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

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  • 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 satisfiesa Pareto-tail condition. Furthermore we give first insights into the existence of such solutions if in addition to production and knowledge exchange theknowledge level evolves by geometric Brownian motion.

    Mathematics Subject Classification: Primary: 49J20, 49N90, 35Q20, 70H20, 35Q91.

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  • Figure 1.  Solution of the time dependent solver converging to a non-trivial BGP

    Figure 2.  Balanced growth path solutions for different diffusivities $\nu$

    Figure 3.  Comparison of the solvers in the case of a knowledge shock

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