Question

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You are the manager of a monopoly, and your demand and cost functions are given by P 200-2Q and C (Q) -2,000+30 , respectively. What price would maximizes your firm's profits? a.

Answer 1

A) price = $160

TR = PQ = 200Q - 2Q^2

MR = dTR/dQ = 200 - 4Q

C(Q) = 200 + 3Q^2

MC = dC(Q) /dQ = 6Q

At Profit maximization, MR = MC

200 - 4Q = 6Q implies Q = 20

P = 200 - 2(20) = 160

B) quantity = 20

C) maximum profit = 0

profit = 160*20 - ( 2000 + 3(20)^2) = 3,200 - 3,200 = 0

D) price = 100 and quantity = 100

put MR = 0

200 - 4Q = 0 implies Q = 50

P = 200 - 2(50) = 100

E) unit elastic

price elasticity of demand = dQ/dP * P/Q = -2 *50/100 = -1