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Many schemes for price discriminating involve some cost. For example, discount coupons take up time and resources from both the buyer and the seller. This question considers the implications of costly price discrimination. To keep things simple, lets assume that our monopolists production costs are simply proportional to output, so that average total cost and marginal cost are constant and equal to each other.a. Draw the cost, demand, and marginal-revenue curves for the monopolist. Show the price the monopolist would charge without price discrimination.b. In your diagram, mark the area equal to the monopolists 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.c. Now suppose that the monopolist can perfectly price discriminate. What is the monopolists profit? (Give your answer in terms of X, Y, and Z.)d. What is the change in the monopolists profit from price discrimination? What is the change in total surplus from price discrimination? Which change is larger? Explain. (Give your answer in terms of X, Y, and Z.)e. Now suppose that there is some cost of price discrimination. To model this cost, lets assume that the monopolist has to pay a fixed cost C in order 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.)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.)g. Compare your answers to parts (e) and (f). How does the monopolists incentive to price discriminate differ from the social planners? Is it possible that the monopolist will price discriminate even though it is not socially desirable?
a) The graphs are shown in the diagram. The monopoly price is Pm and the quantity is Qm. b) The monopolist’s profit consists of the two areas labeled X, consumer surplus is the two areas labeled Y, and the deadweight loss is the area labeled Z. c. If the monopolist can perfectly price discriminate, it produces quantity QC, and has profit equal to X + Y + Z. d. The monopolist’s profit increases from X to X + Y + Z, an increase in the amount Y + Z. The change in total surplus is area Z. The rise in monopolist’s profit is greater than the change in total surplus, since monopolist’s profit increases both by the amount of deadweight loss (Z) and by the transfer from consumers to the monopolist (Y). e. A monopolist would pay the fixed cost that allows it to discriminate as long as Y + Z (the increase in profits)…

exceeds C (the fixed cost). f. A benevolent social planner who cared about maximizing total surplus would want the monopolist to price discriminate only if Z (the deadweight loss from monopoly) exceeded C (the fixed cost) since total surplus rises by Z – C. g. The monopolist has a greater incentive to price discriminate (it will do so if Y + Z > C) than the social planner would allow (she would allow it only if Z > C). Thus if Z < C but Y + Z > C, the monopolist will price discriminate even though it is not in society’s best interest.



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