Suppose Jack and Jill are a married couple who derive utility from C and Z, where C denotes the dollar value of goods bought at market (such as TVs) and Z is the dollar value of commodities produced in the household (such as meals). To buy C, they need cash which they can only get through allocating time to labor market work. To produce Z they need to allocate some time to household production. Assume Jack and Jill have 10 hours a day each (that is, Jack has 10 hours, Jill has 10 hours) to split between market work and household production.

Suppose Jack can produce $10 worth of household goods per hour he spends in the household sector (i.e., engaging in household production), and he can earn a wage rate of $20 per hour he spends in the market sector (i.e., engaging in labor market work). Suppose Jill can produce $25 worth of household goods per hour she spends in the household sector, and she can earn a wage rate of $15 per hour he spends in the market sector.

First in Part A and B well consider the scenario where Jack and Jill have not yet gotten married (i.e., they are single, not a household).

a. Draw Jacks budget constraint when he is a single individual, putting C on the vertical axis and Z on the horizontal axis. Be sure to label everything (slopes, important points on the axes, etc.).

b. Draw Jills budget constraint when she is a single individual, putting C on the vertical axis and Z on the horizontal axis. Be sure to label everything. Now Jack and Jill get married and live in the same household. The remainder of the question concerns this couples household.

c. Draw the households budget constraint, putting C on the vertical axis and Z on the horizontal axis. Be sure to label everything. Depict which regions on the households budget constraint (if any) correspond to:

i. Both Jack and Jill specializing in the household sector

ii. Both Jack and Jill specializing in the market sector

iii. Jack/Jill specializing completely in the market sector and the other spouse specializing in the household sector (you must specify which spouse specializes in what) iv. Jack/Jill specializing completely in the household sector while Jack/Jill splitting his/her time between the market sector and the household sector (you must specify which spouse specializes in what)

d. Given the household budget constraint you drew above, the households actual choice of division of labor between market and household production among Jack and Jill is determined by the highest household indifference curve tangent to the household budget constraint. Illustrate three different outcomes that may arise and briefly describe these outcomes (continue to put C on the vertical axis and Z on the horizontal axis).

e. Suppose Jacks wage rate increases substantially. Illustrate in a graph how this changes the households budget constraint from the one in part (C).

f. Suppose Jills marginal productivity in the household increases substantially, illustrate in a graph how this changes the households budget constraint from the one in part (C).