3 Two-Period Model with Endogenous Out- put 1. i: Suppose that the production function is given by new... N5) =31 1/3.; 1mg (7: = o, 1), where 31 is the total factor productivity. K1 is the capital and N: is the labor demand in each period. Denoting gross investment by In, interest rate by r and depreciation rate by d, write the firm's in- tertemporal profit maximization problem. 2. it K1 is detrimental to the firm in period o, i.e., E = 1. Why wouldn't the firm simply 1 set K1 2 [l to avoid reduction in Hg? 3. 1* Suppose d = a, 1 = % and Nil 2 16. Derive Kl') and 1700'). 4. In item 1 the firm sets their marginal profits with respect to capital equal to D in order to find the profit-maxilnizing level of inputs. How- ever, they do not do so when solving item 3 in section 1. Why not