Question: In the text we focus attention on the case in which household utility features a finite intertemporal substitution elasticity. As an extension we now
In the text we focus attention on the case in which household utility features a finite intertemporal substitution elasticity. As an extension we now study the case for which marginal utility is constant. The lifetime utility function (13.57) is replaced by: A (0) E = Lo c(t)e Pdt, where c(t) is consumption per worker. We study the social planning solution to the household optimization problem. The fundamental differential equation for the capital stock per worker, k(t), is: k(t) = f (k(t)) c(t) (8+n) k(t), (Q13.23) where y(t) = f (k(t)) is output per worker. The production function satisfies the In- ada conditions and there is no technological progress. The solution for consumption must satisfy the following constraints: c(t) f (k(t)), (Q13.24) where is some minimum consumption level (it is assumed that 0
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