Demand, price effects, income effectsincome effects

Demand more !

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DemandDemand

• Back to preferencesp• Price effects

– Normal goods– Perfect complements– Perfect substitutes

• Income effects• Income effects– Normal goods– Giffen goods (?)

• intervention• Observable implications

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Price effects (for standard goods)Price effects (for standard goods)

• ∂X(p,M)/ ∂p<0.(p, )/ p– Changes in demand with respect to own price is negative.

• Elasticity  ‐ (in this case its positive but it can be i h ll h 1either greater or smaller than 1

• Who cares about this?Consumer?– Consumer?

– Producers?• Revenue 

– Government?• Think of taxes to discourage behavior • Think of taxes to raise revenue

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Back to Cobb‐DouglasBack to Cobb Douglas

X pMY

pMpX )1(,)(

1, yxyxuYX pp

Cobb Douglass very practical600

800

15

20

Pelasticitiy Cobb-Douglass very practical

because it’s a one parameter per good, constant elasticity demand curve. It a very good 200

400

5

10

elasticitiydX/dp

place to start.

‐200

0

‐5

0

0 50 100 150 200 250 300

4

‐400‐10

Decomposition into Substitution and ffIncome Effectsy

SubstitutionEffect

IncomeEff tTotal or

x

EffectTotal orObserved Effect

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Demand and Compensated demand• Cobb‐Douglas  U

• Demand for good x is X(p,M).bb l

1, yxyxuM– Cobb‐Douglas

• e(p u) is the expenditure functionX

X pMMpX

),(

e(p,u) is the expenditure function – minimum income to reach a given level of utility.– Min

– Notice we get back the homothetic property (to double utility you must double expenditures)you must double expenditures)

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Demand and Compensated demandDemand and Compensated demand

• Demand for good x MMpX )(Demand for good x

• e(p,u) Expenditure function XX p

MpX ),(

• Compensated demand 

• So we can now find Slutzky’s equationSo we can now find Slutzky s equation

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Slutzky’s equationSlutzky s equation

• Lets evaluate thisLets evaluate this

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Pratical value of Slutzky’s equation

• You can’t measure

• So figuring out how to compensate people say for a sudden shock to heating oil…may be difficult. Except for Slutzky’s equation.

• You can observe x* you can measure the total yeffect      and the income effect        So you can figure out       by the formulag y

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SubstitutesSubstitutes• Blu‐ray vs DVD• Blu ray is better but DVD is cheaper They are used for• Blu‐ray is better but DVD is cheaper.  They are used for the exact same thing.  

• Fix the price of DVD player $32 (amazon sells a Sony p p y ( yDVD 

• Assume rentals of disc cost the same (Netflix $2 more th th th 8 99 t t f ff)per month rather than 8.99, so we are not too far off)

• Now lets worry about how to price a Blu‐ray player• Clearly if we sell it at $31 No one buys a DVD player• Clearly if we sell it at $31, No one buys a DVD player .• Clearly if we sell it at $3000 on those who really care about the increased quality are going to buy it.q y g g y

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Substitutes• So U(X, DVD, BR) where X depends on everything else BR is whether one has Blu‐ray and DVD is ywhether one has DVD. 

• Because they are substitutes no one wants both, for y ,now assume they are a small part of the budget. So we can simply consider that choice

• U(BR,DVD)= DVD+αBR– What do indifference curves look like?

• Max U(BR,DVD)= DVD+αBR sbjt to PD DVD+PBBR<M

So buy Blu‐ray if PB<αPD

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Consumer choice

BR Budget set when BR is expensive

Budget set when BR is Cheap

Indifference curves Slope -1/α

DVDDVD

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Individual Demand

PBRQBR

*31

Buy Blu-ray α*31

1

Blu ray

Buy

31

Buy DVD

Q

PBRα*31

QBR

13

1

Aggregte Demand

PBR Customers with α>10

310

Customers with α=1

31

BRBR

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ComplementsComplements

• Normal goods ∂X/∂px<0, ∂X/∂py≥0g / px , / py• Substitutes goods changes are non linear• Complements goods ∂X/∂px<0, ∂X/∂py<0y

• Example DVD players and DVD rentals– U=(DVD, DISC)= DVD*DISC– But does that quite capture the idea?

• Strict complement X=βY• Strict complement X=βY– So by definition ∂X/∂px = β∂Y/∂px <0– and ∂X/∂py = β∂Y/∂py<0y y

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Summary of Price effectsSummary of Price effects

• Expect own price effect to be negativeExpect own price effect to be negative

• Expect responses to other prices to vary quite a bit– Some cases you buy more (because this good has becomeSome cases you buy more (because this good has become relatively cheaper)

– Some cases you buy less (because you need to reallocate ff d h l )to afford the complement).

• Figuring these characteristics of demand is critical for businesses and governmentbusinesses and government

• The other argument from the budget set is income.

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Income effectIncome effect

• Normal goods ∂X/∂M>0Normal goods ∂X/∂M>0,

• Inferior goods ∂X/∂M<0,

S d d i i l• Standard empirical case– Up to some income M ∂X/∂M>0, then past M∂ /∂ h h h l d∂X/∂M<0, as you switch to higher quality goods.

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Demand for calories ascalories as function of income

Trevon Logan JEHTrevon Logan JEH 2007 

These are annualper person

13=442 000 calories13=442.000 calories a year (1212 year)Range 12=572/day

14 3300/d

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14=3300/day

From Logan JEH 2009,Note that this elasticity is declining over time So there is both cross sectionalNote that this elasticity is declining over time. So there is both cross sectional and time variation

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6070

Energy consumption and Birth rates over time

405060

102030

010

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

1956 1966 19761986 1996 Poly. (1956)Poly. (1976) Poly. (1996)

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Income EffectIncome Effect

• Engel curve traces consumption as incomeEngel curve traces consumption as income rises

yy

21

x

Inferior GoodInferior Goody

x

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Intertemporal ChoiceIntertemporal Choice

• First two slides from last timeFirst two slides from last time

• u(x1, x2) = v(x1) + v(x2)d ( ) ( )• Budget (1+r)x1 + x2 = (1+r)M1 + M2

• FOC  21 )1()(0 xvrxv

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Intertemporal OptimizationIntertemporal Optimization

x2 In this case you are poor

(M1 M2)

In this case you are poor when young rich when old

(M1,M2)

Repayment

Period 1B i

x1

Borrowing

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Interest Rate IncreaseBorrower’s Income Fallsx2

(M1,M2)

x1

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Interest Rate IncreaseCreditor’s Income Rises

x2

(M1,M2)

xx1

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Neither Borrower Nor Lender BeDifferences in Borrowing/Lending Rates

x2

(M1,M2)

x1

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100% propensity to consume100% propensity to consumex2

(M1,M2)( 1, 2)

x1

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Conclusion From Week 2Conclusion From Week 2

• Demand framework useful for a variety of purposesy p p• We did the basics

– No asymmetric information (you always know everything b h k d h d )about the market and the goods)

– No risk (you are sure what you want and what you get)– ContinuityContinuity – NO TRANSACTION COSTS

• More of this in most Econ classes– But EC121ab, EC 106 come back heavily to those topics

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