perloff chapter 4

8/16/2019 Perloff Chapter 4

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Copyright © 2011 Pearson Addison-Wesley. All rights reserved.

Chapter 4

Demand

I have enough money to last me the rest

of my life, unless I buy something.

Jackie Mason


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Copyright © 2011 Pearson Addison-Wesley. All rights reserved. 4-2

Chapter 4 Outline

4.1 Deriving Demand Curves4.2 Effects of an Increase in Income

4.3 Effects of a Price Increase

4.4 Cost-of-Living Adjustment

4.5 Revealed Preference


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4.1 Deriving Demand Curves

• If we hold people’s tastes, their incomes, and theprices of other goods constant, a change in the priceof a good will cause a movement along thedemand curve.

• We saw this in Chapter 2:


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• In Chapter 3, we used calculus to maximize consumerutility subject to a budget constraint.

• This amounts to solving for the consumer’s system ofdemand functions for the goods.

• Example: q1 = pizza and q

2 = burritos

• Demand functions express these quantities in termsof the prices of both goods and income:

• Given a specific utility function, we can find closed-form solutions for the demand functions.


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4.1 Example: Deriving DemandCurves

• Constant Elasticity of Substitution (CES) utility function:

• Budget constraint:

• Y= p1q1 + p2q2

• In Chapter 3, we learned that the demand functions thatresult from this constrained optimization problem are:

• Quantity demanded of each good is a function of the pricesof both goods and income.


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4.1 Example: Deriving DemandCurves• Cobb-Douglas utility function:

• U(q1, q2) = q1a q2(1-a)

• Budget constraint:

• Y= p1q1 + p2q2

• In Chapter 3, we learned that the demand functionsthat result from this constrained optimization problemare:

• With Cobb-Douglas, quantity demanded of each goodis a function of only the good’s own-price and income.


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• Panel a below shows the demand curve for q1,which we plot by holding Y fixed and varying p1.


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4.1 Deriving Demand CurvesGraphically

• Allowing the priceof the good on thex-axis to fall, thebudget constraint

rotates out andshows how theoptimal quantity ofthe x-axis goodpurchased

increases.• This traces out

points along thedemand curve.


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4.2 Effects of an Increase inIncome

• An increase in an individual’s income, holdingtastes and prices constant, causes a shift ofthe demand curve.

• An increase in income causes an increase indemand (e.g. a parallel shift away from theorigin) if the good is a normal good and adecrease in demand (e.g. parallel shift towardthe origin) if the good is inferior .

• A change in income prompts the consumer tochoose a new optimal bundle.

• The result of the change in income and thenew utility maximizing choice can be depictedthree different ways.


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4.2 Effects of an Increase inIncome

• The result of the change in income and thenew utility maximizing choice can be depictedthree different ways.

1.Income-consumption curve: using theconsumer utility maximization diagram, tracesout a line connecting optimal consumptionbundles.

2.Shifts in demand curve: using demanddiagram, show how quantity demanded increases

as the price of the good stays constant.3.Engle curve: with income on the vertical axis,

show the positive relationship between incomeand quantity demanded.


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4.2 Income-Consumption Curve andIncome Elasticities

• The shape of the income-consumption curvefor two goods tells us the sign of their incomeelasticities.


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4.2 Income-Consumption Curve andIncome Elasticities

• The shape of theincome-consumption andEngle curves can

change in waysthat indicate goodscan be both inferiorand normaldepending on an

individual’s incomelevel.


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4.3 Effects of a Price Increase

• Holding tastes, other prices, and incomeconstant, an increase in the price of a goodhas two effects on an individual’s demand:

1.Substitution effect : the change in quantitydemanded when the good’s price increases,holding other prices and consumer utilityconstant.

2.Income effect : the change in quantitydemanded when income changes, holding prices

constant.

• When the price of a good increases, the totalchange in quantity demanded is the sum ofthe substitution and income effects.


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4.3 Income and Substitution Effects

• The direction of the substitution effect isalways unambiguous.

• When price increases, individuals consume lessof it because they are substituting away from thenow more expensive good.

• The direction of the income effect dependsupon whether the good is normal or inferior;it depends upon the income elasticity.

•

When price increases and the good is normal,the income effect is negative.

• When price increases and the good is inferior,the income effect is positive.


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4.3 Income and Substitution Effectswith a Normal Good

• Beginning from budgetconstraint L1, anincrease in the price ofmusic tracks rotatesbudget constraint into

L2.

• The total effect ofthis price change, adecrease in quantityof 12 tracks per

quarter, can bedecomposed intoincome andsubstitution effects.


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4.3

CompensatedDemand Curve


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4.3 Compensated Demand Curve• Deriving the compensated, or Hicksian, demand curve

is straight-forward with the expenditure function:

• E is the smallest expenditure that allows theconsumer to achieve a given level of utility based ongiven market prices:

• Differentiating with respect to the price of the firstgood yields the compensated demand function for thefirst good:

• A $1 increase in p1 on each of the q1 units purchasedrequires the consumer increases spending by $q1 to keeputility constant.

• This result is called Shephard’s lemma.


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4.3 Slutsky Equation

• We graphically decomposed the total effect of a pricechange on quantity demanded into income andsubstitution effects.

• Deriving this same relationship mathematically utilizes

elasticities and is called the Slutsky equation.

• is elasticity of uncompensated demand and the totaleffect

• is elasticity of compensated demand and thesubstitution effect

• is the share of the budget spent on the good

• is the income elasticity

• is the income effect

*


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4.4 Cost-of-Living Adjustment

• Consumer Price Index (CPI): measure of the costof a standard bundle of goods (market basket) tocompare prices over time.

• Example: In 2010 dollars, what is the cost of a

McDonald’s hamburger in 1955?

• Knowledge of substitution and income effects allows

us to analyze how accurately the governmentmeasures inflation.

• Consumer theory can be used to show that the cost-of-living measure used by governments overstatesinflation.


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4.4 Cost-of-Living Adjustment(COLA)

• CPI in first year is the cost of buying the marketbasket of food (F) and clothing (C) that was actuallypurchased that year:

• CPI in the second year is the cost of buying the firstyear’s bundle in the second year:

• The rate of inflation determines how much additionalincome it took to buy the first year’s bundle in thesecond year:


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4.4 Cost-of-Living Adjustment(COLA)

• If a person’s incomeincreases automaticallywith the CPI, he canafford to buy the firstyear’s bundle in the

second year, butchooses not to.

• Better off in thesecond year becausethe CPI-based COLA

overcompensates inthe sense that utilityincreases.


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4.5 Revealed Preference

• Preferences predict consumer’s purchasing behavior

• Purchasing behavior infer consumer’s preferences

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