I only need parts d and e answered please!I have already gotten parts a, b, and c. I ONLY NEED D AND E PLEASE 3. Suppose that QED Inc.'s production function is given by F(L,K) = 4.L¹/2K1/2, where L denotes thequantity of labor and K denotes the quantity of capital. In addition, P₁ is the price of labor per unit oflabor (i.e., the wage rate), PHB is the cost of health benefits per unit of labor, and Pk is the price ofcapital.a) In the short run, suppose that the initial quantity of capital, Kō, is 400 units; i.e., K = 400. DeriveQED's initial short run total product of labor function, TP₁, its marginal product of labor function,MP₁, and its average product of labor function, AP₁.b) Suppose that initially the price of labor (wage rate) is $12 per unit of labor (P₁ = $12), the cost ofhealth benefits is $4 per unit of labor (PHB = $4), and the firm's marginal revenue is $4 per unit(MR = $4). Given the initial quantity of capital, K₁ = 400, derive the firm's marginal revenueproduct of labor function, MRP₁, and its marginal factor cost of labor function, MFC₁.c) Suppose that QED initially employs 225 units of labor along with the 400 units of capital, i.e.(Lo,K₁) = (225, 400). Calculate the firm's initial output level, Q. Is the firm maximizing its short runprofits by hiring L₁ = 225 units of labor? Explain. If not, calculate the short run profit maximizingquantity of labor, LSR*, and the SR profit maximizing output level, QSR*.d) Using the cost minimization approach and given the output constraint Q = 4.L¹/2K¹/2 and the inputprices, P₁, PHB, and Pk, (no longer set equal to the above initial values), construct the Lagrangianfunction. Derive the firm's input demand functions for labor and capital: L = g(Q;P₁,PHB,PK); and, K=h(Q;PL,PHB, PK). Derive the firm's long run total cost function, LRTC(Q;P₁,PHÂ‚Pk).e) Given P₁ = $12, PHB = $4, and Pk = $64, calculate the long run optimal input bundle, (L*,K*), forproducing QSR*-determined in part c) above-and the long run total cost at QSR*, LRTC(QSR*).

QED production function : F(L ,K ) = 4L0.5K0.5 Cost constraint : C = Pl*L + Pk*K Optimization…

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, P₁ 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) In the short run, suppose that the initial quantity of capital, Ko, is 400 units; i.e., Ko = 400. Derive QED's initial short run total product of labor function, TP₁, its marginal product of labor function, MP₁, and its average product of labor function, APL. b) Suppose that initially the price of labor (wage rate) is $12 per unit of labor (P₁ = $12), the cost of

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, P₁ 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) In the short run, suppose that the initial quantity of capital, Ko, is 400 units; i.e., Ko = 400. Derive QED's initial short run total product of labor function, TP₁, its marginal product of labor function, MP₁, and its average product of labor function, APL. b) Suppose that initially the price of labor (wage rate) is $12 per unit of labor (P₁ = $12), the cost of

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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