Question;Industrial Organization;June 4, 2014;Problem Set 2;Due: Monday, June 9;1. A monopoly with constant marginal costs of $50 can sell to three groups of potential con-;sumers, with demandsQ1= 800????0:2p,Q2= 400????p, andQ3= 700????0:4prespectively.;Find the optimal price-quantity combination in each market;(a) if the rm is able to price-discriminate;(b) if it is not able to price-discriminate.;2. A rm with costsC(Q) = 1,000 + 60Q+ 0:1Q2is able to price-discriminate between two;groups of customers, with demandsQ1= 3,000????2p, andQ2= 350????0:5prespectively. How;much does it sell to each group, and at what price? What would happen if it were forced to;charge all its customers the same price?;3. A marketing order for oranges has a xed total supply ofQ= 1,000 crates a month. Demand;in the market for fresh oranges isQ1= 220????0:2pand that in the market for processed orange;products isQ2= 1,000????2p. Calculate the competitive market-clearing price. What is the;deadweight loss in both markets if the price of a crate of fresh oranges is raised to $200?;4. A monopolist has two sets of customers. The inverse demand for Group 1 is described by;P= 200????X. For Group 2, the inverse demand isP= 100????2X. The monopolist faces;constant marginal cost of 40;(a) Show that the monopolist's total demand, if the two markets are treated as one is;X= 0,P200;X= 200????P, 100< P200;X= 250????(3=2)P, 0< P100;(b) Show that the monopolist's prot maximizing price isP= 120 if both groups are to be;charged the same price. At this price, how much is sold to members of Group 1 and;how much to members of Group 2? What is the consumer surplus of each group? What;are total prots?;5. Now suppose that the monopolist in #4 can separate the two groups and charge separate;prot-maximizing prices to each group;(a) What will these prices be? What is consumer surplus? What are total prots?;(b) If total surplus is consumer surplus plus prot, how has price discrimination a;ected;total surplus?
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