A Disneyland Dilemma: Two-Part Tariffs for a mickey mouse monopoly

1. A Disneyland Dilemma: Two-Part Tariffs for a mickey mouse monopoly By Walter Y. Oi Presented by Sarah Noll

2. How Should Disney price? • 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?

3. How should Disney price? • 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.

4. Option 1 • 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 Y’s price is set equal to one Maximizes Utility by U=U(X,Y) subject to this budget constrain

5. Option 1 • 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

6. Option 1 • Π= XP + T – C(X) • Differentiation with respect to T yields: • c’ is the marginal cost of producing an additional ride • If Y is a normal good, a rise in T will increase profits • There is a limit to the size of the lump sum tax • An increase in T forces the consumer to move to lower indifference curves as the monopolist is extracting more of his consumer surplus

7. Option 1 • At some critical tax T* the consumer would be better off to withdraw from the monopolist’s market and specialize his purchases to good Y • T* is the consumer surplus enjoyed by the consumer • Determined from a constant utility demand curve of : X=ψ(P) where utility is held constant at U0=U(0,M) • The lower the price per ride P, the larger is the consumer surplus. The maximum lump sum tax T* that Disneyland can charge while keeping the consumer is larger when price P is lower: • T*=

8. Option 1 • In the case of identical consumers it benefits Disney to set T at its maximum value T* • Profits can then be reduced to a function of only one variable, price per ride P • Differentiating Profit with respect to P: or • In equilibrium the price per ride P= MC • T* is determined by taking the area under the constant utility demand curve ψ(P) above price P.

9. Option 1 • 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

10. Option 2 • 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

11. Option 2 • There are two consumers, their demand curves are ψ1 and ψ2 • When P=MC, CS1=ABC and CS2=A’B’C • Lump sum admission tax T cannot exceed the smaller of the CS • No profits are realized by the sale of rides because P=MC

12. Option 2 • 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 DD’E’B • As long as DD’E’B is larger than DBE Disney will receive a profit

13. Option 2.1 • 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 A’D’P’ • The net profit from consumer 2 is E’BDD’ • As long as E’BDD’> BED Disney will receive a profit

14. Option 2.1 • 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

15. Option 2.2 • 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.

16. Step 1 • For any price P, the monopolist could raise the lump sum tax to equal the smallest of N consumer surpluses • Increasing profits • Insuring that all N consumers remain in the market • Total profit: X is the market demand for rides, T=T1* is the smallest of the N consumer surpluses, C(X) total cost function

17. Step 1 • Optimum price for a market of N consumers is shown by: ) S1= x1/X, the market share demanded by the smallest consumer E is the “total” elasticity of demand for rides • If the lump sum tax is raised, the smallest consumer would elect to do without the product.

18. Step 2 • 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

19. Step 2 • The optimum and uniform two-part tariff that maximizes profits is attained when: • This is attained by restricting the market to n’ consumers • Downward sloping portion of the πA curve where a rise in T would raise profits from admissions

20. Applications of Two-Part Tariffs • 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

21. IBM • Profits from Consumer 1= (0AB)-(0CDB) • Profit from Consumer 2= (0AB)-(0CD’X*)+(D’E’F’G’) • The first X* cause for a loss, but the last X2-X* hours contribute to IBMs profits

22. Questions?