labor-leisure choice 3) The effects of interest rates on household saving New for 2008/2009: The first half of this PowerPoint chapter uses a different example than the text, with different numerical values. (The applications in the second half are as in the textbook.)

In this chapter, look for the answers to these questions: How does the budget constraint represent the choices a consumer can afford? How do indifference curves represent the consumer’s preferences? What determines how a consumer divides her resources between two goods? How does the theory of consumer choice explain decisions such as how much a consumer saves, or how much labor she supplies? 1

Introduction Recall one of the Ten Principles from Chapter 1: People face tradeoffs. Buying more of one good leaves less income to buy other goods. Working more hours means more income and more consumption, but less leisure time. Reducing saving allows more consumption today but reduces future consumption. This chapter explores how consumers make choices like these. THE THEORY OF CONSUMER CHOICE 2

THE THEORY OF CONSUMER CHOICE

Consumer Theory Assumes buyers are completely informed about: Range of products available Prices of all products Capacity of products to satisfy Their income Requires that consumers can rank all consumption bundles based on the level of satisfaction they would receive from consuming the various bundles

Properties of Consumer Preferences Completeness For every pair of consumption bundles, A and B, the consumer can say one of the following: A is preferred to B B is preferred to A The consumer is indifferent between A and B Transitivity If A is preferred to B, and B is preferred to C, then A must be preferred to C Nonsatiation More of a good is always preferred to less

Utility Benefits consumers obtain from goods & services they consume is utility A utility function shows an individual’s perception of the utility level attained from consuming each conceivable bundle of goods

Marginal Utility Addition to total utility attributable to the addition of one unit of a good to the current rate of consumption, holding constant the amounts of all other goods consumed

Consumer’s Budget Line Shows all possible commodity bundles that can be purchased at given prices with a fixed money income

Shifting Budget Lines (Figure 5.7) 120 240 A Panel B – Changes in price of X 200 100 A B 100 250 D 125 C F Z 80 160 Quantity of Y Quantity of Y B 200 Quantity of X Quantity of X Panel A – Changes in money income

Utility Maximization Utility maximization subject to a limited money income occurs at the combination of goods for which the indifference curve is just tangent to the budget line

Utility Maximization Consumer allocates income so that the marginal utility per dollar spent on each good is the same for all commodities purchased

Constrained Utility Maximization (Figure 5.8) 50 A • I • E III • D IV 45 Quantity of pizzas C • B II R T 40 30 20 15 10 10 20 30 40 50 60 70 80 90 100 Quantity of burgers

Marginal Rate of Substitution MRS shows the rate at which one good can be substituted for another while keeping utility constant Negative of the slope of the indifference curve Diminishes along the indifference curve as X increases & Y decreases Ratio of the marginal utilities of the goods

The Budget Constraint: What the Consumer Can Afford Example: Hurley divides his income between two goods: fish and mangos. A “consumption bundle” is a particular combination of the goods, e.g., 40 fish & 300 mangos. Budget constraint: the limit on the consumption bundles that a consumer can afford The two-good assumption greatly simplifies the analysis without altering the basic insights about consumer choice. If your students remember the Production Possibilities Frontier, you might tell them that a budget constraint is, in essence, a “consumption possibilities frontier” for the consumer: it shows all combinations (bundles) of the two goods that the consumer can afford to buy. THE THEORY OF CONSUMER CHOICE 14

A C T I V E L E A R N I N G 1 Budget Constraint Hurley’s income: $1200 Prices: PF = $4 per fish, PM = $1 per mango A. If Hurley spends all his income on fish, how many fish does he buy? B. If Hurley spends all his income on mangos, how many mangos does he buy? C. If Hurley buys 100 fish, how many mangos can he buy? D. Plot each of the bundles from parts A – C on a graph that measures fish on the horizontal axis and mangos on the vertical, connect the dots. A very straightforward exercise. 15

A C T I V E L E A R N I N G 1 Answers D. Hurley’s budget constraint shows the bundles he can afford. Quantity of Mangos B A. $1200/$4 = 300 fish B. $1200/$1 = 1200 mangos C. 100 fish cost $400, $800 left buys 800 mangos C A Quantity of Fish

The Slope of the Budget Constraint From C to D, “rise” = –200 mangos “run” = +50 fish Slope = – 4 Hurley must give up 4 mangos to get one fish. Quantity of Mangos C D Quantity of Fish THE THEORY OF CONSUMER CHOICE

The Slope of the Budget Constraint The slope of the budget constraint equals the rate at which Hurley can trade mangos for fish the opportunity cost of fish in terms of mangos the relative price of fish: THE THEORY OF CONSUMER CHOICE 18

