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 Three sections  Section 1  Discriminatory two-part tariff  Section 2  Uniform two-part tariff  Section 3  Applications of two-part tariff  Volume.

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Presentation on theme: " Three sections  Section 1  Discriminatory two-part tariff  Section 2  Uniform two-part tariff  Section 3  Applications of two-part tariff  Volume."— Presentation transcript:

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2  Three sections  Section 1  Discriminatory two-part tariff  Section 2  Uniform two-part tariff  Section 3  Applications of two-part tariff  Volume Surcharge for IBM  Marginal price discounts (like those used in public utilities)

3  A two-part tariff is one in which the consumer must pay a lump sum fee for the right to buy a product  Examples:  Disneyland: entrance fee + price per ride  Bar: cover charge + price per drink  Rate structures of utility companies  Against:  Standard pricing for the monopolist: single price where MC=MR

4  AKA first degree price discrimination  To globally maximize profits by extracting ALL consumer surpluses  Assumptions for Disneyland model (apparently Mickey is a greedy monopolist based on this article)  Consumers are to derive no utility from going to the park itself  Utility derived from consuming a flow of rides X per unit time period  Problems: difficult and ILLEGAL

5  Consumer’s budget equation XP+Y=M-T [if X>O] Y=M [if X=O] M=income Y= good; price set equal to 1

6 Utility = U=U(X,Y) If the consumer does not want to pay the tariff, T, they will have the following utility: U(X, Y,) = U(O, M,) **without entering the park, the consumer cannot consume the good, X ** Tax, T, allows Disneyland to extract the consumer’s income in order to turn it into Mickey Mouse’s profits (Mickey loves money)

7 Now, if the consumer has a demand for rides, they will have the following demand function: X=D(P, M-T) P is price per ride M is income T is admission This can be interpreted as follows: and increase in the lump sum tax will decrease consumption of the rides, x with respect to a consumer’s given level of income.

8 Total profits are given by: п =XP+T-C(X) where C(X) is the total cost function And differentiating with respect to T we get: Interpretation:  Assume that Y is a normal good.  An increase in T will increase profits  Forces consumer to move to lower indifference curve because they cannot consume more rides due to a decrease in their budget  However, the monopolist extracts more of the consumer’s budget by employing this pricing strategy

9  There is a point T* where the consumer will not purchase this entrance fee and use their income to purchase other goods  Therefore T* is the consumer’s surplus enjoyed by the consumer

10  The larger the T* Disney can charge while keeping their consumers, the lower the price per ride will be  This results in a larger consumer surplus The equation above represents the area under the constant utility demand curve And this step allows for us to reduce the following profit function to one variable: price per ride

11  Here, we differentiate profits with respect to price  Description of what has happened:  Changes in the optimal tax, T* due to a change in P from this equation dT*/dP allows for P to satisfy the necessary condition  Result: P=MC

12  There is a different lump sum tax, or entrance fee in the case of Disneyland, charged per consumer  Price per ride, which is equal to marginal cost is the same across all consumers  Conclusion:  Customers who have larger surpluses for rides will be charged higher entrance fees or purchase privilege taxes  Ie: admission fees transfer the consumer’s income thus putting them on a lower indifference curve

13  Will look at the process of developing a uniform two-part tariff  Monopolist will want to maximize profit subject to the constraint of the number of consumers N  Wants to keep as many consumers in the market as possible  KEY:  Tax T will need to be adjusted whenever the price varies

14  Total profits = X – market demand for rides T=T* -smallest of the N consumer surpluses C(X) – cost function And differentiating with respect to price and setting equal to zero

15  IF: P will exceed c’ if (1- Ns 1 ) >0 (1- Ns 1 ) < 0 means that the price is less than MC And, if the monopolist chooses to raise the price, the smallest consumer would not purchase this product With a smaller amount of consumers, a new tariff needs to be found. Due to this, the tax will then increase and there will thus be a lower price charged per ride

16  Have consumers n  Profits from the lump sum tax: Π A = n T  Profits from the sale of ride: Π S = (P – c)X  An increase in T means that there will be less consumers buying the product  Π A thus changes  therefore profits depends on T

17  If the market contracts, meaning there are less consumers because the monopolist increases T.  This gives the monopolist the ability to control the number of consumers in the park  Increasing T reduces the number of consumers  This then decreases the price per ride  Why do they do this??  To capture the larger surpluses  Result: a decrease in profits from sales

18  The optimum and uniform two-part tariff that globally maximizes profits is reached:  Profits is thus a sum of profits from the tariff and the profit from price per ride

19  IBM as an example of volume surcharge or marginal price discounts  Here’s the story for IBM’s case  Someone who is renting a machine pays a lump sum monthly rental: T dollars  The tax is for the right to buy/rent machine time  The renter gets up to X* hours of machine time with no additional cost to the lump sum tax  If they want to consume more, they are charged an additional fee of k per hour  THUS  Larger consumers have a volume surcharge  This captures part of the surplus lost from smaller consumers

20  MC of machine time is 0  Where the surcharge rate becomes effective, or the demand after X* is equal to the maximum demand by a smaller consumer  No resale of computer time  Rate k is determined by a process that is similar to a monopolist choosing a single price where MC = MR

21  Example: public utilities also employ this type of pricing structure (which is like marginal price discounts)  We thus denote the following for prices with respect to varying demand P 1 and demands up to X* P 2 for a demand greater than X* Result of this: Kinked demand curve

22 XP 1 + Y = M[ if 0 X*] So, a marginal price discount can be like a two- part tariff for the larger consumers. We rewrite the second equation as follows: XP 2 + Y = M – T [T = X*(P 1 - P 2 ) ] The tax is thus the right to buy X at P 2

23  The monopolist can then receive larger surpluses from the larger consumers from this type of pricing discount.  Monopolist has higher profits

24  Charging a two-part tariff instead of a single price by the monopolist  RAISES PRICES  AND, it allows for less discrepancy between marginal rates of substitution in consumption and production


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