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This monograph presents a general equilibrium methodology for microeconomic policy analysis. It is intended to serve as an alternative to the now classical, axiomatic general equilibrium theory as exposited in Debreu`s Theory of Value (1959) or Arrow and Hahn`s General Competitive Analysis (1971). The monograph consists of several essays written over the last decade. It also contains an appendix by Charles Steinhorn on the elements of O-minimal structures.

In this article we examine the competitive equilibria of a dynamic stochastic economy with complete markets and collateral constraints. We show that, provided the sets of asset pay-offs and of collateral levels are sufficiently rich, the equilibrium allocations with sequential trades and collateral constraints are equivalent to those obtained in Arrow-Debreu markets subject to a series of limited pledgeability constraints. We provide both necessary and sufficient conditions for equilibria to be Pareto efficient and show that when collateral is scarce equilibria are not only Pareto inefficient but also often constrained inefficient, in the sense that imposing tighter borrowing restrictions can make everybody in the economy better off. We derive sufficient conditions for the existence of Markov equilibria and, for the case of two agents, for the existence of equilibria that have finite support. These equilibria can be computed with arbitrary accuracy and the model is very tractable.

We compare asset prices in an overlapping generations model for incomplete and complete markets. Individuals within a generational cohort have heterogeneous beliefs about future states of the economy and thus would like to make bets against each other. In the incomplete-markets economy, agents cannot make such bets. Asset price volatility is very small. The situation changes dramatically when markets are completed through financial innovations as the set of available securities now allows agents with different beliefs to place bets against each other. Wealth shifts across agents and generations. Such changes in the wealth distribution lead to substantial asset price volatility.

This paper studies an overlapping generations model with stochastic production and incomplete markets to assess whether the introduction of an unfunded social security system leads to a Pareto improvement. When returns to capital and wages are imperfectly correlated, a system that endows retired households with claims to labor income enhances the sharing of aggregate risk between generations. Our quantitative analysis shows that, abstracting from the capital crowding-out effect, the introduction of social security represents a Pareto-improving reform, even when the economy is dynamically efficient. However, the severity of the crowding-out effect in general equilibrium tends to overturn these gains.

Abstract.  A comment on Brainard and Scarf's article in this volume.