# Consider the setting of the exchange economy is as follows: There are only two goods. There are only two individuals (economic agents). No production: only exchange between these two people is p

Consider the setting of the exchange economy is as follows: There are only two goods. There are only two individuals (economic agents). No production: only exchange between these two people is possible; goods are consumed. The first agent has the utility function u(q1, q2) The second agent has the utility function v(z1, z2) The total endowments of these goods are 1 and 2.Assume that utility functions are Cobb-Douglas form, that is:u(q1, q2)=(q1^_)(q2^(1-_))v(z1, z2)=(z1^_)(z2^(1-_))To make the analysis easier, assume that 1 = 2 = 1(1) Find the contract curve as a function of q1 vs q2 and graph it on the q1 _ q2 plane when _= _ = 1/2.(2) Similarly, find the contract curve and graph it when _ = 2/3 and _= 1/2.Hint: Recall that on the contract curve, marginal rates of substitution (MRSs) must be equalized: MRS1=MRS2Also, recall that MRS=marginal utility for good 1/marginal utility for good 2.Use the relations: z1 = W1 _ q1, z2 = W2 _ q2.

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