The Average-Marginal Relationship and Tractable Equilibrium Forms

55 Pages Posted: 30 Dec 2012 Last revised: 27 Oct 2016

Michal Fabinger

University of Tokyo - Graduate School of Economics

E. Glen Weyl

Microsoft Research; Yale University

Date Written: October 26, 2016

Abstract

Economic variables with familiar tractable functional forms (constant-elasticity or linear) are only reweighted in the change from their average to marginal versions. They are also simple, featuring only one or two terms. These properties allow for closed-form solutions. We explicitly characterize all equilibrium systems obeying a generalization of these properties, showing they form a hierarchy of tractability. The resulting forms are more realistic (e.g. bell-shaped demand and U-shaped cost) but highly tractable. These forms have importantly different implications for policy analysis, as we illustrate with applications from innovation, industrial, international, auction and public economics.

The online appendix for this paper are available at the following URL: http://ssrn.com/abstract=2575471

Keywords: average, marginal, Laplace transforsm, tractability, closed-form solutions, supply-chain bargaining, labor bargaining, monopolistic competition

JEL Classification: C63, C68, D40, D58, E24, F11, H22, L10

Suggested Citation

Fabinger, Michal and Weyl, E. Glen, The Average-Marginal Relationship and Tractable Equilibrium Forms (October 26, 2016). Available at SSRN: https://ssrn.com/abstract=2194855 or http://dx.doi.org/10.2139/ssrn.2194855

Michal Fabinger

University of Tokyo - Graduate School of Economics ( email )

Tokyo
Japan

HOME PAGE: http://sites.google.com/site/fabinger/

Eric Glen Weyl (Contact Author)

Microsoft Research ( email )

641 Avenue of the Americas
7th Floor
New York, NY 10011
United States
(857) 998-4513 (Phone)

HOME PAGE: http://www.glenweyl.com

Yale University ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

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