Please Solve

5. Consider a representative rm with the following real prot function over their two-period planning horizon: - a o: . it"s-1'" wane ins\" Prof=t=(1T)lk1\"i 'w1\"1)_i\"\"id+l1_7l( if? _ 1+1\") 1:1' where T is a tax on the rm's revenues less wage expense, lth m] = kiln?\" is the Cobb- Douglas production function, as is the real wage rate paid to labor input m, r is the real interest rate, and imrlmt is the real flow of net investment dened as: :7an = n+1 (1 as where It: is the current-period real stock of capital which depreciates at rate 5 >2 0. Assume that in is predetermined. (a) Using the real prot function, derive the optimality conditions for 124,112, and k2. (h) Let the demand for the rm's output he represented by q; = nk". Use the optimality conditions from part (a) to express the rm's demand function for labor in periods 1 and 2, and the rm's demand function for capital in period 2, as derived demand function. (c) Use your demand functions from part (b) to derive an expression for the capital labor ratio #2 a: In; it. (:1) Use comparative static analysis on your answers from part (c) to show mathematically how an increase in the tax rate affects the rm's demand for capital relative to labor. (e) With reference to the marginal products of capital and labor, explain the economic intuition for your result in part [d]