7) Consider a competitive exchange economy with two individuals, Adam and Beth, and two goods, candy bars X and cookies, Y. The economy has 30 units of each good. Initially, Adam has 30 candy bars, and Beth has 30 cookies. Preferences are presented by the following utility functions: 0,, = X;'3Y/3 (1,, = x},'3yf,'3 Where U A represents Adam's preferences and Us represents Beth's. Let py = 1 and 17;; = p. a. Write down the budget constraint for each consumer. [4 POMS] b. Write down each consumer's constrained optimisation problem. [4 points] c. Find the demand curves for the two goods for Adam and Beth. [8 points] d. Write down two market clearing conditions. Hence find the Walrasian equilibrium relative price and allocation of this economy. , | [5 POMS] e. Draw an Edgeworth box, putting good X on the x-axis and good Y on the y-axis. Identify . the initial endowment, the budget line and the Walrasian equilibrium allocation; sketch indifference curves for each consumer at the Walrasian equilibrium allocation. [8 points] f. A government official proposes a redistribution of goods between Adam and Beth in order to attain allocation (XA,K.,) = (X313) = (15,15). Sketch the utility possibilities set and identify the competitive general equilibrium allocation and the proposed allocation in your diagram. Which of the two allocations would a Rawlsian social\" planner prefer? How about '_ a Utilitarian social planner? Explain your answer. $[10 points]