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

Martin Burger, Alexander Lorz, Marie Therese Wolfram

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)117-140
Number of pages24
JournalKinetic and Related Models
Volume10
Issue number1
DOIs
StatePublished - Nov 18 2016

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