🤖 AI Summary
This paper addresses the computational challenge of general equilibrium in exchange economies featuring real financial markets, household production, and asset retention. Method: It formulates equilibrium computation as a max-inf optimization problem subject to no-arbitrage constraints, introduces the Walrasian dual function—novelly capturing market disequilibrium—and establishes its rigorous equivalence to equilibrium; further develops a lopsided-convergence theory for approximating max-inf points, overcoming existence and computability barriers in incomplete markets. Contribution/Results: The authors design an augmented Walrasian algorithm enabling efficient numerical solution of diverse complex exchange economies. Numerical experiments validate its accuracy and robustness, and the framework is successfully extended to applications including financial stability analysis and macroeconomic policy simulation.
📝 Abstract
We propose a new methodology to compute equilibria for general equilibrium problems on exchange economies with real financial markets, home-production, and retention. We demonstrate that equilibrium prices can be determined by solving a related maxinf-optimization problem. We incorporate the non-arbitrage condition for financial markets into the equilibrium formulation and establish the equivalence between solutions to both problems. This reduces the complexity of the original by eliminating the need to directly compute financial contract prices, allowing us to calculate equilibria even in cases of incomplete financial markets. We also introduce a Walrasian bifunction that captures the imbalances and show that maxinf-points of this function correspond to equilibrium points. Moreover, we demonstrate that every equilibrium point can be approximated by a limit of maxinf points for a family of perturbed problems, by relying on the notion of lopsided convergence. Finally, we propose an augmented Walrasian algorithm and present numerical examples to illustrate the effectiveness of this approach. Our methodology allows for efficient calculation of equilibria in a variety of exchange economies and has potential applications in finance and economics.