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Complete closed-form solution to a stochastic growth model and corresponding speed of economic recovery

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  • Feicht, Robert
  • Stummer, Wolfgang

Abstract

We consider a continuous-time neoclassical one-sector stochastic growth model of Ramsey-type with CRRA utility and Cobb-Douglas technology, where each of the following components are exposed to exogeneous uncertainties (shocks): capital stock K, effectiveness of labor A, and labor force L; the corresponding dynamics is modelled by a system of three interrelated stochastic differential equations. For this framework, we solve completely explicitly the problem of a social planner who seeks to maximize expected lifetime utility of consumption. In particular, for any (e.g. short-term) time-horizon t > 0 we obtain in closed form the sample paths of the economy values Kt,At, Lt and the optimal consumption copt(Kt,At, Lt) as well as the non-equilibrium sample paths of the per capita effective capital stock kt = Kt / At Lt . Moreover, we also deduce explicitly the limiting long-term behaviour of kt expressed by the corresponding steady-state equilibrium distribution. As illustration, we present some Monte Carlo simulations where the abovementioned economy is considerably disturbed (out of equilibrium) by a sudden crash but recovers well within a realistic-size time-period.

Suggested Citation

  • Feicht, Robert & Stummer, Wolfgang, 2010. "Complete closed-form solution to a stochastic growth model and corresponding speed of economic recovery," FAU Discussion Papers in Economics 05/2010, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
  • Handle: RePEc:zbw:iwqwdp:052010
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    Cited by:

    1. Schnitzlein, Daniel D., 2012. "How important is cultural background for the level of intergenerational mobility?," Economics Letters, Elsevier, vol. 114(3), pages 335-337.
    2. Tinkl, Fabian, 2010. "A note on Hadamard differentiability and differentiability in quadratic mean," FAU Discussion Papers in Economics 08/2010, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    3. Herbst, Anthony F. & Wu, Joseph S.K. & Ho, Chi Pui, 2012. "Relationship between risk attitude and economic recovery in optimal growth theory," Global Finance Journal, Elsevier, vol. 23(3), pages 141-150.

    More about this item

    Keywords

    stochastic Ramsey-type growth; utility maximization; stochastic differential equations; explicit closed-form sample path dynamics; economic recovery; Monte Carlo simulations; steady-state;

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