Consider the following numerical example using the Solow growth model. Suppose that F (K, N) = zK1/2N 1/2 Furthermore, assume that 5% of the capital is lost each period due to depreciation, the population grows by 1% each period, the consumer in this economy saves 20% of his income and the total factor productivity is z = 2. The unit period is one year.

1. Find the steady state per-capita quantity of capital (k*), production (y*) and consumption (c*).

2. Find the steady state quantity of capital per worker that maximize consumption per worker in this model.

3. Derive the golden rule steady state per-capita consumption (c**), production (y**) and saving (s**).