income & substitution effect ch05

8/6/2019 Income & Substitution Effect Ch05

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Chapter 5INCOME AND SUBSTITUTION

EFFECTS

Copyright 2005 by South-Western, a division of Thomson Learning. All rights reserved.


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D emand FunctionsThe optimal levels of x 1, x 2,, x n can beexpressed as functions of all prices and

incomeThese can be expressed as n demandfunctions of the form:

x 1* = d 1( p 1, p 2,, p n,I ) x 2* = d 2( p 1, p 2,, p n,I )

x n* = d n( p 1, p 2,, p n,I )


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D emand FunctionsIf there are only two goods ( x and y ), wecan simplify the notation

x * = x ( p x , p y ,I )y * = y ( p x , p y ,I )

Prices and income are exogenous the individual has no control over these

parameters


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H omogeneityIf we were to double all prices andincome, the optimal quantities demandedwill not change the budget constraint is unchanged

x i * = d i ( p 1, p 2,, p n,I ) = d i (tp 1,tp 2,, tp n,t I )

Individual demand functions arehomogeneous of degree zero in all pricesand income


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HomogeneityWith a Cobb-Douglas utility function

utility = U ( x ,y ) = x 0.3 y 0.7

the demand functions are

Note that a doubling of both prices andincome would leave x * and y *unaffected

x

x I 3.0

* !y p

y I 7.0

* !


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HomogeneityWith a CES utility function

utility = U ( x ,y ) = x 0.5 + y 0.5

the demand functions are

Note that a doubling of both prices andincome would leave x * and y *unaffected

x y x

x I

/1

1*

y x y p p py

I

/1

1*


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Changes in Income An increase in income will cause thebudget constraint out in a parallelfashionSince p x / p y does not change, the MRS will stay constant as the worker moves

to higher levels of satisfaction


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Increase in IncomeIf both x and y increase as income rises, x and y are normal goods

Quantity of x

Quantity of y

C

U3

B

U2

A

U1

As income rises, the individual choosesto consume more x and y


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Increase in IncomeIf x decreases as income rises, x is aninferior good

Quantity of x

Quantity of y

C

U3

As income rises, the individual choosesto consume less x and more y

Note that the indifferencecurves do not have to beoddly shaped. Theassumption of a diminishingMRS is obeyed.

B

U2 A

U1


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N ormal and Inferior Goods A good x i for which x x i/x I u 0 over somerange of income is a normal good in thatrange

A good x ifor which x x

i/x I < 0 over some

range of income is an inferior good inthat range


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Changes in a Goods Price A change in the price of a good altersthe slope of the budget constraint

it also changes the MRS at the consumersutility-maximizing choices

When the price changes, two effects

come into play substitution effect income effect


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Changes in a Goods PriceEven if the individual remained on the sameindifference curve when the price changes,his optimal choice will change because theMRS must equal the new price ratio the substitution effect

The price change alters the individualsreal income and therefore he must moveto a new indifference curve the income effect


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Changes in a Goods Price

Quantity of x

Quantity of y

U1

A

Suppose the consumer is maximizingutility at point A .

U2

B

If the price of good x falls, the consumer will maximize utility at point B.

Total increase in x


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U1

Quantity of x

Quantity of y

A

To isolate the substitution effect, we holdreal income constant but allow therelative price of good x to change

Substitution effect

C

The substitution effect is the movementfrom point A to point C

The individual substitutesgood x for good y

because it is nowrelatively cheaper


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U1

U2

Quantity of x

Quantity of y

A

The income effect occurs because theindividuals real income changes whenthe price of good x changes

C

Income effect

BThe income effect is the movementfrom point C to point B

If x is a normal good,the individual will buymore because realincome increased


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U2

U1

Quantity of x

Quantity of y

B

A

An increase in the price of good x means thatthe budget constraint gets steeper

C The substitution effect is themovement from point A to point C

Substitution effect

Income effect

The income effect is themovement from point C to point B


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Price Changes for N ormal Goods

