Question 1
Grace Erickson is a college student who maximizes her utility that depends on leisure (L) and consumption (C) measured in dollars. Her utility function is given as U(C, L) = C*L. It follows from the above utility function that her marginal utility from L and C (MUL and MUC) is MUL = C and MUC = L. Ms. Erickson’s hourly wage (W) is equal to $10 an hour at the bookstore and her parents provide her $45 of non-labor income (V). Ms. Erickson has 18 hours in the day of which she can choose to leisure (i.e., school time) or work.

(1) Solve for Ms. Erickson’s reservation wage.

(2) Find the equation of Ms. Erickson’s budget constraint and draw the graph showing all relevant points.

(3) Solve for and draw the equilibrium level of L and C and place on your graph in (2). How many hours does she work and how much does she earn?

(4) Draw a new budget constraint and solve for the new equilibrium level of L and C if Ms. Erickson pays a 10% tax (t) on her hourly wage. How many hour does she work and how much does she earn net of taxes?

(5) Sketch the labor supply curve of Ms. Erickson implied by (3) and (4) above.

(6) Suppose instead of the tax in (4), Ms. Erickson pays a tax in the same amount directly from her non-labor income (V – tax). Draw her new budget constraint and solve for the new equilibrium level of L and C.

(7) Ms. Erickson pays the same amount of tax in (4) and (6) above, but her consumption of L and C differs under the two different tax schemes. Why? [Hint: how do the budget constraints in (4) and (6) differ? What do these differences imply about opportunities?]

(8) Which tax scheme does Ms. Erickson prefer? In other words, which of the tax schemes provides Ms. Erickson the highest level of utility? [Hint: the utility function indicates the relationship between the goods C and L and utility U.]

(9) Ms. Erickson’s parents have decided that she is spending too much time in non-school activities. To punish her, they have decided to take away her $45 of non-labor income. Is this a rational strategy by Ms. Erickson’s parents if their ultimate objective is to have her spend more time in school?

Question 2
Consider a family that ranks the combination of household production time (N) and purchased goods (Y) according to the formula
U = NY,

where U represents the level of utility (associated with the production of some household commodity). Suppose the maximum time available in a day is 16 hours and currently a spouse devotes 7 hours to market work (H) at a wage of $5 per hour. Suppose the family also receives $10 per day in non-labor income (e.g., food stamps).
(1) What is the level of utility associated with the current mix of market work and household production?

(2) Assume that a recession occurs and the worker is laid off from his or her job. What is the level of utility at the new mix of market work and household production?

(3) Suppose the probability of finding a comparable job during this recession is π. What is the return to taking an hour away from household production activities to look for a job [Hint: What is the expected wage from job search]?

(4) Assuming π=o.5, would an hour spent in the labor force searching for a job make this person better off or worse off? Would the worker continue to be a member of the labor force under these conditions? If not, how would he or she be categorized?

(5) Assuming π=0.1, would an hour spent in the labor force searching for a job make this person better off or worse off? Would the worker continue to be a member of the labor force under these conditions? If not, how would he or she be categorized ?

(6) Suppose that if the worker were willing to accept a job paying only $2 per hour, the probability of finding a job would rise to π=1/3. Would the worker continue to be a member of the labor force under these conditions?

Question 1 Grace Erickson is a college student who maximizes her...