A Bewley-Huggett model with many consumption goods
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We study a pure-exchange incomplete markets model with heterogeneous agents. In each period, the agents choose how much to save and which bundle of goods to consume while their endowments are fluctuating. We focus on a competitive stationary equilibrium (CSE) in which the wealth distribution is invariant, the agents maximize their expected discounted utility, and both the prices of goods and the interest rate are market-clearing. Our main contribution is to extend some general equilibrium results to an incomplete markets setting. Under mild conditions on the agents' preferences, we show that the aggregate demand for goods depends only on their relative prices and we prove the existence of a CSE. When the agents' preferences can be represented by a CES (constant elasticity of substitution) utility function with an elasticity of substitution that is higher than or equal to one, we prove that the CSE is unique. Under the same preferences, we show that a higher inequality of endowments does not change the equilibrium prices of goods, and decreases the equilibrium interest rate.
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