Let T = 24 be total available hours, L be hours of leisure, and n be hours of work. Let w > 0 be the hourly wage and p > 0 be the price of the consumption good. Finally, let C be consumption. Assume that the utility function is u(C, L) = C * L

(a) Suppose that an agent receives a lump-sum amount of B dollars if he works more than 8 hours. Find the optimal bundle (L*, C*) and illustrate graphically your solution.

(b) Suppose that if an agent decides to work beyond regular hours (say 8 hours), then he is given an additional s dollars for every hour (beyond 8 hours). Find (L*, C*) and illustrate graphically your solution.

(c) Suppose that the law forces an agent to work no less than 3 hours and no more than 8 hours. Find (L*, C*) and illustrate graphically your solution.

(d) Suppose that an agent receives an amount B > 0 only if the agent is inactive, i.e., n = 0. Find (L*, C*) and illustrate graphically your solution.

*Questions are all independent and conditions in each question have no relation to the other questions