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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

- 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?

- 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.

- 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

- 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

- 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

- 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*=

- 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.

- 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 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

- 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

- 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

- 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

- 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

- 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.

- 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

- 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.

- 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

- 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

- 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

- 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