A disneyland dilemma two part tariffs for a mickey mouse monopoly
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A Disneyland Dilemma: Two-Part Tariffs for a mickey mouse monopoly. By Walter Y. Oi Presented by Sarah Noll. How Should Disney price?. Charge high lump sum admission fees and give the rides away? OR

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A disneyland dilemma two part tariffs for a mickey mouse monopoly

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

By Walter Y. Oi

Presented by Sarah Noll

How should disney price
How Should Disney price? monopoly

  • Charge high lump sum admission fees and give the rides away?


  • Let people into the amusement park for free and stick them with high monopolistic prices for the rides?

How should disney price1
How should Disney price? monopoly

  • 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.

Option 1
Option 1 monopoly

  • 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

Option 11
Option 1 monopoly

  • 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

Option 12
Option 1 monopoly

  • 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

Option 13
Option 1 monopoly

  • 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*=

Option 14
Option 1 monopoly

  • 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:


  • 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.

Option 15
Option 1 monopoly

  • 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

Option 2
Option 2 monopoly

  • 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

Option 21
Option 2 monopoly

  • 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

Option 22
Option 2 monopoly

  • 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

Option 2 1
Option 2.1 monopoly

  • 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

Option 2 11
Option 2.1 monopoly

  • 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

Option 2 2
Option 2.2 monopoly

  • 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.

Step 1
Step 1 monopoly

  • 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

Step 11
Step 1 monopoly

  • 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.

Step 2
Step 2 monopoly

  • 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

Step 21
Step 2 monopoly

  • 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

Applications of two part tariffs
Applications of Two-Part Tariffs monopoly

  • 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

IBM monopoly

  • 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

Questions? monopoly