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2. (25 points total) The government has a welfare program that pays a welfare payment

G

if a person has no labor income. As they earn labor income, the welfare payment is taxed away at a 75% rate. That is, if

w

is the wage, and

H

is hours, then the actual payment is

GÃ¢â‚¬â„¢ = G

Ã¢Ë†â€™ .75

Ã¢Ë†â„¢wÃ¢Ë†â„¢H

and

GÃ¢â‚¬â„¢

= 0 if .75

Ã¢Ë†â„¢wÃ¢Ë†â„¢H > G

.

a. (5)

In the absence of the welfare program

, draw the budget constraint over leisure and money spent on consumption goods (

M

) for an individual worker, clearly labeling all points, slopes, etc. (Denote the endowment of time

T

.)

b. (5) Draw the new budget constraint created by the welfare program, clearly labeling all points, slopes, etc.

c. (5) A critic argues that this welfare program encourages some people not to work. Use a graph to show why this critic is right.

d. (5) The critic says that, to avoid work disincentives from the welfare program, the government should tax away

G

at a lower rate of 25%. Will this reduce the labor supply disincentives? Show why in a graph.

e. (5) What are the potential disadvantages of the proposal to lower the rate at which

G

is taxed away?

3. (15 points total) An individual has utility function over spending on consumption (

M

) and leisure (

L

) of

U(M,L) = MÃ¢Ë†â„¢L.

The amount of non-labor income is

Y

, the wage is

w

, and the individual has

T

hours available for work or leisure.

a. (5) What is the utility maximizing labor supply a function of? Why?

b. (5) Derive the labor supply function. Show that when

T

= 16,

w =

2, and

Y

= 16, optimal labor supply is

H

= 4.

c. (5) Suppose there are fixed costs of working equal to 8. (That is, the person loses \$8 of her exogenous income

Y

with the first hour of work.) Draw the budget constraint with these fixed costs of working. Now what is the utility-maximizing labor supply decision?

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