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ps2 - Problem Set 2(Due on 8th Oct ECON105 Industrial...

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Problem Set 2 (Due on 8th Oct) ECON105 Industrial Organization and Firm Strategy Professor Michael Noel University of California San Diego 1. Imagine there are ten consumers, each with individual demand curve: D i (q) = i q, where i=1..10. Note that consumers now have multiunit demands, but their demand curves differ. Assume a first degree price discriminating monopolist’s c ost function is C(Q) = Q/2, where Q = q 1 +…+q 10 . If a monopolist can perfectly price discriminate, find its profits and the consumer surplus to each consumer. 2. A monopolist faces the inverse market demand curve D(Q) = 1 - Q, and cost function C(Q) = cQ where c < 1. Assume the demand curve is made up of many consumers each with unit demand for this good (ie. each consumer will either buy one or nothing and the market demand curve is the aggregation of all these unit-demand consumers.) a. If the monopolist cannot price discriminate, find the equilibrium price, total quantity, profits, consumer surplus and welfare. (This is similar to questions 1a and 1j). b. What assumptions are necessary for the monopoly to be able to perfectly (1 st degree) price discriminate? c. If the monopolist can perfectly (1 st degree) price discriminate, solve for profits, consumer surplus, and welfare. (Hint: since consumers have unit demand, the “package” contains exactly one good and every consumer receives a price equal to her valuation. Don’t be confused, the “package price” and the “per unit price” is the same thing, because of unit demand.) Compare these outcomes to part a. d. Now assume that that arbitrage is possible, but the monopolist does not realize this until after all goods are sold. Each consumer still has unit demand (ie. has no personal use for more than one) but can now buy more and resell as many as it likes in the open market. Find the monopolist’s profits, consumer surplus, and welfare in this case. Hint: we haven’t done this exact problem in class so think carefully about who will buy and resell. Then think about what the monopolist ends up selling, to whom, and for how much.) Compare your answer to part a.

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e. If the monopolist is aware that this kind of arbitrage will occur, what price should it charge to each consumer (which may vary consumer to consumer) to maximize profits? f. Comparing your answers in c. and e., does welfare increase or decrease because of arbitrage? Does consumer surplus increase or decrease because of arbitrage? . g. (Challenging.) Assume again arbitrage is not possible, but now imports of the identical good are allowed into the country at a competitive and constant price 1 > p o > c. Find profits to the monopolist, consumer surplus and welfare, and compare this to your previous answers. Hint: draw a diagram of the demand curve and think about the surplus
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ps2 - Problem Set 2(Due on 8th Oct ECON105 Industrial...

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