A Decomposition Algorithm for General Equilibrium Computation with Application to International Trade Models
提出一种固定点分解算法，通过求解一系列小规模子均衡问题来计算纯交换经济的一般均衡，并报告了在国际贸易模型（含贸易品与非贸易品）上的数值实验执行时间。
In this paper we outline the computation of general equilibrium in a pure exchange economy via a fixed point decomposition procedure. For general equilibrium models of the required structure, a full equilibrium may be computed through the solution of a sequence of smaller scale 'sub-equilibrium' problems. The text contains a presentation of the methods involved along with a discussion of initial computational experience for some numerical examples. IN THIS PAPER we describe the computation of general equilibrium in a pure exchange economy via a fixed point decomposition procedure similar in spirit to the Dantzig-Wolfe decomposition algorithm for the solution of linear programming problems (Dantzig and Wolfe [2]). The method involves the generation of labels for vertices on a master simplex through the separate solution of subequilibrium problems whose parameters are determined by the coordinates of the vertex on the master simplex. For general equilibrium models of the required structure, it is possible to compute a full equilibrium through the solution of a sequence of smaller scale 'sub-equilibrium' problems. The analogues to the common constraints in the Dantzig-Wolfe procedure are common commodities with common prices, and the block diagonal structure on non-common constraints in Dantzig-Wolfe is replaced by an analogous block diagonal pattern of demands and endowments of agents over non-common goods. A natural application of the method is to international trade models with 'traded' and 'non-traded' goods. Traded goods are common to all countries, non-traded goods are traded only within the country involved. We report execution times for numerical examples using Merrill's [5] algorithm for solution of both full dimensional problems and the same problems by the decomposition procedure. We do not discuss the application of these procedures to economies with production, although it seems likely to us that a similar procedure can be applied if a comparable block diagonal structure characterizes the production set. The economic interpretation we offer for our procedure draws on the partition of the full list of commodities in a general equilibrium model into 'common' goods traded among all agents, and 'non-common' goods traded among a subset of agents. The assignment of non-common goods to agents is represented in a block diagonal pattern of demands and asset ownership by agent. Agents have