The production function of a typical firm in the economy is Cobb-Douglas: Y = 2KN1-Q. Today, the firm owns some capital stock K and decides how much capital it needs in the future, knowing that the future level of capital stock will depend on its investment expenditures in the following way: K' = (1 -d). K +I If the firm doesn't want to invest in new capital stock, it has the option to purchase government bonds which pay the annual real interest rate of r. We will make one more simplifying assumption: the price of the good the firm produces is the same as the price of capital goods (machines). (a) For a typical firm, what is the marginal benefit of increasing future capital stock by 1 unit, expressed in units of future output? (b) For a typical firm, what is the marginal cost of increasing future capital stock by 1 unit, expressed in units of future output? (c) Equate marginal benefit and marginal cost from parts (a) and (b). Solve for K'. d) Use the solution from (c) and plug it back into the law of motion for capital stock: K' = (1 - d). K + 1. Solve for I. (2) In part (d), you derived the analytical formula for investment demand as a function of (among other things) the real interest rate r. On the graph below, plot the graph of the investment demand I(r). Show the effect of a destruction of part of today's capital stock. r The production function of a typical firm in the economy is Cobb-Douglas: Y = 2KN1-Q. Today, the firm owns some capital stock K and decides how much capital it needs in the future, knowing that the future level of capital stock will depend on its investment expenditures in the following way: K' = (1 -d). K +I If the firm doesn't want to invest in new capital stock, it has the option to purchase government bonds which pay the annual real interest rate of r. We will make one more simplifying assumption: the price of the good the firm produces is the same as the price of capital goods (machines). (a) For a typical firm, what is the marginal benefit of increasing future capital stock by 1 unit, expressed in units of future output? (b) For a typical firm, what is the marginal cost of increasing future capital stock by 1 unit, expressed in units of future output? (c) Equate marginal benefit and marginal cost from parts (a) and (b). Solve for K'. d) Use the solution from (c) and plug it back into the law of motion for capital stock: K' = (1 - d). K + 1. Solve for I. (2) In part (d), you derived the analytical formula for investment demand as a function of (among other things) the real interest rate r. On the graph below, plot the graph of the investment demand I(r). Show the effect of a destruction of part of today's capital stock. r