If a good is normal, substitution and

income effects reinforce one another when price falls, both effects lead to a rise inquantity demanded

when price rises, both effects lead to a dropin quantity demanded


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Price Changes for Inferior Goods

If a good is inferior, substitution andincome effects move in opposite directionsThe combined effect is indeterminate when price rises, the substitution effect leads

to a drop in quantity demanded, but the

income effect is opposite when price falls, the substitution effect leads

to a rise in quantity demanded, but theincome effect is opposite


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Giffens ParadoxIf the income effect of a price change isstrong enough, there could be a positive

relationship between price and quantitydemanded an increase in price leads to a drop in real

income since the good is inferior, a drop in income

causes quantity demanded to rise


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ASummaryUtility maximization implies that (for normal

goods ) a fall in price leads to an increase inquantity demanded the substitution effect causes more to be

purchased as the individual moves along anindifference curve

the income effect causes more to be purchasedbecause the resulting rise in purchasing power allows the individual to move to a higher indifference curve


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ASummary

Utility maximization implies that (for normalgoods ) a rise in price leads to a decline in

quantity demanded the substitution effect causes less to be

purchased as the individual moves along anindifference curve

the income effect causes less to be purchasedbecause the resulting drop in purchasingpower moves the individual to a lower indifference curve


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ASummary

Utility maximization implies that (for inferior goods ) no definite prediction can be madefor changes in price the substitution effect and income effect move

in opposite directions

if the income effect outweighs the substitutioneffect, we have a case of Giffens paradox


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The Individuals

Demand Curve

An individuals demand for x dependson preferences, all prices, and income:

x * = x ( p x , p y ,I )It may be convenient to graph theindividuals demand for x assuming that

income and the price of y ( p y ) are heldconstant


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x

quantity of x demanded rises.

T he Individuals D emand Curve

Quantity of y

Quantity of x Quantity of x

p x

x

p x

U2

x2

I = p x + p y

x

p x

U1

x1

I = p x + p y

x

p x

x3

U3

I = p x + py

As the priceof x falls...


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T he Individuals D emand Curve

An individual demand curve shows therelationship between the price of a good

and the quantity of that good purchased byan individual assuming that all other determinants of demand are held constant


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Shifts in the D emand CurveThree factors are held constant when ademand curve is derived

income prices of other goods ( p y ) the individuals preferences

If any of these factors change, thedemand curve will shift to a new position


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Shifts in the D emand Curve A movement along a given demandcurve is caused by a change in the price

of the good a change in quantity demanded

A shift in the demand curve is caused by

changes in income, prices of other goods, or preferences a change in demand


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D emand Functions and Curves

If the individuals income is $100, these

functions become

x p x

I 3.0* !

y py

I 7.0* !

We discovered earlier that

x p x

30* !

y py

70* !


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D emand Functions and Curves Any change in income will shift thesedemand curves


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CompensatedD

emand CurvesThe actual level of utility varies alongthe demand curve

As the price of x falls, the individualmoves to higher indifference curves it is assumed that nominal income is held

constant as the demand curve is derived this means that real income rises as theprice of x falls


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CompensatedD

emand Curves An alternative approach holds real income(or utility) constant while examining

reactions to changes in p x the effects of the price change arecompensated so as to constrain theindividual to remain on the same indifferencecurve

reactions to price changes include onlysubstitution effects


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CompensatedD

emand Curves A compensated (Hicksian ) demand curveshows the relationship between the priceof a good and the quantity purchasedassuming that other prices and utility areheld constantThe compensated demand curve is a two-dimensional representation of thecompensated demand function

x * = x c ( p x , p y ,U )


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x c

quantity demanded

rises.

Compensated D emand Curves

Quantity of y

Quantity of x Quantity of x

p x

U2

x

p x

x

y

x

p p

slope''

x

p x

y

x

p p

s l pe'

x x

p x y

x

p p

s l pe'''

!

x

Holding utility constant, as price falls...


