Extend the analysis of an OLG model (with no natural resource just a capital labor production function) to the case of a general utility function with a constant elasticity of marginal utility:
u'(c) = c1-?
Assume population grows at a rate 1+n and capital depreciates at the rate d.
Begin by finding the savings of each young generation (t) given the wage wt and the interest rate rt+1. What is the saving rate at time t as a function of these and the preferences (discount rate and elasticity of marginal utility).
Extend the analysis of an OLG model (with no natural resource just a capital labor production function) to the case of a general utility function with a constant elasticity of marginal utility:
u'(c) = c1-?
Assume population grows at a rate 1+n and capital depreciates at the rate d.
Begin by finding the savings of each young generation (t) given the wage wt and the interest rate rt+1. What is the saving rate at time t as a function of these and the preferences (discount rate and elasticity of marginal utility).
How does the savings rate depend on the interest rate? Does your answer depend on the value of the elasticity of marginal utility? Can you think of an explanation?
Assume a Coub-Douglass production function and deduce the dynamics of the capital stock in the economy by relating the wage and interest rate to the partial derivatives of the production function.
Now assume that technology grows at an exogenous rate 1+g. Repeat the analysis by using the same trick used to solve the Solow and Ramsey models with exogenous technological progress.
Attachments: