answer all with equations

Consider the following numerical example using the Solow growth model. Suppose that F(K, N) = zK 1 3 N 2 3 and d = 0.10, so = 0.2, n = 0.02, N = 100 and z = 1. Suppose K = 400 in period 0 and the unit period is one year. Suppose that the economy is initially in the steady state (at t=0) and in year one (t=1) saving rate increase to 0.4 and stay there forever. [hint: k 0 = szf(k) + (1 d)k 1 + n And Aggregate quantities are given by, eg. X = x N where x = X N , where x is per-worker quantity]

1. Find k ? the steady state per-capita capital stock, consumption per capita (c ? ) and output per capita (y ? ) for time t = 0. 2.

2. Determine the golden rule saving rate, s, capital per worker, k ? gr, output per capita, y ? gr, and consumption, c ? gr for time t=0 3.

3.Determine 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.