2. (25 points total) The government has a welfare program that pays a welfare payment
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
is the wage, and
is hours, then the actual payment is
GÃ¢â‚¬â„¢ = G
= 0 if .75
Ã¢Ë†â„¢wÃ¢Ë†â„¢H > G
In the absence of the welfare program
, draw the budget constraint over leisure and money spent on consumption goods (
) for an individual worker, clearly labeling all points, slopes, etc. (Denote the endowment of time
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
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
is taxed away?
3. (15 points total) An individual has utility function over spending on consumption (
) and leisure (
U(M,L) = MÃ¢Ë†â„¢L.
The amount of non-labor income is
, the wage is
, and the individual has
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
= 16, optimal labor supply is
c. (5) Suppose there are fixed costs of working equal to 8. (That is, the person loses $8 of her exogenous income
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?