Chapter 7 Two-Tier Pricing under Liberalization *

Transcription

1 hapter 7 Two-Tier ricing under Liberalization * Michael A. rew enter for Research in Regulated Industries, Rutgers University aul R. Kleindorfer The Wharton School, University of ennsylvania The British ost Office introduced two-tier pricing in the 970s. The basic idea was to differentiate First lass from Second lass mail according to service quality rather than content. rocessing of Second lass Mail is deferred during peak periods, recognizing inter alia the added cost of meeting fixed service standards at such times. The introduction of two-tier pricing was a maor breakthrough at the time, both from a practical as well as a theoretical point of view, and it has been employed successfully in varying forms by several other ost Offices (Os) since then. rew, Kleindorfer and Smith (990) (KS) showed how two-tier pricing was related to the mainstream of the theory of peak-load pricing, which can be traced back at least to Boiteux (949). KS demonstrated that such servicedifferentiated pricing offered an efficient solution to the peak-load problem. In practice, the system of First lass and Second lass has continued basically unchanged from the original path-breaking idea of the 70 s, with some adustments being made in the application, definition and measurement of service standards. In other areas of the postal sector, considerable change has taken place, not least in the continuation of the process of liberalization of postal markets worldwide and especially in the EU. In addition, Os are facing significant electronic competition, principally from the Internet, which was not envisaged a decade ago. This paper examines the structure and role of the * The authors acknowledge the helpful comments of John anzar, Ian Reay, and Frank Rodriguez on an earlier version of this paper.

2 8 hapter 7 two-tier pricing system in the new environment. We examine, in particular, the relationship between the markups for First and Second lass mail under competition and under varying levels of USO. We utilize a Ramsey framework throughout. In the new environment, a number of questions arise from an economic and business policy point of view concerning the role of the two-tier pricing structure. From an economic point of view, the structure of Ramsey-optimal pricing must reflect the effects of entry not only from liberalization of postal markets but also from electronic technologies. The interaction of the breakeven constraint and surplus losses due to price increases is more complicated as pricing must also account for revenue losses to entrants. The USO considerably complicates the matter since price uniformity and ubiquity of service further constrain the ability of the O to respond to entrants. A key question that arises is whether two-tier pricing can mitigate the effects of these constraints by providing an additional element of pricing flexibility to the O. Section is concerned with the background and motivation of the analysis. Section develops the basic Ramsey model for a O with a product portfolio of First lass, and regular and presort Second lass, but with no entry. Section analyzes a simpler model with only First and Second lass, but with entry. Section 4 provides conclusions and implications.. BAKGROUND AND MOTIVATION The traditional peak-load problem envisages an economically nonstorable commodity, for example electricity, whose demand fluctuates on an hourly basis. eak-load prices are set according to time of day. ostal service differs from electricity in that there is some ability to defer mail and this deferability is the basis of the price differential in the two-tier pricing system. By being able to put Second lass letters aside during the rush to sort mail and get it out for the evening deadline, Os save costs by requiring less capacity and labor to process the mail immediately. It is this cost differential that drives the difference in price between the two classes of mail. In the tradition of Boiteux, KS developed marginal-cost based prices for First and Second lass letters. KS analyzed in detail the familiar firm peak case, where First lass drives the peak and pays for all the capacity and the shifting peak case, where the peak is driven by both First and Second lass with each contributing to the cost of capacity. The approach First lass would still contribute more to the capacity cost, as it is the peak demand in the sense that at the same price its quanity would be higher than that of Second lass.

