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Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth

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Burger, Martin, Lorz, Alexander and Wolfram, Marie-Therese (2017) Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth. Kinetic and Related Models, 10 (1). pp. 117-140. doi:10.3934/krm.2017005

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Official URL: http://doi.org/10.3934/krm.2017005

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Abstract

In this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas and Moll [15] to model knowledge growth in an economy. Agents can either increase their knowledge level by exchanging ideas in learning events or by producing goods with the knowledge they already have. The existence of balanced growth path solutions implies exponential growth of the overall production in time. We prove existence of balanced growth path solutions if the initial distribution of individuals with respect to their knowledge level satisfies a Pareto-tail condition. Furthermore we give first insights into the existence of such solutions if in addition to production and knowledge exchange the knowledge level evolves by geometric Brownian motion.

Item Type: Journal Article
Subjects: H Social Sciences > HC Economic History and Conditions
Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Knowledge economy -- Mathematical models, Brownian motion processes
Journal or Publication Title: Kinetic and Related Models
Publisher: American Institute of Mathematical Sciences
ISSN: 1937-5093
Official Date: March 2017
Dates:
DateEvent
March 2017Published
November 2016Available
21 September 2016Accepted
Volume: 10
Number: 1
Page Range: pp. 117-140
DOI: 10.3934/krm.2017005
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Österreichische Akademie der Wissenschaften [Austrian Academy of Sciences], France. Agence nationale de la recherche (ANR)
Grant number: ANR-13-BS01-0004 (ANR)

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