Please help

3. Suppose that QED lnc.'s production function is given by F(L.K) = 4-L""K"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). Pm, is the cost of health benets per unit of labor, and PK is the price of capital. III In the short run, suppose that the initial quantity of capital, K0, is 400 units: i.e., K, = 400. Derive QED's initial short run total product of labor function. TPL. its marginal product of labor function. MPL, and its average product of labor mction. APL. b) Suppose that initially the price of labor (wage rate) is $12 per unit of labor (PL = SIZE), the cost of health benets is $4 per unit of labor (Pun = $4). and the firm's marginal revenue is $4 per unit (MR = $4). Given the initial quantity ofcapital. K, = 400. derive the rm's marginal revenue product of labor function, MRPL, and its marginal factor cost of labor mction. MFCL. n Suppose that QED initially employs 225 units of labor along with the 400 units of capital, i.e. (1.0,Ko) = (225, 400). Calculate the rm's initial output level, 00. Is the rm maximizing its short run prots by hiring L0 = 225 units of labor? Explain. If not, calculate the short run prot maximizing quantity of labor, Lu', and the SR prot maximizing output level, On\". a) Using the cost minimization approach and given the output constraint 0 '' 4-L"3K'"3 and the input pn'ces. PL. PH... and PK. (no longer set equal to the above initial values), construct the Lagrangian function. Derive the rm's input demand functions for labor and capital: L = g(Q;PL,PHB,PK): and. K. = h(Q;PL,PHB.PK). Derive the firm's long run total cost function. LRTC(Q;PL,PHB,P'). eIGlVCII l'L = SIZ, Pm, = $4, and PK = $64, calculate the long run optimal input bundle. (L*.K'). for producing an'determined in part c) aboveand the long run total cost at QQ", LRTCthR")