Description
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
G’ = G
− .75
∙w∙H
and
G’
= 0 if .75
∙w∙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) = M∙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?
