Computing general equilibrium with incomplete markets and default
computation of equilibria | markets endogenously incomplete | Pareto frontier
The numerical computation of general equilibrium is important for understanding the behavior of the real world economy, and may lead to insights on the effects of regulation and welfare of the economy. We consider a two-period exchange economy with default for two classes of models: collateral and default penalties. In Chapter 1 we compute general equilibrium for these models and solved by an optimization procedure for large computation - ALGENCAN – an Augmented Lagrangian Method for general nonlinear programming problems. We illustrate the proposed method by computing equilibria for some examples, showing its robustness. In Chapter 2 we examine the effects of default and scarcity of collateralizable durable. There are at least as many assets available for trade as there are states of the world. In our examples if, the collateralizable durable good is scarce or if some agents do not own enough of the collateralizable durable good, markets can be endogenously incomplete, not all of the available assets are traded in the competitive equilibrium and allocations are not Pareto optimal. We give examples that show that welfare losses can be quantitatively large and examine the scope for government intervention. In Chapter 3 we examine, through numerical examples, when the equilibria allocations can approach the Pareto frontier by the use of a default mechanism. In our examples, if the endowment distribution displays only heterogeneity between periods (e.g., one agent is the richest in the first period and another is the richest in all states of nature of the second period), collateral equilibria are Pareto optimal. If the heterogeneity of the endowments is also manifest between states of nature, default penalties equilibria are often Pareto superior with respect to collateral equilibria.