Consider a two person exchange economy where each agent has utility given by u(xi1, xiz) =...
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Consider a two person exchange economy where each agent has utility given by u₁(xi1, xiz) = v(xi1) + xi2. Suppose that v is a strictly concave and increasing function that has a continuous first derivative. Suppose also that v(0) = 0 and v(x) < 1 for all x. Agent 1 has endowment (1,10) and agent 2 has endowment (0,10). a) Describe the Walrasian equilibria of this economy, including specifying the unique ratio of equilibrium prices (P₁/P2). What are the Pareto efficient allocations of this economy? b) c) For each Pareto efficient allocation, suggest how we might change the endowments so that the Pareto efficient allocation in question is a Walrasian equilibrium. Consider a two person exchange economy where each agent has utility given by u₁(xi1, xiz) = v(xi1) + xi2. Suppose that v is a strictly concave and increasing function that has a continuous first derivative. Suppose also that v(0) = 0 and v(x) < 1 for all x. Agent 1 has endowment (1,10) and agent 2 has endowment (0,10). a) Describe the Walrasian equilibria of this economy, including specifying the unique ratio of equilibrium prices (P₁/P2). What are the Pareto efficient allocations of this economy? b) c) For each Pareto efficient allocation, suggest how we might change the endowments so that the Pareto efficient allocation in question is a Walrasian equilibrium.
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