Question 1 all parts

Consider the following endowment economy. Jake has a utility function of uj(C1, C2) = In (c1) + ; In (c2) and Amy has a utility function of UA(C1, C2) = = In (C1) + In (c2) . lake is endowed with ey = (0,4) and Amy's endowment is eA = (4,0) . Please answer the following questions. a. Define the competitive equilibrium for this economy. (2 points) b. Provide a definition of Pareto efficiency for this economy. (2 points) c. Characterize the set of Pareto optimal allocations for this economy. (5 points) d. Calculate the market clearing prices and the equilibrium allocation. (6 points) e. The government wants both Jake and Amy to consume (2, 2) in equilibrium. Is (2,2) Pareto efficient? If not, explain why not. If it is Pareto efficient, characterize the set of transfers on initial endowments such that (2, 2) is implemented in equilibrium. (5 points)