3 7. Two-Tier ricing under Liberalization 9 was readily extended in rew and Kleindorfer (99, 99) by the inclusion of Ramsey markups to these marginal costs to derive economically efficient prices for a break-even constrained O. Os that employed two-tier pricing recognized the potential flexibility that it offered them and saw the differential between First and Second lass as an import-pricing tool for meeting their financial obligations imposed by their governments and the USO. This can be illustrated in the case of the British ost Office and of the United States ostal Service (USS). In case of the British ost Office First lass postage increased from 4 pence in 99 to 7 pence in 00 with Second lass going from 8 pence to 0 pence. For USS First lass Mail increased from.9 cents to 6.7 cents while Third lass, which changed its name to Standard A, increased from 5.4 cents to 8.7 cents. Thus, the differential decreased in absolute and relative terms in the U.S. from 55% to 4% while the differential rose slightly in absolute and relative terms in the U.K. from.% to 5%. In both countries the differential is sizeable. Similarly, Nikali (999) points out for Finland that the price differential between and rates has decreased significantly over the past 0 years, partly because of the differences in elasticity of and mail, with the latter being considerably less elastic. 4 Given this and the increased competition and increased automation since the early 90s when the topic was last given serious attention, a further examination is now warranted. Automation has also increased in the last decade and can affect two-tier pricing in a number of ways. The usual effect of automation is to reduce 4 Other countries have systems very similar to the U.K., for example: Finland, France, ortugal and Sweden. These products are not exactly the same. The U.K. rates are single piece rates while in the U.S. these rates are only available for bulk presort; single pierce mailers may not use Standard A. In addition, First lass Mail gets air transportation while Standard A gets surface. Nikali (997) estimates own price elasticities of -.78 for, and cross-elasticity of w.r.t. the price of of 0.5. The elasticity estimates for in Nikali s study were not significant, but he argues that the demand was quite inelastic through 995. These results are rather typical for estimates to date. For example, De Rycke et al. (00) estimated for small firms in France (using a cross-sectional study for a single month in 998) a own-price elasticity of 0.8, and a cross-elasticity w.r.t. the price of (? ) of 0.. They estimated own-price elasticity of 0.7 and a cross-elasticity w.r.t. the price of (? ) of Nankervis et al. (00) estimated long-run elasticities for letter mail in the UK over the period as follows: own-price elasticity of 0.9; cross-elasticity w.r.t. the price of (? ) of 0.56; own-price elasticity of 0.6; crosselasticity w.r.t. the price of (? ) of 0.8. We will see that the general finding that is more elastic than and that? <? leads to some rather simple bounds on the price differential between and.

4 0 hapter 7 flexibility. This ceteris paribus will result in an increase in the differential because automation equipment acts very much like base-load technology in the classical peak-load problem. However, automation will reduce costs and possibly increase quality, and improve reliability. These combined effects could be ambiguous in terms of the differential, for reasons explained in more detail in rew and Kleindorfer (99), ompetition also affects the differential in two-tier pricing. ompetition takes several forms. First lass, for example in the U.K. and Sweden, is at least a partial substitute for courier service since chances are that First lass will be delivered overnight. Nonetheless, if entry is allowed into Os basic letter markets, it seems likely that the direct impact will be greater on Second lass. Electronic competition could presumably affect both First and Second lass. Given the instant and ubiquitous nature of the information provided by the Internet, there may be less demand for courier and First lass letters. Information can be downloaded and printed instantly from the Internet. is essentially instant. The problem with is that it has become so ubiquitous and the volume has grown so rapidly that getting attention through has become more difficult. This negative feature of may make letters a substitute for . The problems affecting two-tier pricing facing Os today are much more complicated because of competition. As noted in rew and Kleindorfer (00), a O with a significant USO and facing entry into its traditional letter markets may lose its profitable markets and retain only its unprofitable ones with the possibility of a graveyard spiral. Entry gives rise to losses for the O, and attempts to regain viability by raising prices leads only to further erosion of the O s customer base. The process could continue until the O becomes financially non-viable. In rew and Kleindorfer (000, 00) we analyzed this problem for a single-product (letter mail) case. Here we consider the same problem under a two-tier pricing scheme. It seems likely that the O could address its USO more effectively under the two-tier system, but setting the prices will be more complicated. For example, if the First lass differential is set too high, then entry into the profitable First lass market may be accelerated, but setting it too low results in reduced revenues when they may be needed to achieve stability. Thus, the effect of competition, both through electronic substitutes and through entry, will be to squeeze the Os further making it all the more important to set prices for First and Second lass letters correctly. This intended contribution of this paper is precisely this issue. Assuming that forward-looking demand estimates and the relevant own and cross price elasticities are available, we develop a Ramsey pricing solution that addresses meeting the USO, competitive entry into the letter market and electronic competition. This solution embodies the efficient tradeoff

