a). The Democratic People's Republic of the Congo has two workers in its economy: worker A and worker B. Workers choose a combination of leisure and consumption to maximize their utility. The individual utility functions are as follows:

U_A=C^(7/8) * Z^(1/8)

U_B=C^(1/2)+(30Z)^(1/2)

where C stands for consumption, and Z stands for leisure. Any given worker is constrained by a maximum of 24 hours of leisure, or a maximum of 24 hours spent working for an hourly wage, w. One unit of consumption costs $1. Find the expression for the individual labor supply functions, LA(w) and LB(w) for each worker.

b). The poverty line in this society is at Y=C=66. A program is proposed whereby a subsidy S=66Y is given to anyone whose income Y is below 66. In order to implement this, money is raised by having a marginal tax rate of 60% for incomes above 100. (Assume any budget surplus or deficit on the part of the government is utility-neutral. Assume that the workers can change their time allocations in response to the announced program. Continue to assume w=10.) Calculate the utility levels before and after the program is implemented.

UA,before=

UB,before=

UA,after=

UB,after=a). The Democratic People's Republic of the Congo has two workers in its economy: worker A and worker B. Workers choose a combination of leisure and consumption to maximize their utility. The individual utility functions are as follows:

U_A=C^(7/8) * Z^(1/8)

U_B=C^(1/2)+(30Z)^(1/2)

where C stands for consumption, and Z stands for leisure. Any given worker is constrained by a maximum of 24 hours of leisure, or a maximum of 24 hours spent working for an hourly wage, w. One unit of consumption costs $1. Find the expression for the individual labor supply functions, LA(w) and LB(w) for each worker.

b). The poverty line in this society is at Y=C=66. A program is proposed whereby a subsidy S=66Y is given to anyone whose income Y is below 66. In order to implement this, money is raised by having a marginal tax rate of 60% for incomes above 100. (Assume any budget surplus or deficit on the part of the government is utility-neutral. Assume that the workers can change their time allocations in response to the announced program. Continue to assume w=10.) Calculate the utility levels before and after the program is implemented.

UA,before=

UB,before=

UA,after=

UB,after=