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?

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 C1 = 5Qị and C2 = 10Q2. 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

The films demand for product is =) Marginal cost, MC1- Now cost of producton in factory 1 cost of production in factory 2, 62.5 -2.250 1 il 500 - 8Q1-8Q2 = 20 Q2 where Q = QAQ2 P= 500-4Q cal Now, Total revine, TR = Q = 500Q - 4Q? Marginal revine, MR = dCTR) 500-8Q da 500 - 8 (Q1+Q2) 5) MR= 500- 801-8Q2 Ci 5012 del= 5(201= 10Q1 do, = 10 (2Q 2) (2 = 10 Q 2² =) Marginal cost, MC2 - dC2 dQ2 = 20 Q2 condition for factory 1 c) Now profit maimising MR= Mel 500-801-8Q2 = 100, 1891-8Q2 = 500 qQ1 + 4Q2 = 250 250- 901 = ) Q2 = 4 =) Q2 = =) profit manimising condition in factory 2, MR= MC2 二ノ -80,- 28 Q2 - 500 2Q1 + 7Q2 = 125 =) CS Scanned with CamScanner

Q2 = 62.5-2.25Q, we guts 11.364 mits, tice, QI will fall. howeva, p=500-4Q will rise as Q balls. Substituting from equation is 2) -13.75Q1 = -312,5 Q1 = 22.727 2Q1+7Q2 = 125 -) 2Q1 + 7162.5- 2.25Q1) = 125 2) 2Q17 437.5 - 15,75Q1 = 125 AS Q2 = 62.5- 2,250, = 62.5 - 25 X 22.727 - 11.364 22.727 1 Should ce =(Qit Hance factory produce total quantity produced a 17Q2). = (22.727 +11.364)= 34.091 uits- & and price charred well be P-500-4Q = X34.4 091)=$363.636 500-14 1.091)=4 W As there is an increase in cost of labor in factory 1, Mel cure will shift upward, hence, mc, will cut MRI at relatively Unchanged. Howeves as al Total output Q=(Q1+Q2) will tall and price falls, Q2 will remain CS Scanned with CamScanner