Question: 3. Suppose that QED Inc.'s production function is given by F (L, K) = 4-L1'2K1'2, where L denotes the quantity of labor and K denotes

3. Suppose that QED Inc.'s production function is given by F (L, K) = 4-L1'2K1'2, where L denotes the quantity of labor and K denotes the quantity of capital. In addition, PL is the price of labor per unit of labor (i.e., the wage rate), PHB is the cost of health benefits per unit of labor, and PK is the price of capital. a) Suppose that initially the price of labor [wage rate) is $12 per unit of labor (PL = $12), the cost of health benefits is $4 per unit of labor (PHI; = $4), and the firm's marginal revenue is $4 per unit (MR = 54). Given the initial quantity of capital, K0 = 400, derive the firm's marginal revenue product of labor function, MRPL, and its marginal factor cost of labor function, MFCL. b) Suppose that QED initially employs 225 units of labor along with the 400 units of capital, i.e. (loin) = (225, 400). Calculate the firm's initial output level, 00. Is the firm maximizing its short run profits by hiring L0 = 225 units of labor? Explain. If not, calculate the short run profit maximizing quantity of labor, Lsa\

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