(a) Draw the cost, demand, and marginal-revenue curves for the mo- nopolist. Show the price the monopolist would charge without price discrimination. See graph below. 6
(b) In your diagram, mark the area equal to the monopolist’s profit and call it X . Mark the area equal to consumer surplus and call it Y . mark the area equal to the deadweight loss and call it Z . See above. (c) Now suppose that the monopolist can perfectly price discriminate. What is the monopolist’s profit? (Give your answer in terms of X, Y, and Z ) If the monopolist can price discriminate, then it means it can charge a price exactly equal to each consumer’s willingness to pay . Therefore, the monopolist can capture all of the consumer surplus (which was the difference between consumer’s willingness to pay and the market price). So, monopolists profit is π = X + Y + Z (d) What is the change in the monopolist’s profit from price discrim- ination? What is the change in total surplus from price discrim- 7
ination? Which change is larger? Explain. (Give your answer in terms of X, Y, and Z . So the change in profit is simply Y + Z . That is, they capture the consumer surplus, and also the old deadweight loss since they produce more. The change in total surplus is area Z , which was a deadweight loss before but is now monopolist’s profit. Clearly, the change in profit is greater than the change in surplus, since the monopolist now captures the consumers’ surplus. (e) No suppose that there is some cost of price discrimination. To model this cost, let’s assume that the monopolist has to pay a fixed cost C to price discriminate. How would a monopolist make the decision whether to pay this fixed cost? (Give your answer in terms of X, Y, Z, and C .) A monopolist will price discriminate so long as the extra profit is greater than the cost. That is, so long as Y + Z > C (f) How would a benevolent social planner, who cares about total surplus, decide whether the monopolist should price discriminate? (Give your answer in terms of X, Y, Z, and C .) A benevolent social planner who would allow the monopolist to price discriminate so long as the additional total surplus from doing so outweighed the cost, i.e. Z > C (g) Compare your answers to parts (e) and (f). How does the monop- olist’s incentive to price discriminate differ from the social plan- ner’s? Is it possible that the monopolist will price discriminate even though it is not socially desirable? The monopolist cares about it’s profits, which depends in part on re-distributing surplus from consumers to the monopolist. The social planner doesn’t value that transfer of surplus, it’s only total surplus that matters. So it is possible that the monopolist will price discriminate even when it is not socially desirable. This will happen precisely when Y + Z > C > Z 8
5. Pete’s SunMoney is one firm of many in the market for coffee, which is in long-run equilibrium.
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