Let's work out 5 periods of a Solow model with labor augmenting productivity (Z) growth. In your toy economy, the savings rate is 10% and the depreciation rate is 50% (the high depreciation rate will get us to steady-state faster--think of each period as a decade). Population is fixed (treat it as one worker, N=1 forever). You always start off 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: One where labor augmenting productivity (Z) grows 20% per period, and one where labor augmenting productivity (Z) grows 10% per period

Answer the following questions for each of the two worlds

1. What is capital each year, in years 1-5?
2. What is GDP each year, in years 1-5?
3. What is the marginal product of capital each year (MPK) in years 1-5?
4. What is the wage in each period?
5. In steady state, what will MPK be?
6. In steady state, what will the market interest rate, MPK - (depreciation rate) be?