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Compensated &Uncompensated D emand

Quantity of x

p x

x

x c

x

p x

At p x , the curves intersect becausethe individuals income is just sufficient

to attain utility level U 2


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Quantity of x

p x

x

x c

p x

x *** x

p x

At prices below p x 2

, incomecompensation is negative to prevent anincrease in utility from a lower price


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For a normal good, the compensateddemand curve is less responsive to pricechanges than is the uncompensateddemand curve the uncompensated demand curve reflects

both income and substitution effects the compensated demand curve reflects only

substitution effects


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Compensated D emandFunctions

Suppose that utility is given by

utility = U ( x ,y ) = x 0.5

y 0.5

The Marshallian demand functions are x = I /2 p x y = I /2 p y

The indirect utility function is)utility

y x y x p p

p pV I

I !!


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To obtain the compensated demandfunctions, we can solve the indirectutility function for I and then substituteinto the Marshallian demand functions

x

y

pVp x ! 5.0

5.0

y

x

pVpy !


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Demand now depends on utility ( V ) rather than income

Increases in p x reduce the amount of x demanded only a substitution effect

.

5.

x

y

pV p

x ! 5.05.0

y

x

p p

y !


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A Mathematical Examinationof a Change in Price

Our goal is to examine how purchases of good x change when p

x changes

x x /x p x Differentiation of the first-order conditionsfrom utility maximization can be performedto solve for this derivativeHowever, this approach is cumbersomeand provides little economic insight


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Instead, we will use an indirect approach Remember the expenditure function

minimum expenditure = E ( p x , p y ,U )

Then, by definition

x c ( p x , p y ,U ) = x [ p x , p y ,E ( p x , p y ,U )] quantity demanded is equal for both demand

functions when income is exactly what isneeded to attain the required utility level


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We can differentiate the compensateddemand function and get

x c ( p x , p y ,U ) = x [ p x , p y ,E ( p x , p y ,U )]

x x x

c

p

E

E

x

p

x

p

x

x

x

x

x

x

x

x

x

x x

c

x p x

p x

p x

xx

xx

xx

xx


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The first term is the slope of thecompensated demand curve

the mathematical representation of thesubstitution effect

x x

c

x p

x

p x

p x

xx

xx

xx

xx


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The second term measures the way inwhich changes in p x affect the demandfor x through changes in purchasingpower the mathematical representation of the

income effect

x x

c

x pE

E x

p x

p x

xx

xx

xx

xx


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The Slutsky Equation

The substitution effect can be written as

constant effectonsubstituti

!xx

!xx

!U x x

c

p

x

p

x

The income effect can be written as

x x p

E x p

E E x

x

x

x

x

x

x

x

x

I effectincome


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Note that x E /x p x = x a $1 increase in p x raises necessary

expenditures by x dollars $1 extra must be paid for each unit of x

purchased


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The Slutsky EquationThe utility-maximization hypothesis

shows that the substitution and incomeeffects arising from a price change can berepresented by

I x

x

x

x!

x

x

!x

x

!

x x

p x

p x

p x

x x

x

constant

effectincomeeffectonsubstituti


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The first term is the substitution effect always negative as long as MRS is

diminishing the slope of the compensated demand curvemust be negative

I x

x

x

x

x

x x x

p x

p x

U x x constant


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The second term is the income effect if x is a normal good, then x x /x I > 0

the entire income effect is negative if x is an inferior good, then x x /x I < 0

the entire income effect is positive

I x

x

x

x

x

x x x

p x

p x

U x x constant


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ASlutsky

Decomposition

We can demonstrate the decompositionof a price effect using the Cobb-Douglas

example studied earlier The Marshallian demand function for good x was

x x x I I 5.0) !


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ASlutsky

Decomposition

The Hicksian (compensated ) demandfunction for good x was

5.0

5.0

),,( x

x x !

The overall effect of a price change onthe demand for x is

5.

x x

x I !


