A DISNEYLAND DILEMMA: TWO-PART TARIFFS FOR A MICKEY … · DISNEYLAND DILEMMA 79 (2-b) —^
A Disneyland Dilemma
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Transcript of 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?