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Complete Closed-form Solution to a Stochastic Growth Model and Corresponding Speed of Economic Recovery preliminary

  • Robert Feicht
  • Wolfgang Stummer
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    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.

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    File URL: http://degit.sam.sdu.dk/papers/degit_15/c015_041.pdf
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    Paper provided by DEGIT, Dynamics, Economic Growth, and International Trade in its series DEGIT Conference Papers with number c015_041.

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    Length: 29 pages JEL Classification:
    Date of creation: Sep 2010
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    Handle: RePEc:deg:conpap:c015_041
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