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ASlutsky

Decomposition

This total effect is the sum of the twoeffects that Slutsky identified

The substitution effect is found bydifferentiating the compensated demandfunction

effectonsubstituti x

y

x

c

pVp

p x

x

x


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ASlutsky

Decomposition

We can substitute in for the indirect utilityfunction ( V )

25.1

5.05.05.0 25.0)5.0(5.0 effectonsubstituti x x

y y x I I


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ASlutsky

Decomposition

Calculation of the income effect is easier

effectincome x x x p p p

x x I I I

Interestingly, the substitution and incomeeffects are exactly the same size


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Marshallian D emandElasticities

Most of the commonly used demandelasticities are derived from theMarshallian demand function x ( p x , p y ,I )

Price elasticity of demand ( e x , px )

x p

p x

p p x x e x

x x x p x x x

x(

(//

,


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Marshallian D emandElasticities

Income elasticity of demand ( e x ,I )

x

x x x x

I I I I

I ((

//

,

Cross-price elasticity of demand ( e x , py )

x

p

p x

p p x x

ey

y y y p x y (

(

/

/,


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Price Elasticity of D emandThe own price elasticity of demand isalways negative the only exception is Giffens paradox

The size of the elasticity is important if e x , px < -1, demand is elastic if e x , px > -1, demand is inelastic if e x , px = -1, demand is unit elastic


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Price Elasticity and T otalSpending

Total spending on x is equal tototal spending = p

x x

Using elasticity, we can determine howtotal spending changes when the price of

x changes]1[( , x p x

x x

x

x e x x p x

p p

x p


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Price Elasticity and T otalSpending

The sign of this derivative depends onwhether e x,px is greater or less than -1

if e x,px >

-1, demand is inelastic and price andtotal spending move in the same direction if e x,px < -1, demand is elastic and price and

total spending move in opposite directions

1( ,xx

x

x

x p x

x

x

x

x e x x p

x p

p

x p


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Compensated Price ElasticitiesIt is also useful to define elasticitiesbased on the compensated demandfunction


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Compensated Price ElasticitiesIf the compensated demand function is

x c = x c ( p x

, py ,U )

we can calculate compensated own price elasticity of

demand ( e x c , px ) compensated cross-price elasticity of

demand ( e x c , py )


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Compensated Price ElasticitiesThe compensated own price elasticity of demand ( e x c , px ) is

c x

x

c

x x

c c c p x x

p p x

p p x x e

x x

x

//

,

The compensated cross-price elasticityof demand ( e x c , py ) is

c y

y

c

y y

c c c

p x x

p

p x

p p x x

ey (

(

/

/,


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Compensated Price ElasticitiesThe relationship between Marshallianand compensated price elasticities can

be shown using the Slutsky equation

I xx

xx

xx x

x x p

p x

x p

e p x

x p x

x

c

c x

p x x

x x ,

I ,,, x x c

p x p x esee x x

If s x = p x x /I , then


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Compensated Price ElasticitiesThe Slutsky equation shows that thecompensated and uncompensated priceelasticities will be similar if the share of income devoted to x is small the income elasticity of x is small


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H omogeneityDemand functions are homogeneous of degree zero in all prices and income

Eulers theorem for homogenousfunctions shows that

I I

x

x

x

x

x

x!

x

p

x

p p

x

p y y x x 0


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H omogeneityDividing by x , we get

I ,,,0 x p x p x eee y x

Any proportional change in all pricesand income will leave the quantity of x

demanded unchanged


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Engel A ggregationEngels law suggests that the incomeelasticity of demand for food items isless than one this implies that the income elasticity of

demand for all nonfood items must be

greater than one


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Engel A ggregationWe can see this by differentiating thebudget constraint with respect to

income (treating prices as constant )

I I x

x

x

x! y p p y 1

I I I

I

I I

I

I ,,1 y y x x y x eses

y

y y p

x

x x p


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Cournot A ggregationThe size of the cross-price effect of achange in the price of x on the quantityof y consumed is restricted because of the budget constraintWe can demonstrate this by

differentiating the budget constraint withrespect to p x


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Cournot A ggregation

x

y

x

x

x py p x

p x p

p xx

xx

xx

0I

y

y p

p

y p

p x

x

x p

p

x p x

x

y x x

x

x I I I 0

x x py y x p x x esses ,,!

x py y p x x seses x x !

