2. Welfare Theorems (35 points) Consider the following endowment economy. Mr. Peanutbutter and Princess Car- 1 olyn have the same utility function: u (c1, (2) = 08 03 . Mr. Peanutbutter has endow- ment ep = (4,6) and Princess Carolyn has endowment ec = (6,4) . a. State the first and second welfare theorems. (5 points) b. Define Pareto efficient allocation for this economy. (5 points) c. Define the competitive equilibrium for this economy. (5 points) d. Solve for the competitive equilbrium. (8 points) e. The government wants both Mr. Peanutbutter and Princess Carolyn to con- sume (5,5) in equilibrium. Is (5,5) Pareto efficient? If not, explain why not. If it is Pareto efficient, characterize the set of transfers on initial endowments such that (5,5) is implemented in equilibrium. (5 points) f. Find the set of Pareto efficient allocations. (7 points)