Question 3: Consider a firm that operates for two periods and produces output in both periods using the following production function: Y = 2K + 2NY The productivity level is z = 3 and 2' = 4. Capital in the current period is given as K = 8.57. a = 0.3 and y = 0.5. The depreciation rate is d = 0.10 and the interest rate is r = 0.10. The wage rate is w = 0.5 and w' = 0.5. Part A: Write down the value of the firm. Then solve for the firm's choice of optimal N, N' and K'. Part B: Assume now that instead of being able to sell 1 unit of capital at the end of the future period for 1 unit of consumption goods, the firm can sell 1 unit of capital for Pk = 0.8 units of consumption good. Solve for the firm's choice of optimal N, N' and K'. Part C: Determine the level of firm investment I as a function of r and pk. Plot the firm's demand for investment goods I, with the quantity of investment goods on the horizontal axis and the real interest rate r on the vertical axis. Part D: Assume that pk falls. How does this change the level of firm investment? Why? Explain in 1-2 sentences. Draw any changes in the firm's demand for investment goods on the graph in part C. Question 3: Consider a firm that operates for two periods and produces output in both periods using the following production function: Y = 2K + 2NY The productivity level is z = 3 and 2' = 4. Capital in the current period is given as K = 8.57. a = 0.3 and y = 0.5. The depreciation rate is d = 0.10 and the interest rate is r = 0.10. The wage rate is w = 0.5 and w' = 0.5. Part A: Write down the value of the firm. Then solve for the firm's choice of optimal N, N' and K'. Part B: Assume now that instead of being able to sell 1 unit of capital at the end of the future period for 1 unit of consumption goods, the firm can sell 1 unit of capital for Pk = 0.8 units of consumption good. Solve for the firm's choice of optimal N, N' and K'. Part C: Determine the level of firm investment I as a function of r and pk. Plot the firm's demand for investment goods I, with the quantity of investment goods on the horizontal axis and the real interest rate r on the vertical axis. Part D: Assume that pk falls. How does this change the level of firm investment? Why? Explain in 1-2 sentences. Draw any changes in the firm's demand for investment goods on the graph in part C