Consider an economy with its production possibilities represented by the function Y = A √ K √ L where Y represents total output (i.e GDP), K is capital, L is labor, and A is total factor productivity (TFP). This economy devotes a share of 30% of its output to gross investment. Capital depreciates at a rate of 10% per period. The TFP level is one and there are 2 units of labor available for production.

a) Suppose the economy starts with a capital stock at time t = 0 equal to 1 unit. Write down the values of gross investment, net investment, capital, consumption, and output observed during the subsequent 10 periods.

b) What is the steady state level of capital, assuming A = 1 and L = 2?

c) Suppose that at the beginning of some time period t = T there is an increase in the depreciation rate from 0.10 to 0.15. Write down the values of gross investment, net investment, capital, consumption, and output observed during the subsequent 10 periods. What is the new steady state value for capital? Discuss your results.