QUESTION 10 A monopolist is seeking to price discriminate by segregating the mar

Question

QUESTION 10 A monopolist is seeking to price discriminate by segregating the market. The demand in each market is given as follows: Market A: P 134- 2Q Market B: P = 1 64-4Q The monopolist faces a marginal cost of $19 and has no fixed costs. Given this information, what are the monopolists total profits across both markets when they price discriminate? Round your answer to two decimal places. Do not include a s sign Note: The demand equations presented above show P equal to a function of Q, rather than the usual other way around. This is so you can use the same trick used in Unit 11 to find the marginal revenue curve.

Explanation / Answer

Market A:

Revenue (R) = P x Q = 134Q - 2Q2

MR = dR/dQ = 134 - 4Q

Profit is maximized where MR = MC:

134 - 4Q = 19

Q = 28.75, P = 76.5

Profit = Q x (P - MC) = 28.75 x 57.5 = $1653.125

Market B:

Revenue (R) = P x Q = 164Q - 4Q2

MR = dR/dQ = 164 - 8Q

Profit is maximized where MR = MC:

164 - 8Q = 19

Q = 18.125, P = 91.5

Profit = Q x (P - MC) = 18.125 x 72.5 = $1314.0625

Total profit = 1653.125 + 1314.0625= $2967.19

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