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 0p 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.
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
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
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
"name": " 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.",
"description": "◦ Revenues lost to inframarginal consumers is not too great because Q/s
Set low to get more customers Positive externalities Example, ◦ Telephone company offers more people to call when there are more customers accessing their lines
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