Two-Part Tariffs: A Pricing Scheme for Discrimination and Incentive Manipulation | Study notes Social Welfare

T000188 Two-part tariﬀs

<first_para>A two-part tariﬀ is a pricing scheme according to which the

buyer pays to the seller a ﬁxed fee and a constant charge for each unit

purchased. When it is used, the average price paid decreases as more units are

purchased. Further, it is the marginal charge and not the ﬁxed fee that

determines how many units will be purchased. Therefore, a two-part tariﬀ can

be used as a vehicle for price discrimination and also for manipulating the

incentives given to the buyers, allowing also the sellers to capture part of the

residual surplus through an appropriately chosen ﬁxed fee.</first_para>

Introduction and deﬁnitions

A two-part tariﬀ is a pricing scheme according to which the buyer pays to the

seller a ﬁxed fee and a constant charge for each unit of the product or service

purchased.

There are several examples of two-part tariﬀs in retail markets, including

amusement parks, various types of sports, museums, bookstores, discount

shopping or other clubs, telephone services, and access to website

information. Two-part tariﬀs are also often used in wholesale markets,

where manufactures charge a lump sum to a retailer for the right to carry

their product plus a constant charge per unit ordered by the retailer. Many

technology licensing agreements also tend to have this structure, specifying a

ﬁxed fee and a royalty for each unit produced.

A two-part tariﬀ represents a special case of non-linear pricing, with the

distinguishing feature that the charge for each additional unit purchased – in

other words, the marginal price – is constant. Under a more general multi-

part tariﬀ, the charge for each additional unit would be allowed to change

according to the number of units purchased, with the marginal price being

constant for a range of units and increasing or decreasing when a larger

quantity of units are purchased. Under an even more general non-linear

pricing scheme, the marginal price could be continuously changing for each

unit purchased. Further, linear pricing may be understood as an extreme case

of a two-part tariﬀ where the ﬁxed fee is set to zero; the other extreme case is

that of only a lump sum payment, independently of the units purchased.

Key characteristics

There are two key implications when a two-part tariﬀ is used. The ﬁrst is that

the average price paid decreases as more units are purchased. Therefore

larger buyers pay less per unit than smaller buyers. Second, for the buyer

who trades according to a two-part tariﬀ, the ﬁxed fee represents a ﬁxed cost.

Hence the ﬁxed fee does not determine how many units the buyer will

purchase, but only whether the buyer will enter into this trading transaction

or not. The volume purchased will depend only on the marginal price. These

two features of a two-part tariﬀ represent the main reasons why such a

pricing arrangement can be used. First, since the average price diﬀers among

buyers according to their usage, a two-part tariﬀ can be used as a vehicle for

price discrimination, in particular when these buyers will have to self-select.

Second, since a two-part tariﬀ essentially allows the simultaneous use of two

independent instruments, it could imply a more eﬃcient trading transaction

than linear pricing: the ﬁxed fee may be used to transfer money from the

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T000188 Two-part tariffs

<first_para>A two-part tariff is a pricing scheme according to which the

buyer pays to the seller a fixed fee and a constant charge for each unit purchased. When it is used, the average price paid decreases as more units are purchased. Further, it is the marginal charge and not the fixed fee that determines how many units will be purchased. Therefore, a two-part tariff can be used as a vehicle for price discrimination and also for manipulating the incentives given to the buyers, allowing also the sellers to capture part of the residual surplus through an appropriately chosen fixed fee.</first_para>

Introduction and definitions

A two-part tariff is a pricing scheme according to which the buyer pays to the seller a fixed fee and a constant charge for each unit of the product or service purchased. There are several examples of two-part tariffs in retail markets, including amusement parks, various types of sports, museums, bookstores, discount shopping or other clubs, telephone services, and access to website information. Two-part tariffs are also often used in wholesale markets, where manufactures charge a lump sum to a retailer for the right to carry their product plus a constant charge per unit ordered by the retailer. Many technology licensing agreements also tend to have this structure, specifying a fixed fee and a royalty for each unit produced. A two-part tariff represents a special case of non-linear pricing, with the distinguishing feature that the charge for each additional unit purchased – in other words, the marginal price – is constant. Under a more general multi- part tariff, the charge for each additional unit would be allowed to change according to the number of units purchased, with the marginal price being constant for a range of units and increasing or decreasing when a larger quantity of units are purchased. Under an even more general non-linear pricing scheme, the marginal price could be continuously changing for each unit purchased. Further, linear pricing may be understood as an extreme case of a two-part tariff where the fixed fee is set to zero; the other extreme case is that of only a lump sum payment, independently of the units purchased.

Key characteristics

There are two key implications when a two-part tariff is used. The first is that the average price paid decreases as more units are purchased. Therefore larger buyers pay less per unit than smaller buyers. Second, for the buyer who trades according to a two-part tariff, the fixed fee represents a fixed cost. Hence the fixed fee does not determine how many units the buyer will purchase, but only whether the buyer will enter into this trading transaction or not. The volume purchased will depend only on the marginal price. These two features of a two-part tariff represent the main reasons why such a pricing arrangement can be used. First, since the average price differs among buyers according to their usage, a two-part tariff can be used as a vehicle for price discrimination, in particular when these buyers will have to self-select. Second, since a two-part tariff essentially allows the simultaneous use of two independent instruments, it could imply a more efficient trading transaction than linear pricing: the fixed fee may be used to transfer money from the

buyer to the seller in a lump sum (and, hence, less distorting) way, while the marginal price may be set independently to determine the optimal quantity traded.

