1COMM/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, eachwith 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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