h10_ans - 1 =MR 2 = MC P 1 = 55 Q 1 TR 1 =P 1 Q 1 = Q 1...

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1 The Colorado College Department of Economics and Business Block 7 Econ 207 HW 10 ans. 1. (a) Q = 53 – P P = 53 – Q TR = P.Q. = 53Q – Q 2 MR = d(TR)/dQ = 53 – 2Q For maximum profits, set MR = MC: MR = 53 – 2Q = MC = 5. Q = 24, P = 29. Profit = P.Q – AC.Q = 29(24) – 5.(24) = 24(24) = 576. At Q= 0, P =53. Consumer surplus = ½(24)(53-29) = 288. (b) If the monopolist was forced to charge a perfectly competitive price then P = MC 53 – Q = 5 Q = 48. P = 5. (c) DWL = ½ (29-5)(48-24) = 288. 2. (a) A multiple plant monopolist maximizes profits where MR = MC 1 =MC 2 2 1 2 1 2 2 100 ) ( ) ( q q dq TR d dq TR d - - = = = MR Setting MR = MC 1 100-2q 1 -2q 2 = q 1 -5 => 105 –3q 1 = 2q 2 (1) 100-2q 1 -2q 2 = 0.5q 2 -5 MC = AC P=AR MR Q P, C, Rev A B C DWL 29 24 5 48 53 53
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2 => 105 – 2q 1 = 2.5q 2 q 1 = (105 – 2.5q 2 )/2 (2) Using (2) in (1), 2q 2 = 105 – 3(105-2.5q 2 )/2 2q 2 = 105 – 157.5 + 3.75q 2 52.5 = 1.75q 2 q 2 = 52.5/1.75 = 30 . Solving next for q 1 we get, q 1 = 15 . Q = 15 +30 = 45 . (b) For a price discriminating monopolist, equilibrium condition is MR
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Unformatted text preview: 1 =MR 2 = MC P 1 = 55 Q 1 TR 1 =P 1 Q 1 = Q 1 (55-Q 1 ) = 55Q 1 Q 2 1 MR 1 = d(TR 1 )/dQ 1 = 55 2Q 1 Setting, MR 1 =MC => 55 2Q 1 = 5 Q 1 = 25. P 1 = 55-25 = 30. Profit in market 1 = P 1 Q 1 Q 1 (AC) = 30(25) 25(5) = 750 125 = 625. Q 2 = 70- 2P 2 2P 2 = 70 - Q 2 P 2 = 35 - .5 Q 2 TR 2 = P 2 Q 2 = 35Q 2- .5Q 2 2 MR 2 = d(TR 2 )/dQ 2 = 35 Q 2 Setting, MR 2 =MC => 35 Q 2 = 5 Q 2 = 30 P 2 = 35-.5(30) = 35 -15 = 20. Profit in market 2 = P 2 Q 2 Q 2 (AC) = 20(30) 30(5) = 600 150 = 450 Total profits = 625+450 = 1075. 3. (a) Q = 70 P P = 70 Q TR = P.Q = 70Q Q 2 MR = 70 -2Q. TC = .25Q 2 5Q + 300. MC = d(TC)/dQ = .5Q 5 (b) Profit maximization occurs at MR = MC 70 2Q = .5Q 5 75 = 2.5Q Q = 75/2.5 = 30 P = 70 30 = 40 Profits = TR TC = 40(30) [.25(30) 2- 5(30) + 300] = 1200 375 = 825. 3 (c) At Q = 0, P = 70 Consumer surplus = (70-40)(30) = 450....
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h10_ans - 1 =MR 2 = MC P 1 = 55 Q 1 TR 1 =P 1 Q 1 = Q 1...

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