Economics 2 Professor Christina Romer Spring 2016 Professor David Romer LECTURE 6 CONSUMERS AND UTILITY MAXIMIZATION FEBRUARY 4, 2016 I. T HE B UDGET C ONSTRAINT 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. U TILITY M AXIMIZATION A. Utility and marginal utility B. Diminishing marginal utility C. The rule for utility maximization (the rational spending rule) III. W HY D EMAND C URVES S LOPE DOWN A. Substitution effect B. Income effect C. Marginal utility and the price elasticity of demand D. Individual and market demand curves IV. W HY D EMAND C URVES S HIFT A. A change in tastes B. A change in income C. A change in the price of a substitute or complement
Economics 2 Christina Romer Spring 2016 David Romer L ECTURE 6 Consumers and Utility Maximization February 4, 2016
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 https://www.econ.berkeley.edu/undergrad/home/ t utoring. • 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 http://slc.berkeley.edu/economics-1.
I. B UDGET C ONSTRAINTS
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.
The Case of Just Two Goods – Symbols P food • q food + P clothing • q clothing = Income
The Case of Just Two Goods – Diagram q food Budget constraint 0 0 q clothing
The Case of Just Two Goods – Diagram Income q food Intercept = P f P c − P { Slope = − c P f P f { 1 Income Intercept = P c 0 0 q clothing
A Rise in Income q food Constraint 2 Constraint 1 q clothing
“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.
An Equal Percentage Rise in Both Prices q food Constraint 1 Constraint 2 q clothing
A Rise in the Price of Clothing q food Constraint 1 Constraint 2 q clothing
II. U TILITY M AXIMIZATION
Marginal Utility • The extra utility derived from consuming one more unit of a good.
Diminishing Marginal Utility • As a household consumes more of a good, the marginal utility of the good declines. Marginal Utility MU q
Diminishing Marginal Utility Total Utility q Marginal Utility q
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.
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.
The Rule for Utility Maximization (the Rational Spending Rule) in Symbols 𝑁𝑁 𝑏 𝑁𝑁 𝑐 𝑁𝑁 𝑨 𝑄 𝑏 = 𝑄 𝑐 = … = 𝑄 𝑨 , 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.
The Rule for Utility Maximization with Just Two Goods • Example 1 – Clothing and food: 𝑁𝑁 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 𝑁𝑁 𝑔𝑑𝑑𝑔 . 𝑄 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑄 𝑔𝑑𝑑𝑔 • Example 2 – Blueberries and everything else: = 𝑁𝑁 𝑐𝑓𝑐𝑐𝑓𝑑𝑑𝑑𝑑𝑑 𝑐𝑑𝑐𝑐 𝑁𝑁 𝑐𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑑𝑐𝑐 . 𝑄 𝑐𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑑𝑐𝑐 𝑄 𝑐𝑓𝑐𝑐𝑓𝑑𝑑𝑑𝑑𝑑 𝑐𝑑𝑐𝑐
III. W HY D EMAND C URVES S LOPE D OWN
A Rise in the Price of Clothing • Suppose the household starts with: 𝑁𝑁 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 𝑁𝑁 𝑔𝑑𝑑𝑔 , 𝑄 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑄 𝑔𝑑𝑑𝑔 and that P clothing rises. • If the household didn’t change its purchases, 𝑁𝑁 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 < 𝑁𝑁 𝑔𝑑𝑑𝑔 . 𝑄 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑄 𝑔𝑑𝑑𝑔 • 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.
A Rise in the Price of Clothing (cont.) • Recall that a rise q food in the price of a Constraint 1 good moves the budget constraint in. Constraint 2 q clothing • This tends to make the household want to decrease its consumption of both goods. • This is the income effect of a price change.
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.
The Household’s Demand Curve for Clothing P clothing d q clothing
Marginal Utility and the Price Elasticity of Demand Good a Good b MU a MU b q a q b Demand likely to be Demand likely to be quite inelastic quite elastic
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.
IV. W HY D EMAND C URVES S HIFT
A Positive Change in Tastes or Information MU blueberries MU 2 MU 1 q blueberries
Restoring the Rational Spending Rule When There Is a Positive Change in Tastes • If the household didn’t change its purchases, > 𝑁𝑁 𝑐𝑓𝑐𝑐𝑓𝑑𝑑𝑑𝑑𝑑 𝑐𝑑𝑐𝑐 𝑁𝑁 𝑐𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑑𝑐𝑐 . 𝑄 𝑐𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑑𝑐𝑐 𝑄 𝑐𝑓𝑐𝑐𝑓𝑑𝑑𝑑𝑑𝑑 𝑐𝑑𝑐𝑐 • So, the household changes the mix of its purchases toward more blueberries.
A Positive Change in Tastes or Information P blueberries d 2 d 1 q blueberries
A Rise in Income • If the household didn’t change its purchases, 𝑁𝑁 𝑏 𝑁𝑁 𝑐 𝑄 𝑏 = 𝑄 𝑐 would still hold. • 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 ).
A Rise in Income P a d 2 d 1 q a
Duflo, “Grandmothers and Granddaughters”
Marginal Utilities for Two Goods Grandmothers’ marg. utilities Grandfathers’ marg. utilities Food for grandkids Food for grandkids MU MU q f q f Everything else Everything else MU MU q ee q ee
A Fall in the Price of Ice Cream MU hot fudge 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?
A Fall in the Price of Ice Cream P hot fudge d 2 d 1 q hot fudge
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