Problem 2 (Covered In Recitation) Before 1996, in the U.S. the largest income maintenance program was Aid to Families with Dependant Children (AFDC). The entitlement program, financed with Federal and States funds, targeted single parents and their children. Under the program, parents with no income were given a monthly money grant of G. For working parents, the grant was reduced by a dollar for each dollar of earnings.
a) In a Y/N diagram, draw the budget line of a single parent who could work at an hourly wage rate of $10, assume the single parent has a time endowment T = 320.
b) Consider a single parent with high-school age children. Before the introduction of the program, this single parent chose to work full time (N* = 160). Add an indifference curve to illustrate this single parent optimal allocation of time.
c) In the same diagram, show how eligibility for the AFDC program affects the single parent's budget constraint. Assume that G = $600.
d) How is the program likely to affect the labor supply of this type of single parent?
e) Consider now a single parent with toddlers. Before the introduction of the program, this parent chose to work part-time (N* = 80). In a separate diagram, illustrate this parent budget constraint before the program and her optimal choice.
f) To this second diagram, show how the AFDC program affected this parent's budget constraint. Is this type of parent more likely to take-up welfare? If it did so, would this parent work at all? How would the program affect this parent's household income?
g) The AFDC program was overhauled so that working parents' grant was reduced by only 50cents for each dollar of earnings. What is the likely effect on the size of the labor force? How would this change in policy affect the labor supply of the two types of parents?
h) Last, model the two parents' utilities for consumption and leisure with Cobb-Douglas functions. What parameters would you assign to consumption and leisure in the case of the first parent? What parameters would you use in the case of the second parent?
i) Show that when N* = 160 and C* = 1600 the first parent's MRSC1 is equal to the wage rate.
j) Show that the second parent's MRS when N* = 0 and C = $600 is higher than the wage rate.