Consider a dynamic representative rm's problem. This representative rm is given K unit of capital to produce in the current period. Firm can choose (current-period and future- period) labor demands and investment (to adjust future-period's capital stock) to maximize its presentvalue lifetime prot. Given that the market interest rate is 7" and the capital depreciation rate is 6 after production in each period. Let's further assume that this rm sells all the capital after future-period production. (a) Clearly denite the prot functions for both periods and write down this representative rm's problem. (b) Write down the optimal condition on investment. Intuitively explain the optimal condi tion. (c) Show the optimal investment curve is downward sloping respect to 7'. (d) Suppose K increases, graph the change of investment curve. Intuitively explain the changes on the graph you just drew. (e) Derive (graphically) the output supply curve