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Creator: Kehoe, Timothy Jerome, 1953, Levine, David K., and Romer, Paul Michael, 1955 Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 400 Abstract: We consider a production economy with a finite number of heterogeneous, infinitely lived consumers. We show that, if the economy is smooth enough, equilibria are locally unique for almost all endowments. We do so by converting the infinite dimensional fixed point problem stated in terms of prices and commodities into a finite dimensional Negishi problem involving individual weights in a social value function. By adding a set of artificial fixed factors to utility and production functions, we can write the equilibrium conditions equating spending and income for each consumer entirely in terms of time zero factor endowments and derivatives of the social value function.
Keyword: Consumer, Equilibrium, and Dynamic model Subject (JEL): C62  Existence and Stability Conditions of Equilibrium 
Creator: Kehoe, Timothy Jerome, 1953 and Levine, David K. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 445 Abstract: We develop a theory of general equilibrium with endogenous debt limits in the form of individual rationality constraints similar to those in the dynamic consistency literature. If an agent defaults on a contract, he can be excluded from future contingent claims markets trading and can have his assets seized. He cannot be excluded from spot markets trading, however, and he has some private endowments that cannot be seized. All information is publicly held and common knowledge, and there is a complete set of contingent claims markets. Since there is complete information, an agent cannot enter into a contract in which he would have an incentive to default in some state. In general there is only partial insurance: variations in consumption may be imperfectly correlated across agents; interest rates may be lower than they would be without constraints; and equilibria may be Pareto ranked.

Creator: Kehoe, Timothy Jerome, 1953, Levine, David K., and Romer, Paul Michael, 1955 Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 436 Abstract: We characterize equilibria of general equilibrium models with externalities and taxes as solutions to optimization problems. This characterization is similar to Negishi’s characterization of equilibria of economies without externalities or taxes as solutions to social planning problems. It is often useful for computing equilibria or deriving their properties. Frequently, however, finding the optimization problem that a particular equilibrium solves is difficult. This is especially true in economies with multiple equilibria. In a dynamic economy with externalities or taxes there may be a robust continuum of equilibria even if there is a representative consumer. This indeterminacy of equilibria is closely related to that in overlapping generations economies.

Creator: Kehoe, Timothy Jerome, 1953, Levine, David K., and Woodford, Michael, 1955 Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 404 Abstract: This paper uses a simple general equilibrium model in which agents use money holdings to self insure to address the classic question: What is the optimal rate of change of the money supply? The standard answer to this question, provided by Friedman, Bewley, Townsend, and others, is that this rate is negative. Because any revenues from seigniorage in our model are redistributed in lumpsum form to agents and this redistribution improves insurance possibilities, we find that the optimal rate is sometimes positive. We also discuss the measurement of welfare gains or losses from inflation and their quantitative significance.

Creator: Kehoe, Timothy Jerome, 1953 and Levine, David K. Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 380 Abstract: Typical models of bankruptcy and collateral rely on incomplete asset markets. In fact, bankruptcy and collateral add contingencies to asset markets. In some models, these contingencies can be used by consumers to achieve the same equilibrium allocations as in models with complete markets. In particular, the equilibrium allocation in the debt constrained model of Kehoe and Levine (2001) can be implemented in a model with bankruptcy and collateral. The equilibrium allocation is constrained efficient. Bankruptcy occurs when consumers receive low income shocks. The implementation of the debt constrained allocation in a model with bankruptcy and collateral is fragile in the sense of Leijonhufvud’s “corridor of stability,” however: If the environment changes, the equilibrium allocation is no longer constrained efficient.
Subject (JEL): D61  Allocative Efficiency; CostBenefit Analysis, D52  Incomplete Markets, D50  General Equilibrium and Disequilibrium: General, and G13  Contingent Pricing; Futures Pricing; option pricing 
Creator: Kehoe, Timothy Jerome, 1953, Levine, David K., and Romer, Paul Michael, 1955 Series: Staff report (Federal Reserve Bank of Minneapolis. Research Department) Number: 118 Abstract: We consider a production economy with a finite number of heterogeneous, infinitely lived consumers. We show that, if the economy is smooth enough, equilibria are locally unique for almost all endowments. We do so by converting the infinitedimensional fixed point problem stated in terms of prices and commodities into a finitedimensional Negishi problem involving individual weights in a social value function. By adding artificial fixed factors to utility and production functions, we can write the equilibrium conditions equating spending and income for each consumer entirely in terms of timezero factor endowments and derivatives of the social value function.