Notes

 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

 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

 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

 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

 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

 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  P 1 MC 2  Encourages entry ◦ Circular reasoning  Pricing depends on revenue, gross revenue determines pricings ◦ Under-produce elastic goods

 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

 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)

 Marginal price paid decreases in steps as the quantity purchased increases  If the consumer purchases q  He pays ◦ p 1 * q +t, if 0<q≤q 1 ◦ p 2 *(q- q 1 ) + p 1 * q 1 +t, if q 1 < q ≤q 2 ◦ p 3 *(q- q 2 ) + p 2 *(q 2 - q 1 ) + p 1 * q 1 +t, if q 2 < q ≤q 3 ◦ If p 1 >p 2 >p 3 => declining block 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

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

 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

 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.

P Q MC D Q P c AC b f a e

 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

 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

 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

 Θ = consumer index  Example ◦ Θ A = describes type A ◦ Θ B = 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

 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

 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

◦ w(θ) weight by marginal social value ◦ Maximizing this equation ensures Pareto Optimality

 max L=V+λπ  by choosing p, t, λ  FOCs

 Where is the change # of consumers caused by a change in p  and the marginal consumer receives zero surplus

 Simplifies to  From the individual’s utility max  Where v y (θ) MU income for type θ.

 Let v y =-v t because the access fee is equivalent to a reduction in income  Ignore income distribution and let ◦ w(θ)=1/v y (θ) ◦ Each consumer’s utility is weighted by the reciprocal of his MU of income  Substituting into V p reveals

 And let  From the FOC  Where  s=Q p +Q/s Q y  D= deficit

 where

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

 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

 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

 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.

 p 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

 Set low to get more customers  Positive externalities  Example, ◦ Telephone company offers more people to call when there are more customers accessing their lines