The Capital Accumulation Equation is determined by the following information, (write down step-by-step): \"Capital stock next year, $K_{t+1}$, comes from capital stock this year, $K_t$, depreciated by $\bar{d}$ and investment this year, $I_t$. Investment is a fixed proportion of $\bar{s}$ of output, $Y_t$. The output is given by $Y_t = \bar{A}K_t^{1/3}\bar{L}^{2/3} = \bar{A}K_t^{1/3}L^{2/3}$. Labor supply, $\bar{L}$, and productivity, $\bar{A}$, are exogenously constant.\" a. (4 pts) Express the capital accumulation equation in terms of capital stock, $K_t$, and per capita capital stock, $k_t = \frac{K_t}{\bar{L}}$. That is an equation for $K_{t+1}$ as a function of $K_t$ and $\bar{L}$ and an equation for $k_{t+1}$ as a function of $k_t$. (Hint: In terms of capital stock per capita, you can get the capital accumulation equation by dividing labor on both sides.)
