By Walter Y. Oi Presented by Sarah Noll. Charge high lump sum admission fees and give the rides...
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Transcript of By Walter Y. Oi Presented by Sarah Noll. Charge high lump sum admission fees and give the rides...
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
Let people into the amusement park for free and stick them with high monopolistic prices for the rides?
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.
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 incomeGood Y’s price is set equal to oneMaximizes Utility by U=U(X,Y) subject to this budget constrain
OPTION 1 Consumers demand for rides depends
on the price per ride P, income M, and the lump sum admission tax TX=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 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
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*=
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.
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 consumersEach 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 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 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
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
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
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
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.
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
STEP 1 Optimum price for a market of N
consumers is shown by:)S1= x1/X, the market share demanded by the smallest consumerE 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 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 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
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 tariffEach 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 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?