,,


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Demand Elasticities

The Cobb-Douglas utility function isU ( x ,y ) = x Ey F (E+ F=1)

The demand functions for x and y are

x p

x I E

!

y p

y I F

!


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Demand ElasticitiesCalculating the elasticities, we get

, !

E

E!xx!

x

x

x

x

x

x

x

x e

x I

I

00, !!xx

!

x x

x e y y

y

x y

1, !

!

x

x!

x

x x

p

p x x

eI

I I

I I


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Demand ElasticitiesWe can also show

homogeneity

,,, !!I x p x p x eee x

Engel aggregation

,, ! FE! FE!I I y y x x eses

Cournot aggregation

x py y p x x seses x x !E! FE! 0)1(,,


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Demand ElasticitiesWe can also use the Slutsky equation to

derive the compensated price elasticity

F!E!E!! ,,, I x x p x c p x esee x x

The compensated price elasticitydepends on how important other goods(y ) are in the utility function


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Demand Elasticities

The CES utility function (with W = 2,H = 5 ) is

U ( x ,y ) = x 0.5

+ y 0.5

The demand functions for x and y are

)(! y x x p p p x I

)1( 1 y x y p p py !I


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Demand Elasticities

We will use the share elasticity toderive the own price elasticity

x x x p x x

x

x

x ps e

s

p

p

se

xx

In this case,

y x

x x

x s

I


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Demand Elasticities

Thus, the share elasticity is given by

, x

x

y x

y x

y x

x

y x

y

x

x

x

x

p p p

p p

p p p

p p

p p p x x

Therefore, if we let p x = py

,, !!! x x x s x ee


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Demand Elasticities

The CES utility function (with W = 0.5,H = -1 ) is

U ( x ,y ) = - x -1

- y -1

The share of good x is

0.01

1

x y

x

x p p

x ps

I


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Demand ElasticitiesThus, the share elasticity is given by

5.05.0

5.05.0

15.05.025.05.0

5.15.0

,

1

5.0

1()1(

5.0

!

!!

x y

x y

x y

x

x y

x y

x

x

x

x ps

p p

p p

p p

p

p p

p p

s

p

p

se

x x

Again, if we let p x = py

0125.0

1,, !!! x x x ps p x ee


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Consumer Surplus An important problem in welfareeconomics is to devise a monetarymeasure of the gains and losses thatindividuals experience when priceschange


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Consumer WelfareOne way to evaluate the welfare cost of aprice increase (from p x

0 to p x 1) would beto compare the expenditures required toachieve U 0 under these two situations

expenditure at p x 0 = E 0 = E ( p x

0 , p y ,U 0)

expenditure at p x 1 = E 1 = E ( p x 1, p y ,U 0)


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Consumer WelfareIn order to compensate for the price rise,this person would require acompensating variation ( C V ) of

C V = E ( p x 1, p y ,U 0) - E ( p x 0 , p y ,U 0)


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Consumer Welfare

Quantity of x

Quantity of y

U1

A

Suppose the consumer is maximizingutility at point A .

U2

B

If the price of good x rises, the consumer

will maximize utility at point B.

