Consider the following endowment economy. Sam has a utility function of uS(c1, c2) = ln (c1) and Diane has a utility function of uD(c1, c2) = c1 2c2. Sam is endowed with eS = (2, 2) and Diane's endowment is eD = (1, 1). Please answer the following questions. a. Define the competitive equilibrium for this economy. (4 points) b. Provide a definition of Pareto efficiency for this economy. (4 points) c. Characterize the set of Pareto optimal allocations for this economy. (8 points) d. Calculate the market clearing prices and the equilibrium allocation. Hint: the competitive equilibrium may not be unique. (8 points) e. The government wants Sam to consume (2, 0) and Diane to consume (1, 3) in equilibrium. Is this allocation Pareto efficient? If not, explain why not. If it is Pareto efficient, propose a s transfer on initial endowments such that the proposed allocation is implemented in equilibrium. Hint: You only need to present one particular transfer, i.e., no need to present a set of transfers. (6 points)