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 Simon Board, Todd D. Sarver, Juuso Toikka, Rakesh Vohra, Pierre-Olivier Weill

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