Consider an exchange economy with two consumers (Consumer 1 and Consumer 2) and two goods (good...

 

Transcribed Image Text:

Consider an exchange economy with two consumers (Consumer 1 and Consumer 2) and two goods (good 1 and good 2). Suppose that the Consumer 1's preferences are given by the Cobb- Douglas utility function U (x11, X21) = X11X21 and that for Consumer 2 the goods are perfect substitutes with his utility function being U (X12, X22) = x12 + X22 where xen is the amount of good consumed by consumer n. Suppose that the endowments are w1 = 2, W21 = 8, W12 W22 = 2, where wen is consumer n's endowment of good l. Normalise the price vector so that p2 = 1. = 6, and (1) Find each consumer's Walrasian demand functions for each good, that is, her demand for each good as a function of the prices, given her initial endowment. (3 marks) (2) Find the competitive equilibrium price and the competitive equi- librium allocation. (4 marks) (4 marks) (3) Find the contract curve. (4) Draw the Edgeworth Box. Carefully mark the initial endowment, the equilibrium allocation, the equilibrium price vector, and the contract curve. Be as neat and accurate as you can. Please use a ruler to draw straight lines and to measure distances. (10 marks) (5) Is the allocation ((x11, 21), (X12, X22)) = ((6, 6), (2, 4)) Pareto op- timal? If it is, can it be supported as a competitive equilibrium by a reallocation of initial endowments to an allocation that gives Player 1 an initial bundle in which she receives no good 1? If so, what is her reallocated initial endowment? If not, explain why it is not possible. (4 marks) Consider an exchange economy with two consumers (Consumer 1 and Consumer 2) and two goods (good 1 and good 2). Suppose that the Consumer 1's preferences are given by the Cobb- Douglas utility function U (x11, X21) = X11X21 and that for Consumer 2 the goods are perfect substitutes with his utility function being U (X12, X22) = x12 + X22 where xen is the amount of good consumed by consumer n. Suppose that the endowments are w1 = 2, W21 = 8, W12 W22 = 2, where wen is consumer n's endowment of good l. Normalise the price vector so that p2 = 1. = 6, and (1) Find each consumer's Walrasian demand functions for each good, that is, her demand for each good as a function of the prices, given her initial endowment. (3 marks) (2) Find the competitive equilibrium price and the competitive equi- librium allocation. (4 marks) (4 marks) (3) Find the contract curve. (4) Draw the Edgeworth Box. Carefully mark the initial endowment, the equilibrium allocation, the equilibrium price vector, and the contract curve. Be as neat and accurate as you can. Please use a ruler to draw straight lines and to measure distances. (10 marks) (5) Is the allocation ((x11, 21), (X12, X22)) = ((6, 6), (2, 4)) Pareto op- timal? If it is, can it be supported as a competitive equilibrium by a reallocation of initial endowments to an allocation that gives Player 1 an initial bundle in which she receives no good 1? If so, what is her reallocated initial endowment? If not, explain why it is not possible. (4 marks)

Answer rating: 100% (QA)

To solve this problem well go step by step 1 Consumer 1s Walrasian demand functions To find Consumer 1s demand for goods 1 and 2 we need to maximize t... View the full answer