Income & Subsitution Effect

7/29/2019 Income & Subsitution Effect

1/19

Income and Substitution

Effects


2/19

Income and Substitution Effects

Economists decompose the effect of a change inprice on the quantity demanded into an income anda substitution effect.

Income effect: due to the increase in real incomeassociated with a fall in prices (you can buy morewith the same income) or the loss of real incomeassociated with a rise in prices (you cannot buy as

much as you once did with the same income). Substitution effect: due to the change in the relative

price of the good, cheaper goods are substituted formore expensive ones.


3/19

Income and Substitution Effects: PriceDecline, X normal

When the price of a good falls, the quantity demandedrises for two reasons.

The income effect: real income is higher because thesame money income buys more at the lower prices. Fornormal goods, then, the income effect of a price fall ispositive.

The substitution effect: consumers substitute the nowcheaper good for ones whose price has not fallen, real

income held constant. This increase in demand is calledthe substitution effect of a price decline.


4/19

Lis Income and Substitution Effects: Price Fall,

Rice normal

Graph shows the income

and substitution effects ofthe fall in the price ofwheat from $4/lb. (A) to$1/lb. (C).

The movement from point

A to point D is thesubstitution effect: Li buysless rice and more wheat,and would do so even ifshe had an income of only$20 (as the black budget

line shows). The movement from point

D to point C is the incomeeffect, the price decline islike giving Li an additional

$20 of real income.

Li's Income and Substitution Effects

0

5

10

15

20

25

30

0 5 10 15 20Wheat

Rice

I2

I0

4

1

1

C

AD


5/19

Lis Substitution Effect

The substitution effect is the amount bywhich Li's wheat consumption increasedholding real income constant.

Substitution effect is the differencebetween Li's consumption of wheat at thenew and old prices holding her real

income constant, that is, staying on thesame indifference curve (compare points

A and D).


6/19

Lis Income Effect

When the price falls from $4/lb. of wheat to$1/lb. per wheat, Li is able to buy both morewheat and more rice.

The income effect is the difference between

what she would have bought on the oldindifference curve at the lower wheat price (pointD) and what she actually did buy with hernominal income ($40) at the lower price (pointC).

Li increases her consumption of wheat and ricebecause of the increase in her real income fromthe price decline.


7/19

General effect of a price fall

Income effect - you feel richer

X normal

Substitution EffectX now looks relatively cheaper

PX falls

Quantity demanded increases Quantity demanded increasesQuantity demanded decreases

Total effect is the substitution effect AND the income effectworking at the same time.

X inferior


8/19

From Individual to Market Demand

Market demand is the sum of all individualdemands in the economy.

In the following example there are twoconsumers of wheat: Li and Juanita.

The market demand, then, is the sum ofthe quantities demand by Li and Juanita.


9/19

Juanitas Demand for Wheat

Juanitas income isalso $40.

Juanita faces the

same price for rice asLi: $2/lb.

Her preferences aredifferent from Lis.

Her demand forwheat is derived inthe figure at the left.

Juanita's Demand for Wheat

0

5

10

15

20

25

30

0 5 10 15 20

Wheat

Rice

I2

I1I0

4

2

1

CB


10/19

Graph of Juanitas Demand for

Wheat

The points A, B andC correspond toJuanitas best

choices given herincome and thethree prices ofwheat illustrated.

This is her demandcurve for wheat.

Juanita's Demand for Wheat

0

1

2

3

4

0 2 4 6 8 10 12 14 16 18 20

Quantity

Price

A

B

C


11/19

Market Demand The market demand

(green) is the sum of Lis(blue) and Juanitas (red)demand for wheat ateach price.

At PW=4, Li demands 6

lbs., Juanita demands 5lbs. and the marketdemand is 11 lbs.

At PW=2, Li and Juanitademand 10 lbs. and themarket demand is 20 lbs.

At PW=1, Li demands 16lbs., Juanita demands 18lbs. and the marketdemand is 34 lbs.

Market for Wheat

0

1

2

3

4

0 20 40

Quantity of Wheat

PriceofWheat

Li's Demand

Juanita's Demand

Market Demand


12/19

Application: Effect of a Tax & Transfer Program

Suppose I have thepreferences illustratedat the right.

Question A:If Income = $16If Price of food = $1If Price of shelter = $1

Food = ?Shelter = ?Indifference curve = ?

Preferences

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7

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9

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16

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Food

Shelter

I4

I5

I6

I1

I2

I3


13/19

Answer A

PointA:If Income = $16If Price of food = $1If Price of shelter = $1

Food = 7Shelter = 9Indifference curve = I4

Initial Point

0

12

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7

8

9

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11

12

13

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16

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Food

Shelter

I1

I2

I3

I4

I5

I6A


14/19

Effect of a Tax and TransferProgram: Addition of Tax

Question B:If Income = $16If Price of food = $1If Price of shelter = $1

and Tax on shelter =100%

Tax-inclusive price of

shelter = ?Food = ?Shelter = ?Indifference curve = ?

Initial Point

0

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7

8

9

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12

13

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16

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Food

Shelter

I1

I2

I3

I4

I5

I6A


15/19

Effect of a Tax and TransferProgram: Tax & Transfer

Question C:If Income = $16If Price of food = $1If Price of shelter = $1and Tax on shelter =100% andTransfer payment = $8

Food = ?Shelter = ?Indifference curve = ?

Tax Only

0

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7

8

9

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12

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16

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Food

Shelter

I1

I2

I3

I4

I5

I6A

B


16/19

Answer C

Point CIf Income = $16If Price of food = $1If Price of shelter = $1and Tax on shelter =100% andTransfer payment = $8

Food = 10Shelter = 7Indifference curve = I4

Tax and Transfer

0

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7

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9

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16

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Food

Shelter

I1

I2

I3

I4

I5

I6A

B

C


17/19

Tax and Transfer Systems Give PureSubstitution Effects

Notice in the example that the consumer ends up on thesame indifference curve after the tax and transferprogram as in the initial choice (I4).

In public finance (the study of tax and transfer systems)this result usually occurs when the tax and transfersystem is combined with a balanced budget.

In our example, tax receipts are $7 per person (= 7 unitsof shelter x $1 tax), while the transfer is $8 per person.This is as close to balanced as we can get and still beable to graph the consumers choice legibly.

Knowledge of the substitution effect of the price changeinduced by the shelter tax is sufficient to predict theeffect of the complete tax and transfer system.


18/19

Food Stamps vs. $$$$$

Suppose the following for the Parker family:u(F, $aog) where $aog=$all other goods

I=$200

PF = $2/unitPaog = $1

Consider three alternative government policiesno support

$200 in food stamps

$200 in cash


19/19

Food Stamps vs. $$$$$

Food

$aog

BL0

IC0

ICFS

IC$$

Notes:the budget line under

the food stampprogram is the thick

black segment andthe purple segment

The budget line withcash is the red andpurple segments

if this is the case thenthe Parkers prefercash to food stamps

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Income & Subsitution Effect