A C T I V E L E A R N I N G 2 Budget constraint, continued. Show what happens to Hurley’s budget constraint if: A. His income falls to $800. B. The price of mangos rises to PM = $2 per mango Another straightforward problem that will not take much class time. Yet, students will learn these concepts better by figuring out for themselves how the budget line moves in response to income and price changes. 19

A C T I V E L E A R N I N G 2 Answers, part A A fall in income shifts the budget constraint down. Quantity of Mangos Now, Hurley can buy $800/$4 = 200 fish or $800/$1 = 800 mangos or any combination in between. Quantity of Fish

A C T I V E L E A R N I N G 2 Answers, part B An increase in the price of one good pivots the budget constraint inward. Hurley can still buy 300 fish. But now he can only buy $1200/$2 = 600 mangos. Notice: slope is smaller, relative price of fish is now only 2 mangos. Quantity of Mangos Quantity of Fish

Preferences: What the Consumer Wants Indifference curve: shows consumption bundles that give the consumer the same level of satisfaction One of Hurley’s indifference curves Quantity of Mangos I1 B A, B, and all other bundles on I1 make Hurley equally happy – he is indifferent between them. A Quantity of Fish THE THEORY OF CONSUMER CHOICE

Four Properties of Indifference Curves One of Hurley’s indifference curves Quantity of Mangos 1. Indifference curves are downward-sloping. If the quantity of fish is reduced, the quantity of mangos must be increased to keep Hurley equally happy. B A I1 Quantity of Fish THE THEORY OF CONSUMER CHOICE

Four Properties of Indifference Curves A few of Hurley’s indifference curves Quantity of Mangos 2. Higher indifference curves are preferred to lower ones. I2 I1 Hurley prefers every bundle on I2 (like C) to every bundle on I1 (like A). I0 C D A He prefers every bundle on I1 (like A) to every bundle on I0 (like D). Quantity of Fish THE THEORY OF CONSUMER CHOICE

Four Properties of Indifference Curves Hurley’s indifference curves Quantity of Mangos 3. Indifference curves cannot cross. Suppose they did. Hurley should prefer B to C, since B has more of both goods. Yet, Hurley is indifferent between B and C: He likes C as much as A (both are on I4). He likes A as much as B (both are on I1). B C I4 A I1 Quantity of Fish THE THEORY OF CONSUMER CHOICE

Four Properties of Indifference Curves Quantity of Fish Quantity of Mangos 4. Indifference curves are bowed inward. A Hurley is willing to give up more mangos for a fish if he has few fish (A) than if he has many (B). 6 1 B Hurley has more fish at B than at A, so an extra fish would be less valuable at B than at A. 2 1 I1 THE THEORY OF CONSUMER CHOICE

The Marginal Rate of Substitution MRS = slope of indifference curve Marginal rate of substitution (MRS): the rate at which a consumer is willing to trade one good for another. Quantity of Fish Quantity of Mangos A MRS = 6 Hurley’s MRS is the amount of mangos he would substitute for another fish. 1 B At A, Hurley has few fish, so an additional fish is very valuable to him. At B, Hurley already has lots of fish, so an additional one is not as valuable to him. MRS = 2 1 I1 MRS falls as you move down along an indifference curve. THE THEORY OF CONSUMER CHOICE

One Extreme Case: Perfect Substitutes Perfect substitutes: two goods with straight-line indifference curves, constant MRS Example: nickels & dimes Consumer is always willing to trade two nickels for one dime. It is hard to think of examples of perfect substitutes. (Even nickels and dimes are probably not perfect substitutes: I’d rather carry 10 dimes in my pocket than 20 nickels.) But it’s easy to think of examples that are close substitutes, and therefore are likely to have indifference curves that are not very bowed: 1) Movies (at the movie theater) and videos at home. A consumer might be willing to trade two videos for one night at the movies. 2) Coke and Pepsi (for consumers that do not perceive much difference between them). 3) Vacations in Hawaii and vacations in the Bahamas THE THEORY OF CONSUMER CHOICE 28

Another Extreme Case: Perfect Complements Perfect complements: two goods with right-angle indifference curves Example: Left shoes, right shoes {7 left shoes, 5 right shoes} is just as good as {5 left shoes, 5 right shoes} Again, It is hard to think of examples of perfect complements. But it’s easy to think of examples that are good though not perfect complements, and therefore are likely to have indifference curves that are very bowed: 1) Tickets to rock concerts and parking at the arena in which the concert takes place 2) Hot dogs and hot-dog buns 3) Brewed Starbucks coffee and 20 spoons of sugar (If you don’t get this one, you probably haven’t tried brewed Starbucks coffee!) THE THEORY OF CONSUMER CHOICE 29

