Answer to Question #120521 in Microeconomics for christopher

Question #120521
A monopolist faces two totally separated markets with inverse demand p=100 – qA and p=160−2qB respectively. The monopolist has no fixed costs and a marginal cost given by mc= 2 /3 q Find the profit maximizing total output and how much of it that is sold on market A and market B respectively if the monopoly uses third degree price discrimination.
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Expert's answer
2020-06-09T16:23:11-0400

Marginal Costs (MC) = 23q\frac {2}{3}q

Market 1 Inverse demand fxn: P=100 – qA

Total Revenue (TR) = P*Q

TR = (100Q)×Q(100 – Q) \times Q

TR = 100QQ2100Q – Q^2

MR = ΔTR/ΔQ=(100QQ2)/ΔQ\varDelta TR / \varDelta Q = (100Q – Q^2)/ \varDelta Q

MR = 100 – 2Q

Market 2 Inverse demand fxn: p=160−2qB

Total Revenue (TR) = P×QP\times Q

TR = (1602Q)×Q(160 – 2Q) \times Q

TR = 160Q2Q2160Q – 2Q^2

MR = ΔTR/ΔQ=(160Q2Q2)/ΔQ\varDelta TR / \varDelta Q = (160Q – 2Q^2)/ \varDelta Q

MR = 160 – 4Q

Equilibrium

MR = MC

Market 1: 1002Q=23Q100 – 2Q = \frac{2}{3}Q

83Q=100\frac{8}{3}Q = 100

Q = 100×38100\times \frac{3}{8}

Q1=37.5Q_{1} = 37.5

P = 100 – Q

P = 100 – 21.43

P = 78.57

TR = 100QQ2100Q – Q^2

TR = 100(37.5)37.52100(37.5) – 37.5^2

TR = 160(37.5)2(37.52)160(37.5) – 2(37.5^2)

TR = 2,343.75

Market 2: 160 – 4Q = 2/3Q

14/3Q = 100

Q = 100×314100\times \frac{3}{14}

Q2=21.43Q_{2} = 21.43

P = 160 – 2Q

P = 1602×21.43160 – 2\times21.43

P = 160 – 42.86

P = 117.14

TR = 160Q2Q2160Q – 2Q^2

TR = 160(21.43)2(21.432)160(21.43) – 2(21.43^2)

TR = 3,428.8 – 918.4898

TR = 2,510.31


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