Professor Christina Romer LECTURE 6 CONSUMERS AND UTILITY MAXIMIZATION FEBRUARY 4, 2016

Transcription

1 Economics 2 Spring 2016 Professor Christina Romer Professor David Romer LECTURE 6 CONSUMERS AND UTILITY MAXIMIZATION FEBRUARY 4, 2016 I. THE BUDGET CONSTRAINT A. Description B. Diagram for the case of 2 goods C. What causes the budget constraint to change? 1. Changes in income 2. Changes in prices II. UTILITY MAXIMIZATION A. Utility and marginal utility B. Diminishing marginal utility C. The rule for utility maximization (the rational spending rule) III. WHY DEMAND CURVES SLOPE DOWN A. Substitution effect B. Income effect C. Marginal utility and the price elasticity of demand D. Individual and market demand curves IV. WHY DEMAND CURVES SHIFT A. A change in tastes B. A change in income C. A change in the price of a substitute or complement

2 Economics 2 Spring 2016 Christina Romer David Romer LECTURE 6 Consumers and Utility Maximization February 4, 2016

3 Announcements A detailed answer sheet to Problem Set 1 will be posted this evening. The Economics Department offers drop-in Econ 2 tutoring. Information about hours and locations is at tutoring. The Student Learning Center offers drop-in Econ 2 tutoring, M Th 1 5 PM in the SLC Atrium at Cesar Chavez Center. More information is at

4 I. BUDGET CONSTRAINTS

5 A Household s Budget Constraint In words: The total amount the household spends cannot exceed its income. In symbols: P a q a + P b q b + P c q c + + P z q z = Income, where the P s are the market prices of the various goods, and the q s are the quantities that the household buys.

6 The Case of Just Two Goods Symbols P food q food + P clothing q clothing = Income

7 The Case of Just Two Goods Diagram q food Budget constraint 0 0 q clothing

8 The Case of Just Two Goods Diagram q food Intercept = Income P f P c P f { { 1 Slope = P c P f Intercept = Income P c 0 0 q clothing

9 A Rise in Income q food Constraint 2 Constraint 1 q clothing

10 Grandmothers and Granddaughters by Esther Duflo The development that she focuses on: A shift in budget constraints. Specifically, a large expansion in old-age pensions in South Africa in the early 1990s. Affected some households but not others.

11 An Equal Percentage Rise in Both Prices q food Constraint 1 Constraint 2 q clothing

12 A Rise in the Price of Clothing q food Constraint 1 Constraint 2 q clothing

13 II. UTILITY MAXIMIZATION

14 Marginal Utility The extra utility derived from consuming one more unit of a good.

15 Diminishing Marginal Utility As a household consumes more of a good, the marginal utility of the good declines. Marginal Utility MU q

16 Diminishing Marginal Utility Total Utility Marginal Utility q q

17 A Little Bit of Calculus (Only for Those Who Are Interested!) Suppose U = f(q), where q is the quantity of some good (bananas, for example) a household consumes, and U is the total utility the household gets from consuming the good. Then MU = f'(q), where MU is marginal utility.

18 The Rule for Utility Maximization (the Rational Spending Rule) A household is doing the best that it can that is, it is maximizing its utility if: The marginal utility derived from spending one more dollar on a good is the same for all goods.

19 The Rule for Utility Maximization (the Rational Spending Rule) in Symbols MM a P a = MM b P b = = MM z P z, where the P s are the market prices of the different goods, and the MU s are the marginal utilities of an additional unit of the different goods.

20 The Rule for Utility Maximization with Just Two Goods Example 1 Clothing and food: MM cccccccc P cccccccc = MM ffff P ffff. Example 2 Blueberries and everything else: MM bbbbbbbbbbb P bbbbbbbbbbb = MM eeeeeeeeee eeee P eeeeeeeeee eeee.

21 III. WHY DEMAND CURVES SLOPE DOWN

22 A Rise in the Price of Clothing Suppose the household starts with: and that P clothing rises. MM cccccccc P cccccccc = MM ffff P ffff, If the household didn t change its purchases, MM cccccccc P cccccccc < MM ffff P ffff. So, the household needs to change the mix of its purchases toward less clothing (which raises MU clothing ) and more food (which lowers MU food ). This is the substitution effect of a price change.

23 A Rise in the Price of Clothing (cont.) Recall that a rise in the price of a good moves the budget constraint in. q food Constraint 2 Constraint1 This tends to make the household want to decrease its consumption of both goods. This is the income effect of a price change. q clothing

24 Why Demand Curves Slope Down Substitution effect: When the price of a good rises, households want less of the good and more of other goods, because the good is relatively more expensive. Income effect: When the price of a good rises, households tend to want less of all goods, because their budget constraint has changed for the worse.

25 The Household s Demand Curve for Clothing P clothing d q clothing

26 Marginal Utility and the Price Elasticity of Demand Good a Good b MU a MU b q a Demand likely to be quite inelastic q b Demand likely to be quite elastic

27 Individual and Market Demand Curves The total demand (or market demand) for a good at a given price is the sum of individual consumers demands. Because individuals demand curves (d) slope down, the market demand curve (D) slopes down.

28 IV. WHY DEMAND CURVES SHIFT

29 MU blueberries MU 2 A Positive Change in Tastes or Information MU 1 q blueberries

30 Restoring the Rational Spending Rule When There Is a Positive Change in Tastes If the household didn t change its purchases, MM bbbbbbbbbbb P bbbbbbbbbbb > MM eeeeeeeeee eeee P eeeeeeeeee eeee. So, the household changes the mix of its purchases toward more blueberries.

31 A Positive Change in Tastes or Information P blueberries d 1 d 2 q blueberries

32 A Rise in Income If the household didn t change its purchases, MM a would still hold. P a = MM b P b But the household isn t using all its income. So it can spend more on both good a (which lowers MU a ) and good b (which lowers MU b ).

33 A Rise in Income P a d 1 d 2 q a

34 Duflo, Grandmothers and Granddaughters

35 Marginal Utilities for Two Goods Grandmothers marg. utilities Grandfathers marg. utilities Food for grandkids MU Food for grandkids MU MU Everything else q f MU q f Everything else q ee q ee

36 MU hot fudge A Fall in the Price of Ice Cream MU 2 MU 1 q hot fudge Note: How does the fall in the price affect the quantity of ice cream the household buys? How would you expect this change to affect the marginal utility of hot fudge sauce?

37 A Fall in the Price of Ice Cream P hot fudge d 2 d 1 q hot fudge