2. (9 points total) Suppose Mark's utility over consumption and leisure can be expressed as U( c, I) = C. 1'. Assume that the market prevailing wage rate is w=10. Furthermore, assume that a period is a year such that a unit of leisure is a week and Mark's time endowment is T=50 (ie., 50 weeks in a year). Consider the following two economies: Economy A: There are no government transfers. In this economy, individuals do not have any non-labor income. Economy B: Unemployment benefits are the only source of government transfers (and hence, the only source of non-labor income). Everyone is eligible for a maximum of 25 weeks of benefits (it is possible to receive less than 25 weeks). The replacement rate is 0.5 (i.e., weekly unemployment benefits are 0.5w). a) Derive Mark's budget constraint under the two economies. On the same consumption-leisure space, graphically illustrate the two budget constraints. Make sure to label the slopes. (3 points) b) Derive Mark's optimal bundle of (c,I) under the two economies. Describe how the two bundles are different In which economy does Mark work more? (3 points) c) Consider a set of 100 individuals (including Mark) with heterogeneous utility functions (i.e., you should not assume that everyone has the same utility function as Mark). Assume that the market wage rate is still w=10 for both Economy A and B. Explain how the average labor supply would be different in the two economies. (3 points)