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On a mean field model for knowledge growth

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Systemic Risk: Mathematical Modelling and Interdisciplinary Approaches

Lucas and Moll proposed a mean field model for knowledge growth, in which individuals can split their time between producing goods with their knowledge or increasing their knowledge level by meeting other individuals. These meetings are modeled by ‘collisions’, in which knowledge is exchanged. Hence the evolution of the knowledge distribution can by described by a Boltzmann type equation. The choice of how much time is spend on learning or producing goods, is determined by the overall production level. The resulting mean field model corresponds to an optimal control problem with a Boltzmann type constraint. We present first analytic results and discuss the existence of special equilibrium solutions. Furthermore we illustrate the behaviour of the model with numerical simulations.

This talk is part of the Isaac Newton Institute Seminar Series series.

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