Transcript Income and Substitution Effects

Applications of Consumer
Theory
Derivation of Demand; Income and
Substitution Effects; In Kind vs Cash
Transfers; Labor/leisure Tradeoff; CPI
Indifference Curves Describe Tastes of
Individual Consumer
Derivation of demand
Individual Demand
P
2.5
5
10
Q
40
20
10
Income and Substitution Effects
90
80
70
60
U3
50
U4
Px=2.5, I=200
Px=5, I=200
40
Px=5, I New
30
20
10
0
0
10
20
30
XN
40
50
X0
Xs
60
70
80
90
In-Kind vs Cash Transfers

Examples of In-Kind Transfers
– Medicaid and Medicare
– Distribution of Free Food
– Housing Subsidies/vouchers

Is a Gift of 10 units of Good X
(purchased at $5 per unit) equivalent to
$50 in cash?
Budget with Gift of 10 Units of X
Consumer Indifferent Between In-Kind
Transfer and Cash
Consumer Better Off With Cash
60
50
40
30
20
10
0
0
10
20
30
40
50
60
Summary


Cash transfers are more efficient than
in-kind transfers (in this model)
Why are in-kind transfers popular?
– Interdependent utility
– Interest groups -- ex., agricultural lobby
and food stamps
The Labor Supply Decision




Two goods -- leisure and food (Y)
Wage rate fixed -- w
No non - labor income
Price of good Y=1 (Y is numeraire.)
Labor/Leisure Trade Off
Derivation of Labor Supply
Example: Substitution Effect is Offset by Income Effect,
Hours Worked Stay Same
Intercept is w0T
X0-Xs is substitution
effect
Xs to X1 is income
effect
New intercept is
w1T
Wage rate
decreases
Xs
X0=X1
Applications

What happens if there is non - labor income?
– Budget line will have a vertical segment. Consumer can
spend 16 hours at leisure and still consume NL of good Y.
– Additional income will lead consumer to consume more of all
normal goods -- including leisure.
– Hours worked will decrease.

What is the effect of income tax on hours worked?
– Slope of budget line will change to -w(1-t).
– Substitution effect leads consumer to spend more time at
leisure because it has become relatively cheaper.
– Income effect leads consumer to buy less of normal goods -including leisure.
Problems with the CPI
Does the CPI overstate
Inflation?
Problems with the CPI
Income
needed
to be as
happy as
before.
Income
needed
to buy
old bundle