Less Extreme Cases: Close Substitutes and Close Complements Indifference curves for close substitutes are not very bowed Indifference curves for close complements are very bowed Quantity of hot dog buns Quantity of Pepsi When the two goods are close but not perfect substitutes (like Coke and Pepsi), indifference curves are slightly bowed. When the two goods are close but not perfect complements (like hot dogs and buns), indifference curves are very bowed, having a very sharp (but not quite 90-degree) angle. Later in this PowerPoint chapter, an Active Learning exercise asks students to illustrate the substitution effect for these two cases. They will see that a relative price change causes a much bigger movement along an indifference curve when the goods are substitutes than when they are complements. Quantity of Coke Quantity of hot dogs

Optimization: What the Consumer Chooses A is the optimum: the point on the budget constraint that touches the highest possible indifference curve. Quantity of Mangos The optimum is the bundle Hurley most prefers out of all the bundles he can afford. 1200 Hurley prefers B to A, but he cannot afford B. B A 600 Simply put, optimization means buying the bundle that makes the consumer happiest, given his or her income. Hurley can afford C and D, but A is on a higher indifference curve. C D 150 300 Quantity of Fish THE THEORY OF CONSUMER CHOICE

Optimization: What the Consumer Chooses Quantity of Mangos Consumer optimization is another example of “thinking at the margin.” At the optimum, slope of the indifference curve equals slope of the budget constraint: 1200 MRS = PF/PM A 600 marginal value of fish (in terms of mangos) price of fish (in terms of mangos) Consumer optimization is another example of “thinking at the margin.” Remember that MRS = marginal value of the good on the X-axis (fish) in terms of the good on Y-axis (mangos). If MRS > Pf/Pm, the value of another fish is greater than its cost, so Hurley can make himself happier by decreasing his mango purchases and using the proceeds to buy another fish. If MRS < Pf/Pm, the value of another fish is less than its cost, so Hurley should move along his budget line to a bundle with less fish and more mangos to make himself happier. 150 300 Quantity of Fish THE THEORY OF CONSUMER CHOICE

The Effects of an Increase in Income Quantity of Mangos An increase in income shifts the budget constraint outward. B If both goods are “normal,” Hurley buys more of each. A In Active Learning 2, students determined that a fall in income shifts the budget constraint downward. They should readily accept, then, that an increase in income shifts the budget line upward/outward. Quantity of Fish THE THEORY OF CONSUMER CHOICE

A C T I V E L E A R N I N G 3 Inferior vs. normal goods An increase in income increases the quantity demanded of normal goods and reduces the quantity demanded of inferior goods. Suppose fish is a normal good but mangos are an inferior good. Use a diagram to show the effects of an increase in income on Hurley’s optimal bundle of fish and mangos. Instead of merely showing students the diagram for the case where one of the goods is inferior, let’s just remind them of the definition and see if they can figure out how to draw the diagram. 34

A C T I V E L E A R N I N G 3 Answers Quantity of Mangos If mangos are inferior, the new optimum will contain fewer mangos. B A Quantity of Fish 35

The Effects of a Price Change Initially, PF = $4 PM = $1 Quantity of Mangos 1200 600 initial optimum PF falls to $2 budget constraint rotates outward, Hurley buys more fish and fewer mangos. new optimum 600 500 350 In Active Learning 2, students determined that an increase in the price of a good pivots the budget constraint inward. Here, the price of a good is falling, so the budget line pivots outward. 150 300 Quantity of Fish THE THEORY OF CONSUMER CHOICE

The Income and Substitution Effects A fall in the price of fish has two effects on Hurley’s optimal consumption of both goods. Income effect A fall in PF boosts the purchasing power of Hurley’s income, allows him to buy more mangos and more fish. Substitution effect A fall in PF makes mangos more expensive relative to fish, causes Hurley to buy fewer mangos & more fish. Notice: The net effect on mangos is ambiguous. On the previous slide, the fall in the price of fish caused a net decrease in Hurley’s demand for mangos: the substitution effect is greater than the income effect, as depicted on the following slide. However, it could have gone the other way: if the income effect were greater than the substitution effect, then Hurley’s demand for mangos would have risen. THE THEORY OF CONSUMER CHOICE 37

The Income and Substitution Effects Initial optimum at A. PF falls. Substitution effect: from A to B, buy more fish and fewer mangos. Income effect: from B to C, buy more of both goods. Quantity of Mangos In this example, the net effect on mangos is negative. A C This diagram decomposes the movement from the old optimum (A) to the new one (C) into two parts. The first part, from A to B, represents the substitution effect. It shows the change in the optimal bundle due to the relative price change, holding constant the consumer’s level of well-being. The second part, from B to C, represents the income effect. It shows the change in the optimal bundle due to the increase in the purchasing power of the consumer’s income. The dashed line through point B is parallel to the new budget line through point C, indicating that we are holding relative prices constant to see how the increase in income affects the optimal bundle. B Quantity of Fish THE THEORY OF CONSUMER CHOICE

