ON THE FOUNDATIONS OF MATHEMATICAL ECONOMICS

2012 ◽  
Vol 08 (01) ◽  
pp. 53-72 ◽  
Author(s):  
J. BARKLEY ROSSER
Keyword(s):  
General Equilibrium ◽  
Path Integrals ◽  
Delta Function ◽  
Constructive Mathematics ◽  
Mathematical Economics ◽  
Constructivist Perspective ◽  
Second Welfare Theorem ◽  
Intermediate Value ◽  
Welfare Theorem ◽  
Opening Section

Kumaraswamy Vela Velupillai74 presents a constructivist perspective on the foundations of mathematical economics, praising the views of Feynman in developing path integrals and Dirac in developing the delta function. He sees their approach as consistent with the Bishop constructive mathematics and considers its view on the Bolzano-Weierstrass, Hahn-Banach, and intermediate value theorems, and then the implications of these arguments for such "crown jewels" of mathematical economics as the existence of general equilibrium and the second welfare theorem. He also relates these ideas to the weakening of certain assumptions to allow for more general results as shown by Rosser51 in his extension of Gödel's incompleteness theorem in his opening section. This paper considers these arguments in reverse order, moving from the matters of economics applications to the broader issue of constructivist mathematics, concluding by considering the views of Rosser on these matters, drawing both on his writings and on personal conversations with him.

scholarly journals The Second Welfare Theorem with Nonconvex Preferences

Econometrica ◽  
1988 ◽  
Vol 56 (2) ◽  
pp. 361 ◽  
Author(s):  
Robert M. Anderson
Keyword(s):  
Second Welfare Theorem ◽  
Welfare Theorem

scholarly journals Market equilibria and money

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sjur Didrik Flåm
Keyword(s):  
Fixed Point ◽  
Steady State ◽  
Value Added ◽  
Pareto Optimal ◽  
Generalized Gradients ◽  
Market Mechanisms ◽  
Mathematical Arguments ◽  
Second Welfare Theorem ◽  
Market Equilibria ◽  
Welfare Theorem

AbstractBy 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.

General Equilibrium Theory in Soviet Economic Science:bibliometric analysis

2014 ◽  
pp. 106-125 ◽  
Author(s):  
E. Malkov
Keyword(s):  
General Equilibrium ◽  
Qualitative Analysis ◽  
Bibliometric Analysis ◽  
Equilibrium Theory ◽  
General Equilibrium Theory ◽  
Mathematical Economics ◽  
Von Neumann ◽  
Soviet Literature ◽  
Equilibrium Growth ◽  
Disequilibrium Theory

This paper is the first attempt at quantitative and qualitative analysis of the Soviet literature on general equilibrium theory in 1960-1990s. We divide the papers into four subgroups: von Neumann-Gale class of models and equilibrium growth; Arrow-Debreu class of models; disequilibrium theory; other branches of general equilibrium theory. Bibliometric analysis shows that von Neumann-Gale class of models was the most popular one in the Soviet mathematical economics.

Private information, Coasian bargaining, and the second welfare theorem

2006 ◽  
Vol 90 (4-5) ◽  
pp. 871-895 ◽  
Author(s):  
Dagobert L. Brito ◽  
Jonathan H. Hamilton ◽  
Michael D. Intriligator ◽  
Eytan Sheshinski ◽  
Steven M. Slutsky
Keyword(s):  
Private Information ◽  
Second Welfare Theorem ◽  
Coasian Bargaining ◽  
Welfare Theorem

The Second Welfare Theorem in Economies with Non-Walrasian Markets

2015 ◽  
Vol 17 (3) ◽  
pp. 415-432 ◽  
Author(s):  
LEONIDAS C. KOUTSOUGERAS ◽  
NICHOLAS ZIROS
Keyword(s):  
Second Welfare Theorem ◽  
Welfare Theorem

scholarly journals Exploring General Equilibrium Points for Cournot Model

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Bingyuan Gao ◽  
Yueping Du
Keyword(s):  
General Equilibrium ◽  
Demand Function ◽  
Competitive Equilibrium ◽  
Equilibrium Points ◽  
Structure Model ◽  
Cournot Model ◽  
Intermediate Value Theorem ◽  
Cournot Game ◽  
The Stability ◽  
Intermediate Value

In Cournot model, when there are many competitions, the competitive equilibrium becomes chaotic. It is extremely difficult to derive the general equilibrium points. There is no previous research to explore a further problem with the general equilibrium points of n-contenders in Cournot model. In this paper, a general equilibrium Cournot game is proposed based on an inverse demand function. A market spatial structure model is built. Intermediate value theorem, as a realistic method, is introduced to handle a general competitive equilibrium in Cournot model. The number and stability in general equilibrium points are detected by means of celestial motion theory and spatial agglomeration competition model. The existence of general equilibrium points and the stability of Cournot equilibrium points, which are new and future complement of previously known results. Numerical simulations are given to support the research results.

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