Question

Consider the standard Solow growth model. Let productivity be denoted by A and let the production function be Y=AF(K,N). For Simplicity, assume that there is no population growth (n=0 so that N' = N). let depreciation be denoted by d and the savings rate by s.

a) Derive the per capita capital accumulation equation for k=K/N and the steady state level of capital per worker, ??^ss . Please show the details of your derivation to earn points. Draw the Solow model graph showing the savings line and the depreciation line and marking the steady state level of k.

b) Now, consider the “AK model” with production function ?? = ???? , where A is the exogenous productivity level. Again, assume that there is no population growth in the economy. Follow the similar steps in part a. to derive the capital accumulation equation in terms of capital per capita ??.

c) Based on the equations you derived in part b, draw a graph similar to that of the Solow growth model to show the steady state of the model in part b. If you cannot find such a steady state, please explain why.

d) . Recall that Solow growth model implies convergence in capital per capita. Does the model in part b has this feature?

Answer 1