Question

In a monopoly market, if the firm's market demand function is reflected at P = 11,100 - 30 Q, while the company's total cost function is TC = 400.000 + 300Q – 30 Q²+ Q³

Determine:

a. the output level and selling price per unit that maximizes the company’s profit?

b. maximum total profit?

c. quantity at the socially optimum price (P = MC)?

d. quantity at the fair return price (P = ATC)?

Answer 1

Solution Demand Function is. P. 11,100 - 300 a ) 70 = 400.000 300-300?Q? TR =PQ FR = L1H100 - 300) Q TR 11.200Q. -30Q2 s T .TR TO T = || 2002, -30Q2-400.000-300Q +200 103 Maximize profit with respect to a an -11,100 -6OQ-300 + 602 -300 da Q = 10,800 -3Q? 3Q² = 10,800 Q? 18800 3 Que = 3,600 22 too substitute into the Price equation P= = 11,100 -3060) P = 11.100-1800 G - 9.300 CS Scanned with CamScanner

(b) Substitude into the total profit cocation: H, 1000 -30Q² =400,000 - 3000+ 30002-03 TT - 11,100 (3,60o) -363.600)2 - 400.000-30(360) + 30(3660)2-(3,600) 3 = 89.960,000 - 2 16,00,000 -400000 -1,019000+ 380,800 ,000 -4.6656060 - 36,480 poo -4.66566LO At the Secolly op finem price: - P = MC P = 11,100-300 TC- 400.000 7300 Q -30 G2 HQL 300 -60 Q te MC : P = MC 1,100 - 30Q = 300 boa +3Q -3Q? 10,400 302, t6oQ, -3QP-0 tool + 10,800 20 +30Q +10,100 - To find out the value of a obt5 b2_val -32 wa -305562022_4(-3) (1010 21-3) CS Scanned with CamScanner

- 30+ 1900 +19.9600 -6 = 30 + 366-249 -6 Q 265.208. (d) Quality at the fair retum Price P = ATC livom inftrmation is: Pa tt, 100 Q TO = 4109000 + 3000 70Q2+Q2 ATC = 400,000 +300Q -8002 103 Q ATG 4,00.000 +300-800 tQ? now equate 11,100-30Q =4,00,000 +300-30Q to? +1.100-30Q = 4000007 3000–2004@3 Q 1,100 Q-285 400.000 42000, – 30q4FQ3 400 1600 7309 - 11100 Q t Q = UQOÇO 0 - 10,000 Q-Q3 a = 72.260 and 46, hory. 2 CS Scanned with CamScanner