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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
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 | ||||||||
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| Subjects: | H Social Sciences > HC Economic History and Conditions Q Science > QA Mathematics |
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| 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: |
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| 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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