Question: Mike has a utility function represented by U(C, L) = C^1/3 L. He has 16 hours to devote to labor and leisure. He receives welfare of $100 per day.

a. Mike is currently not working and receives welfare. Assume he will not loose his welfare payment if he works. What is his reservation wage if he works 1 hour?

b. Now assume his welfare benefits are terminated. Find his utility maximizing combination of work and leisure hours.

c. Find his reservation wage such that he would be indifferent between accepting welfare (and not working) and your answer in part b.

d. Suppose he is working and receives no welfare, find the minimum overtime pay to get him to work 1 hour of overtime.

e. On one graph, clearly label all your answers from parts a-d. For ease, you can draw a small segment of the budget constraint at the place it is tangent to the utility curve.