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By Walter Y. Oi Presented by Sarah Noll

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Charge high lump sum admission fees and give the rides away? OR Let people into the amusement park for free and stick them with high monopolistic prices for the rides?

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A discriminating two-part tariff globally maximizes monopoly profits by extracting all consumer surpluses. A truly discriminatory two-part tariff is difficult to implement and would most likely be illegal.

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Disneyland establishes a two-part tariff where the consumer must pay a lump sum admission fee of T dollars for the right to buy rides at a price of P per ride. Budget Equation: XP+Y=M-T [if X>0] Y=M[if X=0] M -is income Good Ys price is set equal to one Maximizes Utility by U=U(X,Y) subject to this budget constrain

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Consumers demand for rides depends on the price per ride P, income M, and the lump sum admission tax T X=D(P, M-T) If there is only one consumer, or all consumers have identical utility functions and incomes, the optimal two-part tariff can easily be determined. Total profits: Π= XP+T-C(X) C(X) is the total cost function

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In a market with many consumers with varying incomes and tastes a discriminating monopoly could establish an ideal tariff where: P=MC and is the same for all consumers Each consumer would be charged different lump sum admission tax that exhausts his entire consumer surplus This two-part tariff is discriminatory, but it yields Pareto optimality

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Option 1 was the best option for Disneyland, sadly (for Disney) it would be found to be illegal, the antitrust division would insist on uniform treatment of all consumers. Option 2 presents the legal, optimal, uniform two-part tariff where Disney has to charge the same lump sum admission tax T and price per ride P

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There are two consumers, their demand curves are ψ1 and ψ2 When P=MC, CS 1 =ABC and CS 2 =ABC Lump sum admission tax T cannot exceed the smaller of the CS No profits are realized by the sale of rides because P=MC

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Profits can be increased by raising P above MC For a rise in P, there must be a fall in T, in order to retain consumers At price P, Consumer 1 is willing to pay an admission tax of no more than ADP The reduction in lump sum tax from ABC to ADP results in a net loss for Disney from the smaller consumer of DBE The larger consumer still provides Disney with a profit of DDEB As long as DDEB is larger than DBE Disney will receive a profit

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Setting Price below MC Income effects=0 Consumer 1 is willing to pay a tax of ADP for the right to buy X1*=PD rides This results in a loss of CEDP Part of the loss is offset by the higher tax, resulting in a loss of only BED Consumer 2 is willing to pay a tax of ADP The net profit from consumer 2 is EBDD As long as EBDD> BED Disney will receive a profit

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Pricing below MC causes a loss in the sale of rides, but the loss is more than off set by the higher lump sum admissions tax

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A market of many consumers Arriving at an optimum tariff in this situation is divided into two steps: Step 1: the monopolist tries to arrive at a constrained optimum tariff that maximizes profits subject to the constraint that all N consumers remain in the market Step 2: total profits is decomposed into profits from lump sum admission taxes and profits from the sale of rides, where marginal cost is assumed to be constant.

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Profits from lump sum admission taxes, πA=nT Profits from the sale of rides, πS=(P-c)X MC is assumed to be constant The elasticity of the number of consumers with respect to the lump sum tax is determined by the distribution of consumer surpluses

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The pricing policy used by IBM is a two-part tariff The lessee must pay a lump sum monthly rental of T dollars for the right to buy machine time IBM price structure includes a twist to the traditional two-part tariff Each lessee is entitled to demand up to X* hours at no additional charge If more than X* hours are demanded there is a price k per additional hour

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Profits from Consumer 1= (0AB)- (0CDB) Profit from Consumer 2= (0AB)- (0CDX*)+(DEFG) The first X* cause for a loss, but the last X2-X* hours contribute to IBMs profits

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