Market equilibria and money

Fixed Point Theory and Applications Pub Date : 2021-11-15 DOI:10.1186/s13663-021-00705-4

Flåm, Sjur Didrik

引用次数: 2

Abstract

By the first welfare theorem, competitive market equilibria belong to the core and hence are Pareto optimal. Letting money be a commodity, this paper turns these two inclusions around. More precisely, by generalizing the second welfare theorem we show that the said solutions may coincide as a common fixed point for one and the same system. Mathematical arguments invoke conjugation, convolution, and generalized gradients. Convexity is merely needed via subdifferentiablity of aggregate “cost”, and at one point only. Economic arguments hinge on idealized market mechanisms. Construed as algorithms, each stops, and a steady state prevails if and only if price-taking markets clear and value added is nil.

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市场均衡和货币

根据福利第一定理，竞争市场均衡属于核心均衡，因此是帕累托最优均衡。让货币成为一种商品，这篇文章将这两个内容反过来。更准确地说，通过推广第二福利定理，我们证明了上述解可以重合为同一系统的公共不动点。数学参数调用共轭、卷积和广义梯度。凸性只需要通过总“成本”的次可微性，并且只需要在一点上。经济论点取决于理想化的市场机制。作为一种算法，当且仅当定价市场清晰且附加值为零时，每一种算法都会停止，稳定状态占据主导地位。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fixed Point Theory and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： In a wide range of mathematical, computational, economical, modeling and engineering problems, the existence of a solution to a theoretical or real world problem is equivalent to the existence of a fixed point for a suitable map or operator. Fixed points are therefore of paramount importance in many areas of mathematics, sciences and engineering. The theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Over the last 60 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics. In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed point problems or optimization.