Essays on general equilibrium with limited commitment

This paper studies a competitive general equilibrium model with collateralized contracts under limited commitment. Even though all conceivable collateralized contracts are allowed, with limited aggregate collateral, risk sharing is imperfect and contract markets are endogenously incomplete. I prove that constrained optimal allocations can be decentralized as a general equilibrium with collateral constraints. I show that the equilibrium exists and that the First and Second Welfare theorems hold. There exists a minimal spanning set of finite collateralized contracts that generates the feasible space and that contains more than the complete set of collateralized Arrow securities. Because the capital good serves as collateral, it has an additional value, called collateral value. The collateral value, which is a risk sharing implication of the model, becomes smaller as more collateralizable capital is available. A positive collateral value implies incomplete risk sharing. I show analytically and numerically that a "sufficiently large" amount of collateral leads to perfect risk sharing and complete markets. An economy endowed with a larger amount of collateral could have a greater number of contracts traded in equilibrium. The equilibrium allocation and prices are computed numerically using the Pareto problem. The model is used to study the general equilibrium welfare effects of policies aimed at increasing the amount of collateralizable capital.