Fully Distributed Costs and Two Part Tariff

1. Fully Distributed Costs and Two Part Tariff Notes

2. FDC Pricing • Because Ramsey is difficult to implement must find alternative way to price for multiproduct firm • Each output’s revenue covers its costs • Must be able to separate out costs

3. Joint Costs • NARUC – • Joint costs “occur when the provision of one service is an automatic by-product of the production of another service • Example, • Gas well produces natural gas, propane, butane, and other gases. • The only possible manner of production creates a fixed ratio of the different product • There is no unique way of allocating costs to separate the products

4. Common Costs • Products that cannot be produced simultaneously can incur common costs. • Example, • Petroleum refinery produces gasoline, diesel, heating oil from each barrel of crude oil. • The cost of the refinery depends on the amount produced of each of the products. • Yet, the proportion of each of the products may not be fixed. (i.e. more gasoline means less diesel produced) • Allocating common costs can be difficult

5. Fully Distributed Cost Pricing • 1)relative output • 2)attributable output • 3)gross revenue • We can define these mathematically. • FDC requires each output to generate enough revenue to cover its attributed cost

6. Attributed Cost Examples • Pizza Store • Breadsticks vs. pizza • Common costs = dough • Attributable costs = toppings • Railroad Company • Passenger vs. freight train • Common costs = track • Attributable costs = fuel • Electricity Utility • Residential vs. Industrial Consumers • Common costs = power-plant • Attributable costs = transmission and distribution

7. FDC Pricing • How we split up the common costs depends on the method used. • Limitations • MC is not included => very likely inefficient • Cross-subsidization impossible to detect • P1<MC1 for product 1 implies subsidized by P2>MC2 • Encourages entry • Circular reasoning • Pricing depends on revenue, gross revenue determines pricings • Under-produce elastic goods

8. Two-part Tariff • An attempt to promote efficiency and equity • Move to nonlinear prices • Uniform 2-part tariff • pq-+t • p is price per unit consumed • t is an access fee charged or license/entry fee, which allows a consumer to consume any positive amount • t=0 is linear pricing

9. Examples • Electricity or natural gas • Flat monthly fee (access fee) • Pay per kilowatt hr (usage fee) • Pay per cubic foot of gas (usage fee) • Cell phones • Purchase cell phone (access fee) • Pay per minute used (usage fee)

10. Declining Block Tariff • Marginal price paid decreases in steps as the quantity purchased increases • If the consumer purchases q • He pays • p1 * q +t, if 0<q≤q1 • p2 *(q- q1) + p1 * q1 +t, if q1< q ≤q2 • p3 *(q- q2) + p2 *(q2- q1) + p1 * q1 +t, if q2< q ≤q3 • If p1>p2>p3 => declining block tariff

11. Non-uniform tariff • t varies across consumers • For example, • industrial customers face a lower t b/c they use a constant q level of electricity • Ladies night, where girls get in free • Discriminatory, challenge in court • Often used to meet some social objective rather than increase efficiency. • Initially used to distinguish between fixed costs and variable costs • View demand (Mwh) and peak demand separately (MW) • The two are connected and that must be accounted for

12. Rationale • MC = P creates deficit, particularly if you don’t want to subsidize • Ramsey is difficult, especially if it creates entry

13. Two-part Tariff Discussion • Lewis (1941) – decreases distortions caused by taxes • Coase(1946) – P=MC and t*s=deficit • Gabor(1955) – any pricing structure can be restructured to a 2-part tariff without loss of consumer surplus

14. One Option • MC = P and fee= portion of tariff • Fee acts as a lump-sum tax • Non-linear because consumer pays more than marginal cost for inframarginal units. • Perfectly discriminating monopolist okay with first best because the firm extracts all C.S. • Charges lower price for each unit • The last unit P=MC • Similarly, welfare max regulator uses access fee to extract C.S.

