# In this chapter, look for the answers to these questions:

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21 The Theory of Consumer Choice P R I N C I P L E S O F
F O U R T H E D I T I O N 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 is pure 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 This is a tough chapter for PowerPoint. It is loaded with complex graphs of household optimization. For the initial batch of PowerPoints released in Spring 2006, most of these graphs are not animated. I will be animating more of them when I prepare the annual update to be released in 2007.

In this chapter, look for the answers to these questions:
What determines how a consumer divides her resources between two goods (income, prices, and preferences!)? How does the theory of consumer choice explains the shape of demand curves and their changes? How does the theory of consumer choice explain decisions such as how much a consumer saves, or how much labor she supplies? CHAPTER THE THEORY OF CONSUMER CHOICE

The Budget Constraint: What the Consumer Can Afford
Two goods: pizza and Pepsi A “consumption bundle” is a particular combination of the goods, e.g., 40 pizzas & 300 pints of Pepsi. Budget constraint: the limit on the consumption bundles that a consumer can afford: For example: The consumer’s income: \$ Prices: \$10 per pizza, \$2 per pint of Pepsi 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. CHAPTER THE THEORY OF CONSUMER CHOICE

A C T I V E L E A R N I N G 1: Answers
D. The consumer’s budget constraint shows the bundles that the consumer can afford. Pepsis A. \$1000/\$10 = 100 pizzas B. \$1000/\$2 = 500 Pepsis C. \$400/\$10 = 40 pizzas \$600/\$2 = 300 Pepsis B C A Pizzas 3

The Slope of the Budget Constraint
Pepsis From C to D, “rise” = –100 Pepsis “run” = +20 pizzas Slope = –5 Consumer must give up 5 Pepsis to get another pizza. C D Pizzas CHAPTER THE THEORY OF CONSUMER CHOICE

The Slope of the Budget Constraint
The slope of the budget constraint equals the rate at which the consumer can trade Pepsi for pizza the opportunity cost of pizza in terms of Pepsi the relative price of pizza: CHAPTER THE THEORY OF CONSUMER CHOICE

A C T I V E L E A R N I N G 2: Exercise
Pepsis Show what happens to the budget constraint if: A. Income falls to \$800 B. The price of Pepsi rises to \$4/pint. Pizzas 6

A C T I V E L E A R N I N G 2A: Answers
Pepsis A fall in income shifts the budget constraint inward. Consumer can buy \$800/\$10 = 80 pizzas or \$800/\$2 = 400 Pepsis or any combination in between. Pizzas 7

A C T I V E L E A R N I N G 2B: Answers
An increase in the price of one good pivots the budget constraint inward. Pepsis Consumer can still buy 100 pizzas. But now, can only buy \$1000/\$4 = 250 Pepsis. Notice: slope is smaller, relative price of pizza now only 4 Pepsis. Pizzas 8

Preferences: What the Consumer Wants
Indifference curve: shows consumption bundles that give the consumer the same level of satisfaction Point out the following: The consumer is indifferent between bundles A, B, and C, because they are all on the same indifference curve. Bundle D is on a higher indifference curve, so it is preferred to A, B, and C. (MRS will be introduced on the following slide.) CHAPTER THE THEORY OF CONSUMER CHOICE

Properties of Indifference Curves
They are unique to each consumer, since preferences differ across consumers. A change in preferences is modeled as a shift/change in indifference curves. Indifference curves are downward sloping (for goods that are desirable). Indifference curves can not cross – a logical inconsistency. CHAPTER THE THEORY OF CONSUMER CHOICE

A Critical Dimension of Preferences: Marginal Rates of Substitution
Marginal rate of substitution (MRS): the rate at which a consumer is willing to trade one good for another Also, the slope of the indifference curve In this case, the MRS is the amount of Pepsi a consumer would be willing to give up to get one more pizza. In effect, the MRS is the marginal value of pizza – in terms of Pepsi. CHAPTER THE THEORY OF CONSUMER CHOICE