The consumers utilityfalls from U 1 to U2


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Consumer Welfare

Quantity of x

Quantity of y

U1

A

U2

B

C V is the amount that theindividual would need to becompensated

The consumer could be compensated sothat he can afford to remain on U 1

C


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Consumer WelfareThe derivative of the expenditure functionwith respect to p x is the compensated

demand function

U p p x p

U p py x

x

y x !x

x


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Consumer WelfareThe amount of C V required can be foundby integrating across a sequence of

small increments to price from p x 0

to p x 1

!!1

0

1

0

,,( 0 x

x

x

x

p

p

p

p

x y x c dpU p p x dE CV

this integral is the area to the left of thecompensated demand curve between p x

0

and p x 1


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w elfare loss

Consumer Welfare

Quantity of x

p x

x c (p x U 0)

p x 1

x 1

p x 0

x 0

When the price rises from p x 0 to p x 1,

the consumer suffers a loss in welfare


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Consumer WelfareBecause a price change generallyinvolves both income and substitution

effects, it is unclear which compensateddemand curve should be usedDo we use the compensated demandcurve for the original target utility ( U

0) or

the new level of utility after the pricechange ( U 1)?


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T he Consumer SurplusConcept

Another way to look at this issue is toask how much the person would bewilling to pay for the right to consume allof this good that he wanted at themarket price of p x 0


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T he Consumer SurplusConcept

The area below the compensateddemand curve and above the marketprice is called consumer surplus the extra benefit the person receives by

being able to make market transactions at

the prevailing market price


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Consumer Welfare

Quantity of x

p x

x c (...U 0)

p x 1

x 1

When the price rises from p x 0 to p x 1, the actual

market reaction will be to move from A to C

x c (...U 1)

x ( p x )

A

C

p x 0

x 0

The consumers utility falls from U 0 to U 1


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Consumer Welfare

Quantity of x

p x

x c

(...U 0)

p x 1

x 1

Is the consumers loss in welfarebest described by area p x 1BA p x

0

[using x c (...U 0)] or by area p x 1CD p x 0

[using x c (...U 1)]?

x c (...U 1)

A

BC

D p x

0

x 0

Is U 0 or U 1 theappropriate utilitytarget ?


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Consumer Welfare

Quantity of x

p x

x c

(...U 0)

p x 1

x 1

We can use the Marshallian demandcurve as a compromise

x c (...U 1)

x(p x )

A

BC

D p x

0

x 0

The area p x 1

CA p x 0

falls between thesizes of the welfarelosses defined by

x c (...U 0) and x c (...U 1)


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Consumer SurplusWe will define consumer surplus as thearea below the Marshallian demandcurve and above price shows what an individual would pay for the

right to make voluntary transactions at thisprice

changes in consumer surplus measure thewelfare effects of price changes


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Welfare Loss from a PriceIncrease

Suppose that the compensated demandfunction for x is given by

.0

5.0

),, x

x x !

The welfare cost of a price increase

from p x = 1 to p x = 4 is given by4

1

5.05.04

1

5.05.0 2!

!!! x

X

p

p x y x y pVp pVpCV


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If we assume that V = 2 and p y = 2,

C V = 2 2 2 (4)0.5

2 2 2 (1)0.5

= 8If we assume that the utility level ( V ) falls to 1 after the price increase (andused this level to calculate welfare loss ),

C V = 1 2 2 (4)0.5 1 2 2 (1)0.5 = 4


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98

Welfare Loss from PriceIncrease

Suppose that we use the Marshalliandemand function instead

,,( - x x p p p x I I !

The welfare loss from a price increase

from p x = 1 to p x = 4 is given by4

1

14

1

ln.05.0!

!!! x

x

p

p x x -

x pdp pLoss I I


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99


If income ( I ) is equal to 8,

loss = 4 ln(4 ) -4ln(1 ) =4ln(4 ) = 4(1.39 ) = 5.55

this computed loss from the Marshalliandemand function is a compromise between

the two amounts computed using thecompensated demand functions


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100

R evealed Preference andthe Substitution Effect

The theory of revealed preference wasproposed by

Paul Samuelson in the late

1940sThe theory defines a principle of rationality based on observed behavior and then uses it to approximate anindividuals utility function


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101


Consider two bundles of goods: A and B

If the individual can afford to purchaseeither bundle but chooses A , we say that A had been revealed preferred to BUnder any other price-incomearrangement, B can never be revealedpreferred to A


