Question

1) Company XYZ has a monopoly on a new product. The product can be manufactured in either of two factories. The costs of production for the two factories are LaTeX: C_1=5Q^2_1C 1 = 5 Q 1 2 and LaTeX: C_2=10Q^2_2C 2 = 10 Q 2 2. The firm’s demand for the product is P = 500- 4Q. a. (10) Find the quantity produced by factory 1, the quantity produced by factory 2, the total quantity produced, and the price that maximize profit. b. (10) There is an increase in the cost of labor in Factory 1 but the cost of labor in Factory 2 remains the same. How will this increase in labor cost affect the quantity produced in Factory 1? the quantity produced in Factory 2? Total output? Price?

Answer 1

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solution o- criven p= 500-4Q and Q=Qit QR Therefore total revenue is TR =PQ = (500-400Q 402 A TR = 500Q Marginal Revenue MR = d (TR) da Ed [sooQ-402 2 = MR = 5oo. asoo 500-2(40) 500-BQ- substitute Q=Q1+O2 in MR, we get 500-8 (217Q2) 801-802 Scost of prouction in forctory I' is ci= 50,2 MC = d (CD = (5Q? 10Q, dal cost of production on factory's 'is (2=1092 Merginal cost is Mc2 = d (62) 10 (20) 2002: » profit maxpmization condition for d - factory 1 is MR=MCI a 500- 80,- 80,- 802= 100, -1821-893=-500

Q2 = 250-90) Ч > Q2= 62-5-2-25Q, Now profit maximizing condition for 2 is MR= MC2 > 500-80,-802 = 2002 > -80,- 28Q2 = 500 20, +7Q2 =125 fauctory W from o Q2 = 6205–2-25QI 20, +7Q2 =125 20, +7 (625-2-250)=125 3) 2011 4375- 15-150 =125 -13-750 -312-5 Qi 312-5 13-75 + Q, 2 22.727. To get(Q2 ) Q2 = 62.5-2-250, B = 62-5-2-25 (22-727 Q2 = 62-5- 513575 Q2 = 62-5-51-13575 Q2 C 1103642 → Therefore, Factory I must poroduce 22.727 units. and factory 2 will produce 11-364 units. Total Quantity produced = Q1 +Q2 = 22.727+ 11-364 Q = 34-09) units

*price change = P =500-4Q 500-4 (34-091) 500- 136-364 =$363636 = $363.636

since there is an increase in cost of Cubor in fauctory 1, MC curve will move (or) shift upward Therefore, Me will cut MR, at lower Quantity. Hence' will fallo Anyway 11 MO Qg will stay unchanged → However as "Q,"falls; the total output Q=(@it Q2) will fall and price p=500-4Q will rise as 'a'falls.