Price discrimination and the role of information

Let us now become a little more concrete about the incentives implied by the use of two-part tariffs by a single (monopoly) seller. Suppose that the seller has constant marginal cost of production, c, and faces a buyer who values units at different levels, thus implying a standard downward sloping demand. If the seller could only employ a linear price, this price would be higher than c but lower than the maximum valuation of the buyer – this standard monopoly pricing would imply both a social welfare loss (or a deadweight loss) and also that the seller does not capture the entire consumers’ surplus. In contrast, if the seller could employ a two-part tariff, he would optimally set the per unit charge to c and the fixed fee equal to the entire surplus that the seller would enjoy at that marginal price. In that case, perfect (first degree) price discrimination is achieved. The result would be a socially efficient allocation (that is, no deadweight loss) with the entire surplus being captured by the seller. The situation described above would not change by much if there were multiple buyers, each with a downward sloping demand, assuming that the seller could identify the valuation of each buyer and also prevent resale among buyers. Then the seller could charge a different two-part tariff to each buyer, with a per unit charge equal to c and a fixed fee equal to the valuation that each would enjoy at such a price. However, when the value of each specific buyer is not known to the seller (but only the distribution of values in the population is known) or when arbitrage cannot be prevented, then perfect price discrimination typically cannot be achieved. In such a case, the seller may design a menu of two-part tariffs and allow the buyers to self-select. That is, each buyer will choose the tariff that maximizes his own net surplus among all the tariffs available, at the same time choosing the quantity of the product that he will purchase under the tariff selected. The optimal design of the menu has to take into account the relevant ‘participation constraints’ (in particular, that the fees are not set at levels so high that the buyers will choose not to purchase at all) and ‘incentive compatibility constraints’ (so that the high value buyers do not select a tariff intended for low value buyers). When the buyers’ values can be ranked by type, and under some further conditions, the menu of tariffs that maximizes the seller’s surplus has the following features: all types buy less than the socially efficient quantity, except for the highest value type who purchases the efficient quantity; all types are left with some surplus (‘information rents’: taking advantage of the private information they have about their own values), except for the lowest value buyer from whom all surplus is being extracted by the seller; and the higher the quantity purchased, the lower the average price. The picture described above is complicated when two-part tariffs are being used by rival oligopolists (see, e.g. Stole, 2007 and Armstrong and Vickers, 2010). In general, competition may diminish the ability of sellers to effectively price discriminate. At the same time, the ability to employ two- part tariffs endows the rival sellers with greater freedom to compete and, in the equilibrium of the corresponding game, profit for the sellers could be lower than the profit they could enjoy under linear pricing.

Bibliography

Armstrong, M. [2007] Recent Developments in the Economics of Price Discrimination, in R. Blundell, W. K. Newey and T. Persson (eds.), Advances in Economics and Econometrics, 9th World Congress, vol. II, Cambridge Univ. Press. Armstrong, M., and J. Vickers [2010] ‘‘Competitive non-linear Pricing and Bundling’’, Review of Economic Studies, 77, 30–60. Brander, J. and B. Spencer [1985] ‘‘Export Subsidies and International Market Share Rivalry’’ Journal of International Economics, 18. Fershtman, C. and K. Judd [1987], ‘‘Equilibrium Incentives in Oligopoly’’, American Economic Review, 77, 927–940. Katz, M. L. [1983] ‘‘Non-uniform Pricing, Output and Welfare under Monopoly’’, Review of Economic Studies, 37–56. Motta M. [2005] Competition Policy, MIT Press. Oi, W. [1971] ‘‘A Disneyland Dilema: Two-Part tariffs for a Mickey Mouse Monopoly’’, Quarterly Journal of Economics, 77–96. Saggi, K. and N. Vettas [1999] ‘‘On Intrabrand and Interbrand Competition: The Strategic Role of Fees and Royalties,’’ European Economic Review, 46, 189–200. Schmalensee, R. [1981] ‘‘Monopolistic two-part pricing arrangements’’ Bell Journal of Economics, 445–466. Spence, M. A. [1980] ‘‘Multi-Product Quantity-Dependent Prices and Profitability Constraints’’, Review of Economic Studies, 821–841. Stole L. [2007] Price Discrimination and Imperfect Competition, in M. Armstrong-R. Porter (eds.), Handbook of Industrial Organization, Ch. 34, vol. III, North Holland. Varian, H. R. [1989] ‘‘Price Discrimination’’, in the Handbook of Industrial Organization, R. Schmalensee and R. Willig (eds), Vol. 1, ch.10, 597–654. Wilson R. B. [1993] Nonlinear Pricing, Oxford University Press.

Two-Part Tariffs: A Pricing Scheme for Discrimination and Incentive Manipulation, Study notes of Social Welfare

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T000188 Two-part tariffs

<first_para>A two-part tariff is a pricing scheme according to which the

Introduction and definitions

Key characteristics

Bibliography