Monopoly Price discrimination sol

Monopoly Price discrimination sol - COMM/FRE 295...

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1 COMM/FRE 295 Monopoly/Price discrimination Solutions to Practice Questions Question #1 ACME Widgets is a monopoly producer of widgets in the world. ACME faces 100 consumers, each with a demand curve of Q = 0.7- 0.02P and C(Q)=10+5Q. A. Find the optimal P and Q for ACME when it cannot price discriminate. Also find monopolist’s profits. Demand function: Q = 70 – 2P or P = 35 – ½Q MR = 35 – Q MC = 5 For profit maximization: MR = MC Q = 30 P = $20 Profits = R – C = PQ – (10 + 5Q) = 20*30 – (10+5*30) = ? B. Find DWL (social cost). Please use a diagram in your answer. Optimum solution is at P* = MC = 5; Q* = 70 – 2(5) = 60 DWL = (1/2)(20 – 5)(60 – 30) = $225 C. If ACME could perfectly price discriminate, what would be ACME’s Q? The optimal Q for a perfectly price discriminating monopolist = competitive Q = 60. D. Based only on the cost structure of ACME, is it conceivable that ACME is a natural monopoly? Yes ACME is a natural monopoly: Since AC= 5 + 10/Q, the AC is falling for all Q. E. What are two-part tariff P and Q? Usage fee P* = MC = 5. Entrance fee, T* = CS per consumer = 0.5 (35 – 5)(0.6) = 9.
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2 D (individual) $ Q MC =5.0 P*=5 35/50 35 T * =9 0.6 70 D 60 F. Is the two-part tariff equilibrium of part D more or less efficient than the perfect price discrimination equilibrium of part C? Please explain briefly. Two-part tariff and perfect price discrimination both lead to competitive Q and hence both maximize total surplus. Question #2 (a) Explain why a monopolist, if it chooses to sell a positive quantity, always sets a price in the elastic portion of its demand curve. If a monopolist did not do this – i.e. if it set a price in the inelastic part of its demand curve – then an increase in P would raise revenue. Since Q must fall with the increase in P, costs must fall and therefore the increase in revenue would also bring an increase in profits. The firm could not be at a profit-maximizing price, if it is possible to raise profits further. That is, any profit-maximizing price must be at a point where the elasticity of demand exceeds 1. Or: MR = P / (1 – 1/|e| ) and MR = MC which is positive, implying that |e| must exceed 1. (b) What are some of the practical challenges to be a successful 3 rd degree price discriminator? 1) Must be a price maker, i.e. face demand that is not perfectly elastic. 2) Must be able to identify different demand curves 3) Must be able to prevent arbitrage.
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3 Question #3 DGI is a highly profitable monopolist that sells satellite photos to farmers. The cost of launching the satellite was substantial, and the majority of the launch costs are fully sunk. DGI’s MC of supplying each photo = $5. Its annual non-sunk fixed cost is F. The farmers’ annual demand for photos is given by Q d = 100,000 – 5000P.
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This note was uploaded on 05/11/2011 for the course COMM 295 taught by Professor Ratna during the Winter '09 term at The University of British Columbia.

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Monopoly Price discrimination sol - COMM/FRE 295...

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