A Disneyland Dilemma

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    A Disneyland

    Dilemma: Two-Part

    Tariffs for a mickeymouse monopoly

    By Walter Y. Oi

    Presented by Sarah Noll

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    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?

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    How should Disney price? A discriminating two-part tariff globally

    maximizes monopoly profits by extracting all

    consumer surpluses.

    A truly discriminatory two-part tariff isdifficult to implement and would most likely

    be illegal.

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    Option 1Disneyland 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 incomeGood Ys price is set equal to one

    Maximizes Utility by U=U(X,Y) subject to this

    budget constrain

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    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:

    = XP+T-C(X)

    C(X) is the total cost function

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    Option 1= 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

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    Option 1At some critical tax T* the consumer would be

    better off to withdraw from the monopolists

    market and specialize his purchases to good Y

    T* is the consumer surplus enjoyed by the consumerDetermined from a constant utility demand curve of :

    X=(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 taxT* that Disneyland can charge while keeping the

    consumer is larger when price P is lower:

    T*=

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    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 (P) above price

    P.

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    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

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    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

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    Option 2There are two consumers, their

    demand curves are 1 and 2

    When P=MC, CS1=ABC and

    CS2=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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    Option 2Profits 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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    Option 2.1Setting 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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    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

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    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.

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    Step 1For 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

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    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 smallestconsumer would elect to do without the

    product.

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    Step 2Profits from lump sum admission

    taxes, A=nT

    Profits from the sale of rides,S=(P-c)X

    MC is assumed to be constant

    The elasticity of the number ofconsumers with respect to the

    lump sum tax is determined by the

    distribution of consumer surpluses

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    Step 2The optimum and uniform

    two-part tariff that

    maximizes profits is

    attained when:

    This is attained byrestricting the market to

    n consumers

    Downward sloping portion of

    the A curve where a rise in

    T would raise profits fromadmissions

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    Applications of Two-Part TariffsThe 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 machinetime

    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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    IBMProfits 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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    Questions?