2. GSL Cha ter 12 uestion 2 a Suppose that you have a rm with a Cobb-Douglas production function for production in period t: Y: = ArKiINr1_ The only twist relative to our setup in the main text is that the firm does not use labor to produce output in period H I . The production function in that period is: _ [2 \"2+1 1me {a} Write down the optimization problem for the rm in this setup. It has to pay labor in . . . i . 1 . . period t. wi, and It discounts future dividends by F' It must borrow to finance its investment I at n. The capital accumulation equation is standard. (b) Using this specification of production, derive the rst order optimality conditions for the optimal choices of N: and Km. (c) Rearrange the first order optimality conditions to derive explicit expression for the demand for N: and the demand for Km