Marginal Rates of Substitution change with the mix of goods consumed.
Indifference curves are bowed inward. The less pizza the consumer has, the more Pepsi he is willing to trade for another pizza. The MRS measures the marginal value of the good on the horizontal axis, in terms of the good on the vertical axis. At point A, the consumer has 3 pizzas and 8 pints of Pepsi. The consumer is willing to give up a pizza to get 6 more pints of Pepsi. Thus, MRS = value of a pizza in terms of Pepsi = 6. At point B, the consumer has 7 pizzas and only 3 pints of Pepsi. The consumer only requires one more pint of Pepsi to make her willing to give up a pizza. Thus, MRS = value of a pizza in terms of Pepsi = 1. Why the difference? At point B, she has lots of pizza and not much Pepsi. At point A, she has lots of Pepsi and not much pizza. Thus, at the margin, pizza is more valuable relative to Pepsi at point B (when she has little pizza) than at point A (when she has lots of pizza). In general, as you move down along an indifference curve, you get more and more of the good on the horizontal axis, causing a fall in the marginal value of additional units of this good (in terms of the other good, which is getting scarcer). CHAPTER THE THEORY OF CONSUMER CHOICE

One Special 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. 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 CHAPTER THE THEORY OF CONSUMER CHOICE

Another Special Case: Perfect Complements
Perfect substitutes: 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 (Anyone who’s tried brewed Starbucks coffee, except the heartiest souls, will be able to relate to this example!) CHAPTER THE THEORY OF CONSUMER CHOICE

Optimization: What the Consumer Chooses
The optimal bundle is at the point where the budget constraint touches the highest indifference curve. MRS = relative price at the optimum: The indiff. curve and budget constraint have the same slope. The optimal bundle must satisfy this condition: MRS = relative price Intuition: The relative price is the price of an additional pizza in terms of Pepsi. The MRS is the marginal value of pizza in terms of Pepsi. At the margin, these must be equal; otherwise, a different bundle would make the consumer happier. Suppose, for example, that MRS > relative price. The value of an additional pizza is higher than the price of an additional pizza (in terms of Pepsi). Hence, the consumer would be better off buying more pizza and less Pepsi. Or, if MRS < relative price, then the value of the marginal pizza is smaller than its relative price. The consumer would be happier if she bought one fewer pizza and used the savings to buy more Pepsi. CHAPTER THE THEORY OF CONSUMER CHOICE

The Effects of an Increase in Income
In an earlier Active Learning exercise, students found that a decrease in income shifts the budget constraint inward. It should now be easy for them to understand that an increase in income shifts the budget line outward, as depicted here. With more income, the budget constraint is higher, and the consumer can reach a higher indifference curve. As depicted on this slide, the new optimal bundle has more of both goods, implying that both goods are normal goods. What if one of the goods is inferior? See the next slide…. CHAPTER 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 pizza is a normal good but Pepsi is an inferior good. Use a diagram to show the effects of an increase in income on the consumer’s optimal bundle of pizza and Pepsi. 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. 17

A C T I V E L E A R N I N G 3: Answers

The Effects of a Price Change
In an earlier Active Learning exercise, students found that an increase in the price of Pepsi causes the budget line to pivot inward. So it should now be easy for them to understand why a decrease in the price of Pepsi causes the budget line to pivot outward. In this example, the new optimal bundle has more Pepsi. This is what one would expect, since Pepsi is less expensive relative to pizza. The new optimal bundle also has less pizza. It’s a little less clear that this should be so, because the price change has two opposing effects on the demand for pizza, as discussed on the next slide. 19

The Income and Substitution Effects
A fall in the price of Pepsi has two effects on the optimal consumption of both goods. Income effect A fall in the price of Pepsi boosts the purchasing power of the consumer’s income, allowing him to reach a higher indifference curve. (shifting between indifference curves, constant prices.) Substitution effect A fall in the price of Pepsi makes pizza more expensive relative to Pepsi, causes consumer to buy less pizza & more Pepsi. (Moving along a particular indifference curve.) CHAPTER THE THEORY OF CONSUMER CHOICE

Income and Substitution Effects
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. 21

The Substitution Effect for Substitutes and Complements
The substitution effect is huge when the goods are very close substitutes. If Pepsi goes on sale, people who are nearly indifferent between Coke and Pepsi will buy mostly Pepsi. The substitution effect is tiny when goods are nearly perfect complements. If software becomes more expensive relative to computers, people are not likely to buy less software and use the savings to buy more computers. CHAPTER THE THEORY OF CONSUMER CHOICE

