7) Consider a competitive exchange economy with two individuals, Adam and Beth, and two goods, candy...

 

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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: x1/3y2/3 A UA = X 1/3, UB = X¹/³y²/3 B Where U represents Adam's preferences and UB represents Beth's. Let py= 1 and px = p. a. Write down the budget constraint for each consumer. [4 points] 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. [6 points] 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, YA) = (XB, YB) = (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] 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: x1/3y2/3 A UA = X 1/3, UB = X¹/³y²/3 B Where U represents Adam's preferences and UB represents Beth's. Let py= 1 and px = p. a. Write down the budget constraint for each consumer. [4 points] 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. [6 points] 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, YA) = (XB, YB) = (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]