5 7. Two-Tier ricing under Liberalization between pricing increases and the net revenue generation potential of First and Second lass mail. We derive key bounding results on the differential between First and Second lass mail.. RAMSEY OTIMAL RIING FOR FIRST-LASS AND SEOND-LASS MAIL This section establishes standard benchmarks for Ramsey-optimal pricing, without consideration of entry. We consider an incumbent O offering First-lass () and Second-lass () mail, with the latter differentiated into regular Second-lass and presort Second-lass mail, with presort mail service offered at a discount off the regular price. Following the framework developed in rew, Kleindorfer and Smith (990), we assume that the service quality difference between and implies that demand for will be zero whenever >. Thus, assuming that service is offered, it must be the case that >. Denote the products of the O as, and. onsumer preferences are represented by the standard quasi-linear utility function, with the indirect utility function given by: U ( ) = V ( ) ( ) () where = (,, ) is the price vector and () = ( (), (), ()) is the vector of demands at price, and V() is aggregate willingness-to-pay and satisfies (see rew and Kleindorfer (99, hapter )) V ( ) ( ) = i = i () The incumbent O s profits are represented as Π( ) = ( i i ) i ( ) F () i = where i is the unit cost of lass i mail, with > > and where F is the fixed cost of the USO. The Ramsey problem takes the form:

6 hapter 7 0 i i ) i = Maximize W ( ) = V ( ) ( F (4) subect to: Π() 0 The first-order necessary conditions (FOs) for this problem are derived from L(, µ ) V = i i = i Π µ, i i =, (5) where L(, µ) = W() µ?() is the Lagrangian and µ 0 is the Lagrange multiplier associated with the profit constraint. Using ()-(), we obtain the following from (5): L i = ( µ ) ( ) µ i, i =,, (6) = i The following symmetry conditions on demand hold because of our assumption of no income effects (i.e., quasi-linear utility): i = i, i, (7) Using (7), we can rewrite (6) as follows: L i i ki, = η µ i = i =,, (8) where k = µ/(µ) is the Ramsey number, and η i = ( i / )( / i ) is the (cross-) elasticity of i w.r.t.. We make the following assumptions concerning the demand interdependencies across the set {,, }: ηii < 0, i ; η > 0; η > 0; η > 0; η > 0; η = η = 0 (9) Thus, {, } and {,} are substitutes. Assuming i > 0, we finally obtain the following FOs from (8):

7 7. Two-Tier ricing under Liberalization = η i k = 0, i =,, (0). Unconstrained Ramsey Optimal rices/markups These can be solved for the optimal Ramsey mark-ups in the standard fashion. These were first derived by Boiteux (956), Baumol and Bradford (970), Rohlfs (979) and Sherman and George (979) under general conditions on demand interdependencies. 5 We are interested in the implications of our assumptions (9) for these general results. Solving (0) for the optimal markups M i = ( i i )/ i, i =,,, given (9), yields, after some simple algebra: M = k [ η η ηη ηη ηη ] () M = k [ ηη ηη ηη ] () M = k [ η η ηη ηη ηη ] () where the determinant? is given by (4) = η ( ηη ηη ) ηηη As expected from second-order necessary conditions,? < 0. Technically, this follows from the standard assumptions that own-price effects dominate other price effects. 6 An examination of ()-(), together 5 6 See also rew and Kleindorfer (986) for an alternative derivation and a discussion of the application of these results in the case of substitutes and complements, the latter arising in the case of access goods. The reader will note that = [ ] where i = M i /M. Then using i = i (from (7)) and < 0, < 0, and < 0, a tedious examination of cases establishes that? < 0.