Deriving the Demand Curve for Pepsi
Left graph: price of Pepsi falls from \$2 to \$1 Right graph: Pepsi demand curve The left graph shows that the consumer will demand 250 pints of Pepsi when the price is \$2, and 750 pints when the price is \$1. The right graph plots these quantity-price combinations and draws the demand curve for Pepsi. CHAPTER THE THEORY OF CONSUMER CHOICE

Problem: what happens when both income and prices change?
For example: Your income increases 25%, while at the same time the price of pizzas increases by 20%. How do you alter your spending? You must shift the budget constraint – which is altered by both the increase in income (shift outward) and the price increase (which alters the slope). Are you better or worse off? Consider different preferences (indifference curves) and see if the new budget line leaves you necessarily better or worse off! CHAPTER THE THEORY OF CONSUMER CHOICE

My daughter Rebecca, at college
Dr. Straszheim sends his daughter \$90/week for entertainment. She always buys both movies and CD’s, though she spends most of her money on movies. (CE’s cost \$15, movies cost \$10.) Dr. Straszheim, missing his daughter, increases the payment to \$120/week. His daughter s back: “Thanks for the extra money. Unfortunately the price of CD’s has just increased by 50%, so I am doomed to be definitely worse off than before. … Could you please send more money?” CHAPTER THE THEORY OF CONSUMER CHOICE

Dr. Straszheim’s reply “In response to your regarding your change in well-being, and given our many conversations on consumer theory, I offer the following comments about your changed circumstances … Illustrate graphically and explain what might be said as to the validity of Rebecca’s statement that she is definitely worse off. CHAPTER THE THEORY OF CONSUMER CHOICE

Application: should I work, and how much?
Working is the typical source of income in a market economy. While many enjoy aspects of working, there are obvious ‘costs’ -- including the foregone leisure (and the opportunity to do something else). How do we model the decision to work? Would you work more or less if your wage were increased? What are the effects of gifts or inheritances? CHAPTER THE THEORY OF CONSUMER CHOICE

Application: 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 (and the opportunity cost) 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. CHAPTER THE THEORY OF CONSUMER CHOICE

The Optimal Labor Supply Decision
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. CHAPTER THE THEORY OF CONSUMER CHOICE

Explaining 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. CHAPTER THE THEORY OF CONSUMER CHOICE

Higher Wages increases Labor Supply
For this person, SE > IE So her labor supply increases with the wage A person with the preferences depicted in the left graph will have a positively-sloped labor supply curve, as shown in the right graph. CHAPTER THE THEORY OF CONSUMER CHOICE

Higher Wages lowers Labor Supply
For this person, SE < IE So his labor supply falls when the wage rises A person with the preferences depicted in the left graph will have a negatively-sloped labor supply curve, as shown in the right graph. CHAPTER THE THEORY OF CONSUMER CHOICE

Could This Happen in the Real World???
Cases where the income effect on labor supply is very strong: Over last 100 years, technological progress has increased labor demand and real wages. The average workweek fell from 6 to 5 days. When a person wins the lottery or receives an inheritance, his wage is unchanged – hence no substitution effect. But empirical evidence shows that such persons are more likely to work fewer hours, indicating a strong income effect. Typically, we assume the substitution effect is at least as big as the income effect, and we draw labor supply curves as upward-sloping or perhaps vertical. This slide notes examples from a case study in this chapter in which the income effect is very strong. I would add an additional possibility (not mentioned in the book): A person’s labor supply curve may slope upward for low wages, become steeper, and bend backward at high wages. Here’s why: The size of the substitution effect depends on a comparison of the wage to the marginal rate of substitution between leisure and consumption. The higher the wage relative to the MRS, the stronger the incentive to substitute away from leisure and toward consumption. As a person works more hours, consumption becomes more plentiful while leisure becomes dearer. The marginal value of leisure rises relative to consumption. I.e., the MRS rises as the person moves up an indifference curve. As this occurs, it takes increasingly large wage increases to make the person willing to sacrifice another hour of leisure. I.e., the substitution effect from a given increase in the wage gets weaker. Meanwhile, the income effect is as strong as ever – a person with very high wages can afford to take more time off than a person with lower wages. CHAPTER THE THEORY OF CONSUMER CHOICE