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102


Quantity of x

Quantity of y

A

I 1

Suppose that, when the budget constraint isgiven by I 1, A is chosen

B

I 3

A must still be preferred to B when incomeis I 3 (because both A and B are available )

I 2

If B is chosen, the budgetconstraint must be similar to

that given byI

2 where A

is notavailable


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103

N egativity of theSubstitution Effect

Suppose that an individual is indifferentbetween two bundles: C and D

Let p x C , p y

C be the prices at whichbundle C is chosen

Let p x D

, p y D

be the prices at whichbundle D is chosen


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Since the individual is indifferent betweenC and D When C is chosen, D must cost at least as

much as C

p x C x C + p y

C y C p x C x D + p y

C y D

When D is chosen, C must cost at least asmuch as D

p x D x D + p y

D y D p x D x C + p y

D y C


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105


Rearranging, we get p

x

C (xC - x D ) + py

C (yC -y D ) 0

p x D (xD - x C ) + p y

D (yD -y C ) 0

Adding these together, we get( p x

C p x D )(xC - x D ) + ( p y

C py D )(yC - y D ) 0


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106


Suppose that only the price of x changes( p y

C = p y D )

( p x C p x

D )(xC - x D ) 0

This implies that price and quantity movein opposite direction when utility is heldconstant the substitution effect is negative


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107

Mathematical GeneralizationIf, at prices p i

0 bundle x i 0 is chosen

instead of bundle x i 1 (and bundle x i 1 isaffordable ), then

! !

un

i

n

i i i i i x p x p

1 1

1

Bundle 0 has been revealed preferredto bundle 1


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108

Mathematical GeneralizationConsequently, at prices that prevailwhen bundle 1 is chosen ( p i 1), then

! !

"n

i

n

i i i i i x p x p

1 1

111

Bundle 0 must be more expensive thanbundle 1


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109

Strong A xiom of R evealedPreference

If commodity bundle 0 is revealedpreferred to bundle 1 , and if bundle 1 isrevealed preferred to bundle 2 , and if bundle 2 is revealed preferred to bundle3 ,,and if bundle K-1 is revealed

preferred to bundle K , then bundle K cannot be revealed preferred to bundle 0


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Important Points to N ote:

Proportional changes in all prices andincome do not shift the individuals

budget constraint and therefore do notalter the quantities of goods chosen demand functions are homogeneous of

degree zero in all prices and income


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111

Important Points to N ote:When purchasing power changes(income changes but prices remain the

same ), budget constraints shift for normal goods, an increase in incomemeans that more is purchased

for inferior goods, an increase in income

means that less is purchased


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112

Important Points to N ote: A fall in the price of a good causessubstitution and income effects

for a normal good, both effects cause moreof the good to be purchased for inferior goods, substitution and income

effects work in opposite directions

no unambiguous prediction is possible


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113

Important Points to N ote: A rise in the price of a good alsocauses income and substitution effects

for normal goods, less will be demanded for inferior goods, the net result isambiguous


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115


Compensated demand curves illustratemovements along a given indifference

curve for alternative prices they are constructed by holding utilityconstant and exhibit only the substitutioneffects from a price change

their slope is unambiguously negative (or zero )


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116


Demand elasticities are often used inempirical work to summarize how

individuals react to changes in pricesand income the most important is the price elasticity of

demandmeasures the proportionate change in quantityin response to a 1 percent change in price


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117


There are many relationships amongdemand elasticities

own-price elasticities determine how aprice change affects total spending on agood

substitution and income effects can be

summarized by the Slutsky equation various aggregation results hold among

elasticities


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118


Welfare effects of price changes canbe measured by changing areas below

either compensated or ordinarydemand curves such changes affect the size of the

consumer surplus that individuals receiveby being able to make market transactions


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The negativity of the substitution effectis one of the most basic findings of

demand theory this result can be shown using revealedpreference theory and does notnecessarily require assuming the

existence of a utility function

income & substitution effect ch05

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