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Title:   Complete closedform solution to a stochastic growth model and corresponding speed of economic recovery 
Authors:   Feicht, Robert Stummer, Wolfgang 
Issue Date:   2010 
Series/Report no.:   IWQW discussion paper series 05/2010 
Abstract:   We consider a continuoustime neoclassical onesector stochastic growth model of Ramseytype with CRRA utility and CobbDouglas 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. shortterm) timehorizon 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 nonequilibrium sample paths of the per capita effective capital stock kt = Kt / At Lt . Moreover, we also deduce explicitly the limiting longterm behaviour of kt expressed by the corresponding steadystate 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 realisticsize timeperiod. 
Subjects:   stochastic Ramseytype growth utility maximization stochastic differential equations explicit closedform sample path dynamics economic recovery Monte Carlo simulations steadystate 
Document Type:   Working Paper 
Appears in Collections:   IWQW Discussion Paper Series, FAU ErlangenNürnberg

 

 
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