8 4 hapter 7 with (9), easily confirms that all optimal markups are non-negative (and positive whenever the profit constraint (8) is binding and k > 0). Result : Suppose revenues at the optimal solution satisfy R = > = R and suppose further that demand is more elastic than demand:? >?. Then, in addition to > >, the associated Ramsey optimal prices satisfy M = ( )/ < ( )/ = M, from which it follows that < ( / ) at any Ramsey optimal solution, including the welfare-optimal solution and the profit-maximizing solution. roof: We compute from ()-() at the Ramsey optimum: M M k k = [ η η η η η η η η η η η η η η ] = [ η η η η η ) η ( η η η )] ( We know, however, that?? < 0 since (5) η η = < < 0 (6) where the first inequality follows from > and M /M < 0, and the second inequality follows from the standard presumption that own effects dominate cross effects from a price increase, so the quantity in [ ] is negative. Finally, we conclude from the assumption R > R and = η η (7) and the fact that {, } are substitutes, that?? < 0. Thus, our assumption that? >?, together with (9), (5)-(7) and? < 0, imply that M M < 0, as asserted (with strict inequality holding except for the welfare-maximizing solution where k = 0). The remaining assertions are obtained in straightforward manner from M < M, noting, in particular, that the welfare-optimal and profit-maximizing solutions are Ramsey solutions with k = 0 and k =, respectively.

9 7. Two-Tier ricing under Liberalization 5. Avoided ost resort Discounts We establish an analogous bounding result now for the case in which the presort discount p = is set to equal avoided cost. Note that under the avoided cost rule = (8) Assume that is set from via (8). Then the FOs for solving (4) must take this into account. Substituting = ( ) into (4), differentiating and following the line argument developed above, we obtain the following FOs in place of (0): ( ) ( ) 0 = k (9) ( ) ( ) ( ) 0 ( ) = k (0) Now define total mail T () = () (). Noting from (9) that M /M = 0, and substituting (8) into (0), we obtain the following expressions from (9)-(0): ( ) ( ) 0 = k T () ( ) ( ) 0 = T T k () Solving ()-() for ( i i ), i =,, we obtain: = k T T T () = k T (4) in which

10 6 hapter 7 T = T > 0 (5) where the inequality follows from the dominance of own price effects relative to cross effects. We have the following result, analogous to Result. Result : Suppose the presort discount is set according to the Avoided ost Rule, and suppose R = > T = R T and? >? TT, where? TT = (M T /M )( / T ), the own price elasticity of total mail. Then, in addition to > > = - ( ), the associated constrained Ramsey optimal prices satisfy M = ( )/ < ( )/ = M, from which it follows that < ( / ) at any constrained Ramsey optimal solution (i.e., any Ramsey optimal solution satisfying the Avoided ost Rule for the presort discount), including the welfare-optimal solution and the profitmaximizing solution. roof: Dividing ()-(4) by, respectively, we have M M = (6) k T T T T k T = T T T T k T = [ η η η η ] TT T so that, analogous to the proof of Result, the assertion M < M follows from the assumptions that? >? TT and R > R T (which implies as in (7) that? T <? T ). The other assertions in Result are obvious analogs to those of Result. Note that the conditions on Revenue assumed in Result are more demanding than those in Result. Here what is required is that total revenue from products, both regular and presort, be no greater than for mail. Of course, these are only sufficient conditions and weaker conditions would imply the same result. In particular, if (? T -? T ) is small relative to the difference (?? TT ), then the revenue assumption would obviously not be T

