Q.4 Assume that the production functions of cloth (good C) and food (good F) are respectively Qo = AcLEKL, and Qp=ApLiKE a>8 where A and Ap are parameters. Assume that the markets for both goods and for both factor inputs are perfectly competitive. (a) Calculate the optimal quantities of labor and capital for producing one unit of good C in terms of w, r and the parameters. Simplify the expressions as much as you can. Denote the optimal values of L and K by L_? and }?5 (b) Calculate the optimal quantities of labor and capital for producing one unit of good F in terms of w, r and the parameters. Simplify the expressions as much as you can. Denote the optimal values of Lp and Kp by Lp and Kg. () Compute an expression for the unit cost of good C in terms of w, r and the parameters. (d) Compute an expression for the unit cost of good F in terms of w, r and the parameters. (e) Compute an expression for %'; in terms of > and the parameters. (f) (i) Compute an expression of ;%t, the market-determined labor-capital ratio in the cloth sector, in terms of ** and the parameters. (i1) Compute an expression of '; the market-determined labor-capital ratio in the food sector, in terms of and the parameters. (g) Corresponding to the following diagram, what are the equations for the following curves: SS, FF and CC? Wage-rental, wr Relative price (P./P)? (Pu/P:)! (LefKe )P (L) (LK) (LK) Labor- of cloth, P./Pg capital s _ ratio, Increasing Increasing LIK (h) (i) What is the economic intuition for the CC and FF curves to be downward sloping? (ii) What is the economic intuition for the CC curve to be to the right of the FF curve? (i) What is the economic intuition for the SS curve to be downward sloping? Relate your answer to the extreme case that = 0.9 and 5 =10.1