4 Firm's 2-period investment problem. (10 points) Parts of this problem are based on question from chapter 11 in the book. Suppose we have a firm which series to mascimize the present value of its profit across two periode where is the real profit in period I. -'is the real pitafit in period 2 and r is the real interest rate. . In the first period, the firm is given only determined capital and chooses how much labor N to hire at wage w, and how much to invest I. Output is given by FK,N) = :K"Ni and Investment takes the form of output which is not scold. This tevens az N-I also first period protits are TK ---I-N Between periods, some portion of peexisting capital 5 depreciates, and investment is added to the capital stock, so the form for second period capital is *-*-(1-5)+1 In the second partiod, the firm choose how much labor to hire at the second period's real wage we'. And because time ends after the second period, the firm will delf any remaining capital stock (1-d) and so second period profits are given by Rez"(K)* (*)*** + R"- (1 - 0) 'N bleins() Set up the firm's present-value profit maximization problem (b) Set up the Lagrangiats and desive equations describing the firm's optimal labor-kuiring and investment decisions. These equations should show the optimal relationship between the firm's costs and the marginal product of labor or capital.) Now suppose that we modify the model of firm's investment behavior by assuming that any capital the firm has remaining at the end of period 2 can be sold at the price of Pk units of consumption goods in the setup above, we assumed the capital could be sold at a price of 1, in terms of consumption goods). (c) Write down the new equations for first period's profit cond period's ziotit, and the present value of profits across both time periode (d) Determits how this change affects the optimual investment rule for the firm. (C) Suppose that we interpret pik as the firm's stock price. Ifply increases, wit effect does this have on the firm's optimal investment schedule? (f) What does this imply about the relationsdip between investment expenditures and stock prices? 4 Firm's 2-period investment problem. (10 points) Parts of this problem are based on question from chapter 11 in the book. Suppose we have a firm which series to mascimize the present value of its profit across two periode where is the real profit in period I. -'is the real pitafit in period 2 and r is the real interest rate. . In the first period, the firm is given only determined capital and chooses how much labor N to hire at wage w, and how much to invest I. Output is given by FK,N) = :K"Ni and Investment takes the form of output which is not scold. This tevens az N-I also first period protits are TK ---I-N Between periods, some portion of peexisting capital 5 depreciates, and investment is added to the capital stock, so the form for second period capital is *-*-(1-5)+1 In the second partiod, the firm choose how much labor to hire at the second period's real wage we'. And because time ends after the second period, the firm will delf any remaining capital stock (1-d) and so second period profits are given by Rez"(K)* (*)*** + R"- (1 - 0) 'N bleins() Set up the firm's present-value profit maximization problem (b) Set up the Lagrangiats and desive equations describing the firm's optimal labor-kuiring and investment decisions. These equations should show the optimal relationship between the firm's costs and the marginal product of labor or capital.) Now suppose that we modify the model of firm's investment behavior by assuming that any capital the firm has remaining at the end of period 2 can be sold at the price of Pk units of consumption goods in the setup above, we assumed the capital could be sold at a price of 1, in terms of consumption goods). (c) Write down the new equations for first period's profit cond period's ziotit, and the present value of profits across both time periode (d) Determits how this change affects the optimual investment rule for the firm. (C) Suppose that we interpret pik as the firm's stock price. Ifply increases, wit effect does this have on the firm's optimal investment schedule? (f) What does this imply about the relationsdip between investment expenditures and stock prices