11 7. Two-Tier ricing under Liberalization 7 needed. The only requirement for M < M is that the sum of elasticities in the second [ ] on the r.h.s. of the final equality in (6) be positive. 7 The reader may wonder whether there are other natural bounds on the price differentials between and mail. Our analysis thus far has not revealed any such bounds, except those deriving from the bounds on M and M presented above. One interesting corollary of the above Result is that > ( ), with equality only at the welfare-optimal solution. Thus, avoided cost discounts off price are not optimal for the Ramsey price for, either for the unconstrained Ramsey solution or for the Avoided ost resort Discount Ramsey solution. The reason for this is simple: for the welfare-optimal solution, = ( ), but as the Ramsey number k increases, the gap between and decreases, reflecting the fact that is less elastic than and is therefore relatively advantaged in raising revenues. For similar reasons, it is not generally true that the presort discount is always bounded below by avoided cost in the general Ramsey solution (except at the welfare-optimal solution). The differential will again depend on the relevant elasticities and cross elasticities. Results for other general bounds as well, e.g. on M M or M M, appear difficult to obtain, if indeed any general and interpretable results exist at all. As a final note on Ramsey-optimal solutions, we briefly note the effects of a more demanding profit constraint. This may be thought of in terms of the above model as an increase in the fixed costs F of the O, e.g., because of an increase in USO costs. As is well known, increasing the profit requirement of the O affects the Ramsey solution only to the extent that the Ramsey number k is increased. It seems from (4) and (6) that the impact of increasing k is to make the optimal markup differential M - M more negative (note that M = M = 0 at k = 0, the welfare optimal solution, and by the above Results becomes negative for any k > 0), but this neglects the impact of the price increases induced by increasing k on the elasticities in (4) and (6). The intuition for an increasing differential in M - M with increasing gross profit requirements is the traditional one: namely raising increased profits efficiently requires heavier reliance on the more inelastic product, in this case. However, we have only been able to show that M 7 Thus, in the UK over the 0-year period 990 to 000, mail volumes have actually decreased slightly (from roughly 6.65 billion to 5.5 billion pieces per annum), while mail has grown significantly (from 8.65 to.4 billion pieces per annum), with presorted mail as a percentage of total mail growing also very quickly during this decade (from approximately 45% in to 7% in ). Given this growth in total mail relative to mail, the revenue requirements noted in Result no longer hold, but as Nankervis et al. (00) report (see their Table 4), the total elasticity requirements for the above results do continue to hold.

12 8 hapter 7 - M is monotonically decreasing in k (in fairly tedious calculations spared the reader here) for the case of linear demand.. TWO-TIER RIING UNDER ENTRY This section simplifies the assumed product structure model of the previous section, but allows entry. Our interest is to determine what bounds, if any can be established on the differential between First and Second lass mail. The general approach to Ramsey pricing under entry is due to Sherman and George (979). 8 We note that several recent contributions have addressed the issue of entry and viability of a O with a USO. These include our own work cited previously, but also the contributions of ohen et al. (000) and De Donder et al. (00), where the latter addresses a fairly complex structure of underlying demand including multiple regions and multiple customer types. These papers are all concerned with the general issue of pricing and service quality flexibility of letter mail and their impact on the ability of the O to sustain a USO, but they do not address the issue of concern here, two-tier pricing. We assume that the O offers two services, and mail, but we neglect the presort option here. We assume that mail is less elastic than mail, and that both classes of mail are challenged by products of entrants. As in our earlier work rew and Kleindorfer (000, 00), we assume that entrants form a competitive fringe operating at a zero-profit level. Assuming a similar cost and demand structure to that in the previous section, the Ramsey problem takes the following form: The Ramsey problem of interest takes the form: 4 Maximize 0 W ( ) = V ( ) i i ( ) F (7) i = subect to: Π( ) = ( i i ) i ( ) F (8) i = where = (,,, 4 ), with and 4 being, respectively, the entrants prices for and mail, where i is the unit cost of lass i mail, with > and where F is the fixed cost of the USO. As noted, we assume entrants prices are set at their average costs, with zero profits resulting (and therefore 8 We also note the paper by Ware and Winter (986), which has some useful insights but does not cite the earlier and more general paper by Sherman and George (979).

