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 capital 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. Summarise your results using a table.

3. Find k *the steady-state per-capital 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?

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