A counter example: Workaholics among professionals?
Over the last twenty years, the work week has lengthened for many high income professionals, especially in selected major cities. Working more hours at higher wages implies the substitution effect outweighs the income effect. Why is it difficult for the highly paid to ‘cut back’? Their “preferences/tastes” escalate with income. Keeping up with their peers in consumption. Saving for old age Enjoy satisfaction, challenge of demanding job. CHAPTER THE THEORY OF CONSUMER CHOICE

A father’s son works little, lives modestly
The son’s viewpoint: choices reflect my preferences, and my sense of what maximizes my well-being. The father think … Can I give my son some money but also encourage him to work harder (more)? An unrestricted gift? (e.g. \$20,000/year) A wage “supplement”? (I give him 50 cents for each dollar he earns.) More “restrictive” gifts? CHAPTER THE THEORY OF CONSUMER CHOICE

Application 2: 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. CHAPTER THE THEORY OF CONSUMER CHOICE

Application 2: 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). CHAPTER THE THEORY OF CONSUMER CHOICE

A C T I V E L E A R N I N G 5: Effects of an interest rate increase
Suppose the interest rate rises. Determine the income and substitution effects on current and future consumption, and on saving. This exercise gives students practice identifying and interpreting the income and substitution effects in a new context. 38

A C T I V E L E A R N I N G 5: Answers
The interest rate rises. Substitution effect – leads me to save more. Current consumption becomes more expensive relative to future consumption. Current consumption falls, saving rises, future consumption rises. Income effect Can afford more consumption in both the present and the future. Saving falls. After you display the full contents of the slide, point out that future consumption unambiguously rises. However, the effects on current consumption and saving depend on which of the income and substitution effects is bigger. The following slides show the two cases. 39

Application 2: Interest Rates and Saving
In this case, SE > IE and saving rises The macro chapters of Mankiw’s Principles of Economics typically assume that saving is positively related to the interest rate, as depicted here. CHAPTER THE THEORY OF CONSUMER CHOICE

Application 2: Interest Rates and Saving
In this case, SE < IE and saving falls If the income effect is bigger than the substitution effect, than an increase in the interest rate would reduce saving, not increase it. 41

CONCLUSION: Do People Really Think This Way?
Most people do not make spending decisions by writing down their budget constraints and indifference curves. Yet, they try to make the choices that maximize their satisfaction given their limited resources. The theory in this chapter is only intended as a metaphor for how consumers make decisions. It does fairly well at explaining consumer behavior in many situations, and provides the basis for more advanced economic analysis. CHAPTER THE THEORY OF CONSUMER CHOICE

CHAPTER SUMMARY A consumer’s budget constraint shows the possible combinations of different goods she can buy given her income and the prices of the goods. The slope of the budget constraint equals the relative price of the goods. An increase in income shifts the budget constraint outward. A change in the price of one of the goods pivots the budget constraint. CHAPTER THE THEORY OF CONSUMER CHOICE

CHAPTER SUMMARY A consumer’s indifference curves represent her preferences. An indifference curve shows all the bundles that give the consumer a certain level of happiness. The consumer prefers points on higher indifference curves to points on lower ones. The slope of an indifference curve at any point is the marginal rate of substitution – the rate at which the consumer is willing to trade one good for the other. CHAPTER THE THEORY OF CONSUMER CHOICE

CHAPTER SUMMARY The consumer optimizes by choosing the point on her budget constraint that lies on the highest indifference curve. At this point, the marginal rate of substitution equals the relative price of the two goods. When the price of a good falls, the impact on the consumer’s choices can be broken down into two effects, an income effect and a substitution effect. CHAPTER THE THEORY OF CONSUMER CHOICE

CHAPTER SUMMARY The income effect is the change in consumption that arises because a lower price makes the consumer better off. It is represented by a movement from a lower indifference curve to a higher one. The substitution effect is the change that arises because a price change encourages greater consumption of the good that has become relatively cheaper. It is represented by a movement along an indifference curve. CHAPTER THE THEORY OF CONSUMER CHOICE

CHAPTER SUMMARY The theory of consumer choice can be applied in many situations. It can explain why demand curves can potentially slope upward, why higher wages could either increase or decrease labor supply, and why higher interest rates could either increase or decrease saving. CHAPTER THE THEORY OF CONSUMER CHOICE

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