15. Tariff Size – bcef or aef P a b c P f e AC D MC Q Q

16. Tariff not a Lump Sum • Not levied on everyone • Output level changes, if demand is sensitive to income change • Previous figure shows zero income effect • Demand probably changes when the fee changes

17. Additional Problems • Marginal customer forced out because can’t afford access fee (fee > remaining C.S.) • Trade-off between access fee and price • Depend on • Price elasticity • Sensitivity of market participation • Access fee • price

18. A digression on cost • Example of fixed costs • Wiring, transformers, meters • Pipes, meters • Access to phone lines, and switching units • Per consumer charge = access fee to cover deficit • We examine single-product • Identical to next model if MC of access =0 • Schmalensee (1981) modeled two different output, but one requires the other. • Some consumers can be priced out of the market • Results are the same for single-product model

19. Two-part Tariff Definitions • Θ = consumer index • Example • ΘA = describes type A • ΘB = describes type B • f(Θ)=density function of consumers • The firm knows the distribution of consumers but not a particular consumer • s* is the number of Θ* type of consumer • š is the number of consumers

20. Θ* Type Consumer • Demand • q(p,t,y(Θ*), Θ*) • Income • y(Θ*) • Indirect Utility Function • v(p,t,y(Θ*), Θ*) • ∂v/ ∂ Θ ≤0 • => Θ near 1 =consumer has small demand • => Θ near 0 =consumer has large demand • Assume Demand curves do not cross • => increase p or decrease t that do not cause marginal consumers to leave, then inframarginal consumers do not leave

21. More Defintions • Let be a cutoff where some individuals exit the market at a given p, t • If , no one exits • Number of consumer under cutoff, • Total Output • Profit

22. Welfare • w(θ) weight by marginal social value • Maximizing this equation ensures Pareto Optimality

23. Constrained Maximization • max L=V+λπ • by choosing p, t, λ • FOCs

24. where • Where is the change # of consumers caused by a change in p • and the marginal consumer receives zero surplus

25. Utility FOC • Simplifies to • From the individual’s utility max • Where vy(θ) MU income for type θ.

26. Income • Let vy=-vt because the access fee is equivalent to a reduction in income • Ignore income distribution and let • w(θ)=1/vy(θ) • Each consumer’s utility is weighted by the reciprocal of his MU of income • Substituting into Vp reveals

27. Similarly

28. Substitution Reveals • And let • From the FOC • Where • s=Qp+Q/s Qy • D= deficit

29. Solving Gives • where

30. Interpretation • Let • Marginal consumer’s demand (Roy’s Identity) • To keep utility unchanged, the dt/dp=-qˆ • Differentiate to get • Combining get

31. Result 1 • If the marginal consumers are insensitive to changes in the access fee or price, that is, • then the welfare maximization is • P=MC • t=D/s • Applies when no consumers are driven away • i.e electricity • Not telephone, cable

32. Result 2 • Suppose the marginal consumers are sensitive to price and access-fee changes • Then, the sign of p-MC is the same sign as Q/s-qˆ • And • p-MC≤0, then t=D/s>0 • if p>MC, then t≥0

33. Deviations from MC pricing – Result 2 • Increase in price or fee will cause individuals to leave • Optimality may require raising p above MC in order to lower the fee, so more people stay • p>MC when Q/s>qˆ, because only then will there be enough revenue by the higher price to cover lowering the access fee.

34. Deviations from MC pricing – Result 2 • p<MC and t>0 • Very few consumers enticed to market by lowering t • Consumers who do enter have flat demand with large quantities • A slightly lower price means more C.S. • Revenues lost to inframarginal consumers is not too great because Q/s<qˆ, • Lost revenues are recovered by increasing t without driving out too many consumers • Q/s-qˆ is a sufficient statistic for policy making

35. Low Access Fees • Set low to get more customers • Positive externalities • Example, • Telephone company offers more people to call when there are more customers accessing their lines