Tropical analysis: with an application to indivisible goods

Nicholas Charles Bedard () and Jacob K Goeree ()
Additional contact information
Nicholas Charles Bedard: Department of Economics, Wilfrid Laurier University
Jacob K Goeree: Business School, University of New South Wales

Theoretical Economics, Forthcoming

Abstract: We establish the Subgradient Theorem for monotone correspondences -- a monotone correspondence is equal to the subdifferential of a potential if and only if it is conservative, i.e. its integral along a closed path vanishes irrespective of the selection from the correspondence along the path. We prove two attendant results: the Potential Theorem, whereby a conservative monotone correspondence can be integrated up to a potential, and the Duality Theorem, whereby the potential has a dual whose subdifferential is a conservative monotone correspondence that is the inverse of the original correspondence. We use these results to reinterpret and extend BaldwinKlemperer2019's BaldwinKlemperer2019 characterization of demand in economies with indivisible goods.

Keywords: Conservative correspondences; subgradient theorem; potential theorem; Fenchel duality; Fenchel's duality theorem; tropical geometry; convex analysis; normally labeled polyhedral subdivisions; subdifferentials; indivisible goods (search for similar items in EconPapers)
JEL-codes: C65 (search for similar items in EconPapers)
Date: 2024-12-04
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://econtheory.org/ojs/index.php/te/article/viewForthcomingFile/5831/40768/1 Working paper version. Paper will be copyedited and typeset before publication. (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:the:publsh:5831

Access Statistics for this article

Theoretical Economics is currently edited by Federico Echenique, Mira Frick, Pablo Kurlat, Juuso Toikka, Rakesh Vohra

More articles in Theoretical Economics from Econometric Society
Bibliographic data for series maintained by Martin J. Osborne ().