13 7. Two-Tier ricing under Liberalization 9 entrants profits are not reflected in W()). We assume that all products are substitutes for each other, with mail being more elastic than mail. Forming the Lagrangean as above, the FOs for the Ramsey problem (7)-(8) are derived in analogous fashion to the previous section, yielding: L i = ( µ ) = ( ) i 4 ( i = ) i µ i ; i (9) =, Now using i = i for i =, 4, the second term in (9) drops out and we can proceed as in the standard Ramsey case to obtain the following solutions: M = k [ η η ] (0) M = k [ η η] () where? =?? -?? > 0. As in the previous section, we finally obtain the following expression for the markup differential: k M M = ( η η η η ) () Result : Under entry, and with differentiated products provided by a competitive fringe, suppose that the revenue from First lass mail exceeds that of (all) Second lass mail, R = > = R. Suppose further that First lass mail is more elastic than Second lass mail, i.e.,? >?. Then, in addition to >, the associated entry-constrained Ramsey optimal prices satisfy M = ( )/ < ( )/ = M, from which it follows that < ( / ) at any entry-constrained Ramsey optimal solution, including the entry-constrained welfare-optimal and the profitmaximizing solutions. roof: The proof proceeds exactly as in the previous cases, where the revenue assumption is used to establish that? <?. Note that this result appears to bear the identical logic to the previous results. However, there is a key difference here embodied in the entry assumption. Entry will clearly drive up the O s own elasticity, and it may

14 40 hapter 7 do so differentially for in relation to. One would also expect it to diminish the cross-elasticities for the Os products, since now there would be other products (provided by entrants) to which O customers could turn in the event of price increases by the O. Of course, the elasticities in () are all net of defections to entrants. Another basic effect of entry will be to erode the O s market share, making it more difficult for the O to achieve breakeven operations (as described in detail in rew and Kleindorfer (000, 00)). The effect of this is that the Ramsey number k will be driven up in (). 9 The combined effects of entry are therefore likely to be to drive up Ramsey markups and price levels, though this may have rather different effects on and mail, depending on the impact of entry on elasticities. In any case, we see that the fundamental equation characterizing the bounds on M M is (). Note, in particular, that the conditions given in Result are only sufficient conditions and the conclusions of the Result hold under broader conditions than those given. The revenue assumption R > R, for example, could be significantly relaxed without affecting the conclusions depending on the relative magnitudes of the elasticities. 4. IMLIATIONS AND ONLUSIONS A natural approach for a service provider to improve welfare and to compete more effectively is to expand the product portfolio. This is especially true in postal and delivery services, where there are significant interactions between cost and service quality. At first glance, two-tier pricing may be viewed in simple welfare terms as increasing the product line to provide an improved matching between consumer tastes for different price-cost-quality combinations. But, as this analysis shows, two-tier pricing may have an important further contribution to make under conditions of entry, namely to provide an additional competitive strategy to the O to support its USO. The point that we have attempted to clarify in this paper is the relationship between prices of different service quality products, here and. Faced with increasing USO costs or with entry, there seems to be a tendency on the part of incumbent O managers to increase mail price beyond the increases in mail prices, apparently under the ustification that demand from large business mailers is confronting larger real threats than its cousin. However, if price elasticities of demand from existing 9 Indeed, the required profits to sustain the USO could become infeasible if sufficient share is lost to the entrants, leading to a graveyard spiral. The conditions leading to this effect are noted in rew and Kleindorfer (000, 00).

