This exercise is a modication of our housing economy. Consider a world with a set H...
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This exercise is a modication of our housing economy. Consider a world with a set H consisting of n houses held by an agent (the chief) who is interested only in gold and N merchants who own gold but are III 1 interested only in houses. Denote the chief as agent N + 1 and gold as good N+1. Gold is divisible but the houses are not. The initial bundle of the chief is (1,1,...,1,0) containing 0 units of gold and 1 unit of each house. His consumption set contains all bundles of the form (0,0,...,0,m). Each merchant i owns an initial amount m,> 0 of gold (suppose my > m₂ > ... > m¸ > 0), can consume only one house, and has a strict ordering over the houses a. Define the competitive equilibrium for this economy first in words and then formally. b. Find a competitive equilibria for this economy, if it exists. c. Check if First Welfare Theorem holds for this economy, i.e. whether each competitive equilibrium allocation is Pareto efficient or not. This exercise is a modication of our housing economy. Consider a world with a set H consisting of n houses held by an agent (the chief) who is interested only in gold and N merchants who own gold but are III 1 interested only in houses. Denote the chief as agent N + 1 and gold as good N+1. Gold is divisible but the houses are not. The initial bundle of the chief is (1,1,...,1,0) containing 0 units of gold and 1 unit of each house. His consumption set contains all bundles of the form (0,0,...,0,m). Each merchant i owns an initial amount m,> 0 of gold (suppose my > m₂ > ... > m¸ > 0), can consume only one house, and has a strict ordering over the houses a. Define the competitive equilibrium for this economy first in words and then formally. b. Find a competitive equilibria for this economy, if it exists. c. Check if First Welfare Theorem holds for this economy, i.e. whether each competitive equilibrium allocation is Pareto efficient or not.
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a A competitive equilibrium for this economy is a set of prices p1 pN1 and a set of allocations x1 x... View the full answer
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Data Modeling and Database Design
ISBN: 978-1285085258
2nd edition
Authors: Narayan S. Umanath, Richard W. Scammel
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