Question #47613

A monopolist produces from a single plant but sells it in two markets .The cost and demand curves are given by the following equations..
TC=Q2+10Q Q1=32-0.4P1 Q2=18-0.1P2
(A) Now calculate the profit maximizing values for Price, Output and total pure profit ?

Expert's answer

A monopolist produces from a single plant but sells it in two markets.

TC = Q^2+10Q, Q1 = 32 - 0.4P1, Q2 = 18 - 0.1P2, Q = Q1 + Q2.

(A) To calculate the profit maximizing values for price, output and total pure profit, we should find Q1 and Q2, for which MR1 = MC and MR2 = MC.

MC = TC' = 2Q + 10

P1 = 80 - 2.5Q1, P2 = 180 - 10Q2

MR1 = TR1' = (P1*Q1)' = 80 - 5Q1

MR2 = TR2' = (P2*Q2)' = 180 - 20Q1

MR1 = MC

80 - 5Q1 = 2Q1 + 10

7Q1 = 70,

Q1 = 10 units, P1 = 80 - 2.5*10 = $25

MR2 = MC

180 - 20Q2 = 2Q2 + 10

22Q2 = 170,

Q2 = 7.73 units, P2 = 180 - 10*7.72 = $102.8

TC = Q^2+10Q, Q1 = 32 - 0.4P1, Q2 = 18 - 0.1P2, Q = Q1 + Q2.

(A) To calculate the profit maximizing values for price, output and total pure profit, we should find Q1 and Q2, for which MR1 = MC and MR2 = MC.

MC = TC' = 2Q + 10

P1 = 80 - 2.5Q1, P2 = 180 - 10Q2

MR1 = TR1' = (P1*Q1)' = 80 - 5Q1

MR2 = TR2' = (P2*Q2)' = 180 - 20Q1

MR1 = MC

80 - 5Q1 = 2Q1 + 10

7Q1 = 70,

Q1 = 10 units, P1 = 80 - 2.5*10 = $25

MR2 = MC

180 - 20Q2 = 2Q2 + 10

22Q2 = 170,

Q2 = 7.73 units, P2 = 180 - 10*7.72 = $102.8

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