Substitution & Income Effects Substitution effect Change in consumption of a good after a change in its price, when the consumer is forced by a change in money income to consume at some point on the original indifference curve Income effect Change in consumption of a good resulting strictly from a change in purchasing power

Income & Substitution Effects: A Decrease in Px (Figure 5.12) Total effect of price decrease = Substitution effect + Income effect 9 5 4 Total effect of price decrease = Substitution effect + Income effect 3 5 (-2)

Application 1: Giffen Goods Do all goods obey the Law of Demand? Suppose the goods are potatoes and meat, and potatoes are an inferior good. If price of potatoes rises, substitution effect: buy less potatoes income effect: buy more potatoes If income effect > substitution effect, then potatoes are a Giffen good, a good for which an increase in price raises the quantity demanded. THE THEORY OF CONSUMER CHOICE 41

Application 1: Giffen Goods An increase in the price of potatoes rotates the budget line inward. The substitution effect would cause the consumer to buy fewer potatoes. Imagine moving down along indifference curve I1 until reaching the point where its slope just equals the slope of the new budget line. At that point, demand for potatoes is lower, because consumers are substituting meat for potatoes. But if potatoes are an inferior good, the income effect causes demand for potatoes to rise: the price increase makes the consumer generally worse off. The consumer responds by buying less meat (the normal good) and more potatoes (the inferior good). If potatoes are a Giffen good, the income effect exceeds the substitution effect, so the net effect of a price increase on demand for potatoes is positive!!! As the book notes, Giffen goods are extremely rare – if they exist at all! THE THEORY OF CONSUMER CHOICE 42

Application 2: Wages and Labor Supply Budget constraint Shows a person’s tradeoff between consumption and leisure. Depends on how much time she has to divide between leisure and working. The relative price of an hour of leisure is the amount of consumption she could buy with an hour’s wages. Indifference curve Shows “bundles” of consumption and leisure that give her the same level of satisfaction. THE THEORY OF CONSUMER CHOICE 43

Application 2: Wages and Labor Supply At the optimum, the MRS between leisure and consumption equals the wage. Here, the marginal rate of substitution measures the marginal value of an hour of leisure, in terms of (dollars’ worth of) consumption. The slope of the budget line simply equals the wage: each additional hour of leisure requires working one fewer hour, which causes consumption to fall by an hour’s wages. At the optimum, the marginal value of leisure (in terms of consumption) must equal the relative price of leisure (in terms of consumption), or the wage. If MRS > wage, then the value of leisure is greater than its price, so take more leisure (and work fewer hours) to raise happiness. If MRS < wage, then the value of leisure is less than its price, so take less leisure (and work more hours) to raise happiness. THE THEORY OF CONSUMER CHOICE 44

Application 2: Wages and Labor Supply An increase in the wage has two effects on the optimal quantity of labor supplied. Substitution effect (SE): A higher wage makes leisure more expensive relative to consumption. The person chooses less leisure, i.e., increases quantity of labor supplied. Income effect (IE): With a higher wage, she can afford more of both “goods.” She chooses more leisure, i.e., reduces quantity of labor supplied. The relative magnitude of the substitution and income effects determine the slope of the labor supply curve, as the following slides show. THE THEORY OF CONSUMER CHOICE 45

Application 3: Interest Rates and Saving A person lives for two periods. Period 1: young, works, earns $100,000 consumption = $100,000 minus amount saved Period 2: old, retired consumption = saving from Period 1 plus interest earned on saving The interest rate determines the relative price of consumption when young in terms of consumption when old. Why the interest rate determines the relative price of current in terms of future consumption: If you reduce current consumption by $1, and save this $1, then your future consumption will rise by $(1 + r), where r denotes the interest rate. Similarly, if you wish to increase current consumption by $1, then you must sacrifice the $(1 + r) that you would have been able to consume in the future. Notice that the slide does not say “the interest rate equals the relative price…”. In fact, the relative price of current in terms of future consumption (and also the slope of the budget constraint) equals (1 + r), not r. THE THEORY OF CONSUMER CHOICE 46

Application 3: Interest Rates and Saving Budget constraint shown is for 10% interest rate. At the optimum, the MRS between current and future consumption equals the interest rate. The marginal rate of substitution is the marginal value of current consumption in terms of future consumption; it tells you how much future consumption the person is willing to give up for a unit of current consumption. If the consumer is optimizing, then the MRS must equal (1 + r): the marginal value of current consumption must equal the relative price of current consumption (both in terms of future consumption). If MRS were not equal to (1 + r), then the consumer could increase his satisfaction by changing his level of saving (and hence, his “bundle” of current and future consumption). THE THEORY OF CONSUMER CHOICE 47