I need help with understanding the five periods of a Solow model with labor augmenting productivity (Z) growth. The savings rate is 12%, and the depreciation rate is 50%. The population is fixed (so N=1) and start with 1 unit of capital, and TFP = Z = 1 during the first period. Since TFP and population never change, output each period is created this way: Yt = Kt(1/3)Zt(2/3)

Consider two worlds:

1. Labor augmenting productivity (Z) grows 20% per period, and

2. Where labor augmenting productivity (Z) grows 10% per period.

Answer the following questions for each of the two worlds:

a. What is capital each year, in years 1-5?

b. What is GDP each year, in years 1-5?

c. What is the marginal product of capital each year (MPK) in years 1-5?

d. What is the wage in each period?

e. In steady state, what will MPK be?

f. In steady state, what will the market interest rate, MPK - (depreciation rate) be?