The Capital Accumulation Equation is determined by the following information, (write down step-by-step): “Capital stock next year, Kt+1, comes from capital stock this year, Kt depreciated by d and investment this year, t I. Investment is a fixed proportion of s of output, Yt. The output is given by 1/3 2/3 1/3 2/3 Y AK L AK L t t t t = =. Labor supply, L, and productivity, A, are exogenously constant.”

a. (4 pts) Express the capital accumulation equation in terms of capital stock, Kt, and per capita capital stock, t t K k L =. That is an equation for Kt+1 as a function of Kt and L and an equation for t 1 k + as a function of t k. (Hint: In terms of capital stock per capita, you can get the capital accumulation equation by dividing labor into both sides.)

b.  Numerical Example: Now suppose d s A and L = = = = 10%, 25%, 10, 8 , what is the capital accumulation equation expressed in both Kt and t k .

c.  Draw the Solow Diagram using the capital accumulation equation written in part (a), with Capital on the horizontal axis and depreciation and investment on the vertical axis. Draw investment and depreciation curves separately using the parameter specification from part (b).

d.  Solve for the Steady State level of capital, * K, in terms of parameters outlined in a), then apply for the numbers from part (b). Solve for the steady-state level of output, * Y , in terms of parameters.

e.  What is the long-run growth rate of output in the steady state according to the Solow model? What is an implication of the Solow model once an economy reaches the steady state?