Economics 2 Professor Christina Romer Spring 2016 Professor David - - PDF document

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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

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Economics 2 Professor Christina Romer Spring 2016 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
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LECTURE 6 Consumers and Utility Maximization

February 4, 2016

Economics 2 Christina Romer Spring 2016 David Romer

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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/ 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 http://slc.berkeley.edu/economics-1.

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  • I. BUDGET CONSTRAINTS
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SLIDE 5

A Household’s Budget Constraint

  • In words: The total amount the household spends

cannot exceed its income.

  • In symbols:

Pa•qa + Pb•qb + Pc•qc + … + Pz•qz = Income, where the P’s are the market prices of the various goods, and the q’s are the quantities that the household buys.

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SLIDE 6

The Case of Just Two Goods – Symbols

Pfood•qfood + Pclothing•qclothing = Income

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SLIDE 7

The Case of Just Two Goods – Diagram

qclothing qfood 0 0 Budget constraint

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The Case of Just Two Goods – Diagram

qclothing qfood 0 0

{

{

− P

c

Pf 1

Slope = −

Pc Pf

Intercept =

Income Pf

Intercept =

Income Pc

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SLIDE 9

A Rise in Income

qclothing qfood Constraint2 Constraint1

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SLIDE 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.
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SLIDE 11

An Equal Percentage Rise in Both Prices

qclothing qfood Constraint2 Constraint1

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SLIDE 12

A Rise in the Price of Clothing

qclothing qfood Constraint2 Constraint1

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SLIDE 13
  • II. UTILITY MAXIMIZATION
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SLIDE 14

Marginal Utility

  • The extra utility derived from consuming one

more unit of a good.

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Diminishing Marginal Utility

  • As a household consumes more of a good, the

marginal utility of the good declines. q MU Marginal Utility

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SLIDE 16

q q

Diminishing Marginal Utility

Total Utility Marginal Utility

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SLIDE 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.
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SLIDE 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.

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The Rule for Utility Maximization (the Rational Spending Rule) in Symbols

𝑁𝑁𝑏 𝑄𝑏 = 𝑁𝑁𝑐 𝑄𝑐 = … = 𝑁𝑁𝑨 𝑄𝑨 ,

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.

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The Rule for Utility Maximization with Just Two Goods

  • Example 1 – Clothing and food:

𝑁𝑁𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑄𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 𝑁𝑁

𝑔𝑑𝑑𝑔

𝑄

𝑔𝑑𝑑𝑔

.

  • Example 2 – Blueberries and everything else:

𝑁𝑁𝑐𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑑𝑐𝑐 𝑄𝑐𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑑𝑐𝑐 = 𝑁𝑁𝑐𝑓𝑐𝑐𝑓𝑑𝑑𝑑𝑑𝑑 𝑐𝑑𝑐𝑐 𝑄𝑐𝑓𝑐𝑐𝑓𝑑𝑑𝑑𝑑𝑑 𝑐𝑑𝑐𝑐 .

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  • III. WHY DEMAND CURVES SLOPE DOWN
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A Rise in the Price of Clothing

  • Suppose the household starts with:

𝑁𝑁𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑄𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 𝑁𝑁

𝑔𝑑𝑑𝑔

𝑄

𝑔𝑑𝑑𝑔

, and that Pclothing rises.

  • If the household didn’t change its purchases,

𝑁𝑁𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑄𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 < 𝑁𝑁

𝑔𝑑𝑑𝑔

𝑄

𝑔𝑑𝑑𝑔

.

  • So, the household needs to change the mix of its

purchases toward less clothing (which raises MUclothing) and more food (which lowers MUfood).

  • This is the substitution effect of a price change.
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A Rise in the Price of Clothing (cont.)

  • Recall that a rise

in the price of a good moves the budget constraint in.

  • This tends to make the household want to decrease its

consumption of both goods.

  • This is the income effect of a price change.

qclothing qfood

Constraint1 Constraint2

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Why Demand Curves Slope Down

  • Substitution effect: When the price of a good

rises, households want less of the good and more

  • f 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.

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The Household’s Demand Curve for Clothing

d qclothing Pclothing

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Marginal Utility and the Price Elasticity of Demand

MUa qa Demand likely to be quite inelastic MUb qb Demand likely to be quite elastic Good a Good b

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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.

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  • IV. WHY DEMAND CURVES SHIFT
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qblueberries

A Positive Change in Tastes or Information

MUblueberries MU2 MU1

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Restoring the Rational Spending Rule When There Is a Positive Change in Tastes

  • If the household didn’t change its purchases,

𝑁𝑁𝑐𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑑𝑐𝑐 𝑄𝑐𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑑𝑐𝑐 > 𝑁𝑁𝑐𝑓𝑐𝑐𝑓𝑑𝑑𝑑𝑑𝑑 𝑐𝑑𝑐𝑐 𝑄𝑐𝑓𝑐𝑐𝑓𝑑𝑑𝑑𝑑𝑑 𝑐𝑑𝑐𝑐 .

  • So, the household changes the mix of its

purchases toward more blueberries.

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A Positive Change in Tastes or Information

d2 d1 qblueberries Pblueberries

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A Rise in Income

  • If the household didn’t change its purchases,

𝑁𝑁𝑏 𝑄𝑏 = 𝑁𝑁𝑐 𝑄𝑐 would still hold.

  • But the household isn’t using all its income.
  • So it can spend more on both good a (which

lowers MUa) and good b (which lowers MUb).

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A Rise in Income

d2 d1 qa Pa

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Duflo, “Grandmothers and Granddaughters”

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Grandmothers’ marg. utilities Grandfathers’ marg. utilities Food for grandkids Food for grandkids Everything else Everything else

Marginal Utilities for Two Goods

MU

qf

MU MU MU

qf qee qee

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SLIDE 36

A Fall in the Price of Ice Cream qhot fudge MU2 MU1 MUhot 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?

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qhot fudge

A Fall in the Price of Ice Cream

Phot fudge d2 d1