Presentation on theme: "A Disneyland Dilemma: Two-Part Tariffs for a mickey mouse monopoly"— Presentation transcript:
1 A Disneyland Dilemma: Two-Part Tariffs for a mickey mouse monopoly By Walter Y. OiPresented by Sarah Noll
2 How Should Disney price? Charge high lump sum admission fees and give the rides away?ORLet people into the amusement park for free and stick them with high monopolistic prices for the rides?
3 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.
4 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 Y’s price is set equal to oneMaximizes Utility by U=U(X,Y) subject to this budget constrain
5 Option 1Consumers 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
6 Option 1 Π= XP + T – C(X) Differentiation with respect to T yields: 𝑑𝜋 𝑑𝑇 =𝑃 𝑑𝑋 𝑑𝑇 +1− 𝑐 ′ 𝑑𝑋 𝑑𝑇 =1− 𝑃− 𝑐 ′ 𝑑𝑋 𝑑𝑀c’ is the marginal cost of producing an additional rideIf Y is a normal good, a rise in T will increase profitsThere is a limit to the size of the lump sum taxAn increase in T forces the consumer to move to lower indifference curves as the monopolist is extracting more of his consumer surplus
7 Option 1At some critical tax T* the consumer would be better off to withdraw from the monopolist’s market and specialize his purchases to good YT* is the consumer surplus enjoyed by the consumerDetermined 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*= 𝑃 ∞ ψ 𝑃 𝑑𝑃𝑑𝑇∗ 𝑑𝑃 =−ψ 𝑃 =−𝑋
8 Option 1In 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 PDifferentiating Profit with respect to P: 𝑑𝜋 𝑑𝑃 = 𝑋+𝑃 𝑑𝑋 𝑑𝑃 + 𝑑𝑇∗ 𝑑𝑃 −𝑐′( 𝑑𝑋 𝑑𝑃 )𝑃− 𝑐 ′ 𝑑𝑋 𝑑𝑃 =0 or 𝑃= 𝑐 ′In equilibrium the price per ride P= MCT* is determined by taking the area under the constant utility demand curve ψ(P) above price P.
9 Option 1In 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 surplusThis two-part tariff is discriminatory, but it yields Pareto optimality
10 Option 2Option 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
11 Option 2 There are two consumers, their demand curves are ψ1 and ψ2 When P=MC, CS1=ABC and CS2=A’B’CLump sum admission tax T cannot exceed the smaller of the CSNo profits are realized by the sale of rides because P=MC
12 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 consumersAt price P, Consumer 1 is willing to pay an admission tax of no more than ADPThe reduction in lump sum tax from ABC to ADP results in a net loss for Disney from the smaller consumer of DBEThe larger consumer still provides Disney with a profit of DD’E’BAs long as DD’E’B is larger than DBE Disney will receive a profit
13 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 ridesThis results in a loss of CEDPPart of the loss is offset by the higher tax, resulting in a loss of only BEDConsumer 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
14 Option 2.1Pricing 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
15 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 marketStep 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.
16 Step 1For any price P, the monopolist could raise the lump sum tax to equal the smallest of N consumer surplusesIncreasing profitsInsuring that all N consumers remain in the marketTotal profit:𝜋 𝑁 =𝑋𝑃+𝑁𝑇−𝐶 𝑋X is the market demand for rides,T=T1* is the smallest of the N consumer surpluses,C(X) total cost function
17 Step 1 Optimum price for a market of N consumers is shown by: 𝑐 ′ =𝑃[1+( 1−𝑁𝑠1 𝐸 )S1= x1/X, the market share demanded by the smallest consumerE is the “total” elasticity of demand for ridesIf the lump sum tax is raised, the smallest consumer would elect to do without the product.
18 Step 2 Profits from lump sum admission taxes, πA=nT Profits from the sale of rides, πS=(P-c)XMC is assumed to be constantThe elasticity of the number of consumers with respect to the lump sum tax is determined by the distribution of consumer surpluses
19 Step 2The optimum and uniform two-part tariff that maximizes profits is attained when: 𝑑𝜋(𝑛) 𝑑𝑛 = 𝑑𝜋𝐴 𝑑𝑛 + 𝑑𝜋𝑠 𝑑𝑛 =0This is attained by restricting the market to n’ consumersDownward sloping portion of the πA curve where a rise in T would raise profits from admissions
20 Applications of Two-Part Tariffs The pricing policy used by IBM is a two-part tariffThe lessee must pay a lump sum monthly rental of T dollars for the right to buy machine timeIBM price structure includes a twist to the traditional two-part tariffEach lessee is entitled to demand up to X* hours at no additional chargeIf more than X* hours are demanded there is a price k per additional hour
21 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