Econ 100CSolutions to Problem Set #3Fall 20091.A monopolist has the long run cost function of C(Q) = 250 + Q2. Inverse market demand is equal to P(Q) = 90 – 4Q. a.Assuming uniform pricing, find the monopolist’s profit maximizing price and quantity. What is the firm’s profit? ()()()()()( )()()( )22max904250905250First Order Condition:901009904 954No shutdown condition:2502509936.78549The firm should produce 9 units at a price of 54.QMMMQR QC QQ QQQQQQQPC QAC QQQQACPππ=−=−−+=−−∂=−=∂==−===+=+≈<=b.If the monopolist can practice first degree price discrimination, calculate the profit maximizing output, profit and consumer surplus. Explain pricing in this situation. QP15MCD = MRPS90
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A first degree price discriminating monopolist produces where marginal cost equals inverse demand. The price for each item is its marginal valuation. ()2904*15MC QQQQ==−=Profit is 0.5(15)(90) – 250 = 425. Consumer surplus is zero. c.In this particular situation would the first degree price discrimination be more desirable to society than uniform pricing? You don’t have to provide any calculations but briefly explain. It depends on how society values the monopolist relative to consumers. The first degree price discrimination transfers all of the consumer surplus plus the deadweight loss to the monopolist. 2.Inverse demand for gas in San Diego is P1(Q1) = 10 – Q1. Inverse demand in TJ is P2(Q2) = 6 – Q2. A single monopolist supplies gas for both markets. This monopolist’s short run cost function is C(Q) = 10 + 2.5Qwhere Qis the total produced in the two markets. Initially it is illegal to sell gas produced for one market in the other. a.Assuming no shutdown find the monopolist’s profit maximizing price and quantity in each market. ()()()()()()()1212112212,11221211122212max,106102.5First Order Conditions:1022.503.75622.501.75103.756.2561.754.25Q QMMMMQ QRQRQC QQQQQQQQQQQQQQPPπππ=+−+=−+−−++⎡⎤⎣⎦∂=−−=⇒=∂∂=−−=⇒=∂=−==−=