15 7. Two-Tier ricing under Liberalization 4 studies are any guide to reality, then remains relatively more elastic than, inter alia because mail is a reliable alternative to and switching to it, for bill paying or other routine postal services, does not entail any significant transactions costs for the user. And the results of this paper show for a variety of pricing environments that so long as is more elastic than and generates at least as much revenue then the markup on should never exceed that of the markup on. Exceeding this bound will not only reduce efficiency, it will also reduce profits for the O, potentially damaging the effectiveness of a key strategy to meet the USO, two-tier pricing. REFERENES Baumol, William J., and David F. Bradford Optimal Departures from Marginal ost ricing. American Economic Review 60: Boiteux, Marcel, 949. La tarification des demandes en point: application de la théorie de la vente au coût marginal. Revue Générale de l électricité 58 (August): -40. Boiteux, Marcel Sur la gestion des monopoles public astreints à l équilibre budgétaire. Econometrica, 4 (Janurary) -40; translated by W. J. Baumol as On the Management of ublic Monopolies Subect to Budgetary onstraints. Journal of Economic Theory (September): Braeutigam, Ronald R Socially Optimal ricing with Rivalry and Economies of Scale. Rand Journal of Economics 5: 7-4. ohen, Robert H., William W. Ferguson, John D. Waller and Spyros S. enakis Universal Service without a Monopoly. In urrent Directions in ostal Reform, edited by M. A. rew and. R. Kleindorfer. Boston, MA: Kluwer Academic ublishers. rew, Michael A., and aul R. Kleindorfer. 99. eak-load ricing of ostal Service and ompetition, in ompetition and Innovation in ostal Services, edited by M. A. rew and. R. Kleindorfer. Boston, MA: Kluwer Academic ublishers. rew, Michael A., and aul R. Kleindorfer. 99. The Economics of ostal Service. Boston, MA: Kluwer Academic ublishers. rew, Michael A., and aul R. Kleindorfer Liberalization and the Universal Service Obligation in ostal Service. In urrent Directions in ostal Reform, edited by M. A. rew and. R. Kleindorfer. Boston, MA: Kluwer Academic ublishers. rew, Michael A., and aul R. Kleindorfer. 00. Whither the USO: A Microstructure Approach. In Future Directions in ostal Reform, edited by M. A. rew and. R. Kleindorfer. Boston, MA: Kluwer Academic ublishers. rew, Michael A., aul R. Kleindorfer, and M.A. Smith. 990 eak-load ricing in ostal Service. Economic Journal (September): De Donder, hilippe, Helmuth remer, Jean-ierre Florens, André Grimaud and Frank Rodriguez. 00. Uniform ricing and ostal Market Liberalization. In Future Directions in ostal Reform, edited by M. A. rew and. R. Kleindorfer. Boston, MA: Kluwer Academic ublishers. De Rycke, Marc, Sarah Marcy, and Jean-ierre Florens. 00. Mail Use by Firms. In Future Directions in ostal Reform, edited by M. A. rew and. R. Kleindorfer. Boston, MA: Kluwer Academic ublishers.

16 4 hapter 7 Nankervis, John, Sophie Richard, Soterios Soteri, and Frank Rodrigues. 00. Disaggregated Letter Traffic Demand in the UK, paper presented at the 9 th onference on ostal and Delivery Economics, Sorrento, June. Nikali, Heikki Demand Models for Letter Mail and Its Substitutes: Results from Finland. In Managing hange in the ostal and Delivery Industries, edited by M. A. rew and. R. Kleindorfer. Boston, MA: Kluwer Academic ublishers. Rohlfs, Geoffrey Economically Efficient Bell System rices, Bell Laboratories Discussion aper No. 8. Scott, Frank A Assessing USA ostal Ratemaking: An Application of Ramsey rices. Journal of Industrial Economics 4: Sherman, Roger, and Anthony George Second-best ricing for the U. S. ostal Service. Southern Economic Journal 45: Ware, Roger, and Ralph A. Winter ublic ricing under Imperfect ompetition, International J. of Industrial Organization 4: