8/3/2019 Income Effect

1/12

7. Income and SubstitutionEffects

Varian, Chapter 8.

Decomposing the price change

Good Xhas a price pX= p; good Yhas pY= 1

A reduction in phas two effects:- it makes good Xrelatively less expensive

- it raises purchasing power

The total change in demand for good Xcanbe decomposed into a substitution effectandan income effect

8/3/2019 Income Effect

2/12

The price change

x

y

A B

m

Decomposing the price change

x

y

A

Pivot:

Relative priceof good xfalls

m

8/3/2019 Income Effect

3/12

Decomposing the price change(cont.)

x

y

A BShift:

Purchasing powerincreases

m

m

The change in purchasing power

Starting at A, the consumer can affordmore of both goods if the price of Xfalls

With money m, she can just afford heroriginal bundle, given the new prices

The change in purchasing power is

m-m = -Dpx0

8/3/2019 Income Effect

4/12

Substitution and income effects

x

y

ABC

Substitution effectIncome effect

Demand for good Xat Cisthe compensated demand,X(p,1,m)

m

m

Calculating the substitution effect

Suppose that demand for good Xis

X(p,1,m) = m/(5p)

Initially, m =$120 and p= $3

Consumption of Xis x0 = 8

Price of X fallsto $2

Consumption of Xrises to 12

Here m-m= -Dpx0 =8

Compensated demand is (120-8)/10 = 11.2

Substitutioneffect is

11.2-8 = 3.2

8/3/2019 Income Effect

5/12

The substitution effect of a pricedecreaseis positive

x

y

A C

Substitution effect

m

m

Calculating the income effect

The income effect is equal to the changein demand accompanying a change inmoney of m-m, at the new prices

In the example above, m-m= 8, so wemust find the effect of giving back $8

Income effect is12-11.2 = 0.8

8/3/2019 Income Effect

6/12

The income effect is positive fora normal good

x

y

ABC

Income effect

Xis normal here, so thetotal effect is positive

The income effect is negativefor an inferior good

x

y

A

B

C

Income effect

Xis inferior here, but thetotal effect is still positive

8/3/2019 Income Effect

7/12

Giffen good

x

y

A

B

C

Income effectSubstitution effect

A Giffen goodhas anegative income effect,with greater magnitudethan the substitutioneffect

Perfect complements

x

y

Original budget

New budget

PivotShift

A

B

8/3/2019 Income Effect

8/12

Perfect substitutes

x

y

Original budget

New budget

Pivot

A

B

Quasi-linear preferences

x

PivotShift

A

B

C

y

8/3/2019 Income Effect

9/12

Tax policy: Estate tax

children

GU

BA

m

mm(1t)

C

Tax policy: a tax and a rebate

Per-unit tax on good Xat rate t

Give a lump-sum refund to the consumer

Ifthe refund equals the amount of taxpaid, she consumes less of good Xand isworse-off than without the tax and rebate

8/3/2019 Income Effect

10/12 1

Tax policy: a tax and a rebate

x

y

A

B

Budget line withtax and rebate

Budget linewithout tax

An example

Let utility be u(x,y) = xy

Prices are pX= pY= 1; money is m= 12

X(1,1,12) = Y(1,1,12) = 6

Utility is u(6,6) = 36

8/3/2019 Income Effect

11/12

An example (cont.)

Now consider a per-unit subsidy on goodXof s= and a lump-sum tax of T= 4

X(,1,8) = 8, Y(,1,8) = 4

Utility is u(8,4) = 32

Real time pricing (RTP)

Demand for electricity varies with theweather, but retail prices tend not to vary

Several power companies have optional

RTP programs for large customers that letprices vary with aggregate demand

8/3/2019 Income Effect

12/12

RTP (cont.)

Electricity

Money spenton other goods

RTP budget line

Baseline budget line

Hicksian Decomposition

x

y

A

B

C

m