Consider a pure exchange economy with two agents. A and B. who trade two goods. 1...

 

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Consider a pure exchange economy with two agents. A and B. who trade two goods. 1 and r2. Their utility functions are, respectively: U = ln (¹) + 2 ln (r) [B = 2m (ef) + ln (x2) Naturally, agent A's utility depends on his consumption of and r2. while agent B's utility depends on his consumption of the two goods. Suppose that the initial endowments are described by: (cf. c) = (100.300) (cf.e2) = (200.600) a. Characterize the set of Pareto Efficient allocations (the contract curve). b. Characterize the core of this economy. c. Suppose that A makes a one time take-it-or-leave-it offer to B and no further negotiation is possible. Show how you would find the allocation that A would propose. (Once you set up the problem, you do not need to go through the solution). d. If the price of good 1 if P₁ = 1, find the competitive equilibrium price P2. e. Find the equilibrium allocation. f. Show that the allocation in (e) is in the core. Consider a pure exchange economy with two agents. A and B. who trade two goods. 1 and r2. Their utility functions are, respectively: U = ln (¹) + 2 ln (r) [B = 2m (ef) + ln (x2) Naturally, agent A's utility depends on his consumption of and r2. while agent B's utility depends on his consumption of the two goods. Suppose that the initial endowments are described by: (cf. c) = (100.300) (cf.e2) = (200.600) a. Characterize the set of Pareto Efficient allocations (the contract curve). b. Characterize the core of this economy. c. Suppose that A makes a one time take-it-or-leave-it offer to B and no further negotiation is possible. Show how you would find the allocation that A would propose. (Once you set up the problem, you do not need to go through the solution). d. If the price of good 1 if P₁ = 1, find the competitive equilibrium price P2. e. Find the equilibrium allocation. f. Show that the allocation in (e) is in the core.

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a To characterize the set of Pareto Efficient allocations we need to solve the following optimizatio... View the full answer