Consider a Solow economy with the following production function

F(K, N) = z K^1/3 N ^2/3

and parameters d = 0.05, s = 0.2, N0 = 100 and z = 1.0. Suppose K = 300 in period 0 and the unit period is one year. In contrast to the standard Solow model, we assume that the population growth rate n is no longer exogenous but rather endogenous and determined by

(1 + n) = N ' / N = g(C/N) = (C/N) ^3

as it is the case in the Malthusian model.

1. Determine the dynamics for the per worker capital (k).

2. Determine the per capita quantities k, y, c and the aggregate quantities K, C and Y of the capital stock, consumption and output for years 1, 2 ,3, 4 and 5. Summarize your results using a table.

3. Find k *the steady state per-capita capital stock, consumption per capita (c *) and output per capita (y* ).

4. Show that in the steady state, the population grows at a constant rate. What is this rate?