Proceedings [of the] annual meeting. - AgEcon Search

Papers—Seventh Annual Meeting

"Transportation—An Emerging Science"

December 27, 28, 29, 1966

San Francisco, California

ALSO SELECTED PAPERS FROM

CANADIANSECOND ANNUAL MEETING

TRANSPORTATION RESEARCH FORUMSEPTEMBER 1966

NIAGARA FALLS, ONTARIO, CANADA

TRANSPORTATION RESEARCH FORUM

A Survey of TransportationPricing Strategies

by John R. Meyer* and Martin Wohl**

Introduction: Objectives

Tt is all too obvious that transport pricing policy can be established withmany different purposes in mind. Transport tariffs can assist in properallocation of resources by signalling effective demand for transport. They canprovide revenues for operating, maintaining and financing a facility. Theymay aid the rational allocation of capital among competing modes. They cancontrol congestion. They are a possible means to redistribute income or promote growth of particular regions or industries.

In practice, however, and hardly surprisingly given their multiplicity,transport charges have not always achieved their stipulated purposes. Majorconceptual and practical difficulties in regard to transportation pricing haveparticularly occurred when attempting to set charges to simultaneously"recoup the costs" as well as "properly ration" a fixed investment or capitalcommitment. Specifically, the difficult questions almost always are the same,and are to be found in much the same form in public utility and other industrial pricing as in transport pricing: How much investment should be undertaken? How is the cost associated with this investment to be shared amongdifferent classes of users in different periods and possibly with differentneeds?

Whenever a service is involved, however, as in transportation, the problem can assume additional dimensions. To begin, differentiation of pricescharged to different users within a single time period (infratemporal interpersonal discrimination) may become relatively easy, not to mention themuch more common practice of differentiation of charges between users indifferent time periods (intertemporal discrimination). The reason, of course,is simply that services unlike goods are consumed as they are purchased andtherefore cannot be readily resold within a given time period.1 (Intra temporalinterpersonal discrimination on commodities usually requires some considerable effort at product differentiation, imagined or real.) Given the additionalconsideration that transportation, like public utility services, is quite commonly sold in substantially less than perfectly competitive markets, the number

*Department of Economics, Harvard University.**National Science Foundation Faculty Fellow, University of California,Berkeley.

1 For useful elaborations of the role of these characteristics see James R.Nelson, "Practical Application of Marginal Cost Pricing in the PublicUtility Field," American Economic Review, LIII:474-481 (May, 1963);James M. Buchanan, "Indeterminacy in Peak-Load Pricing," mimeographed (to be published in the Quarterly Journal of Economics) ; andYale Brozen, "Welfare Theory, Technological Change and Public UtilityInvestment," Land Economics, Vol. XXVII, No. 1 (February 1951), pp.67-75 and No. 2 (May 1951), pp. 123-132.

33

34 TRANSPORTATION RESEARCH FORUM

of pricing arrangements that might be feasible in a particular situation andfor a specific set of constraints may be quite large.

Furthermore, if one desires to establish some consistent relationship between transport tariffs and costs additional difficulties arise because the relevant costs for transport facilities often may be difficult to estimate.

These many problems— of cost estimation, of less than perfect markets,of multiple and conflicting objectives— have permitted and created, in theirturn, a multiplicity of suggestions for pricing transport facilities and services.Some of these suggested pricing policies or strategies have arisen from experience and pragmatic adaption to observed circumstances. Others represent

concepts derived from essentially theoretical analyses. It is the purpose ofthis paper to review and state these alternatives more explicitly.

Probably the most fundamental distinction historically between alternativepricing strategies for transport has hinged on the degree to which a particularset of suggested prices was profit or cost oriented. The distinction, needlessto say, is not always clearcut for most suggested strategies involve a role forboth demand and cost considerations. Nevertheless, it is in this matter ofdegree of cost and demand orientation that most of the pricing alternativesderive their practical or effective differences.

Another important practical dimension within which any suggested pricingstrategy must be measured is, quite simply, administrative feasibility. In thispaper, an attempt is made to place these administrative considerations insomewhat broader perspective.

The Traditional Approaches: Value of Service and Average Cost Pricing

One of the most common and popular of transport pricing strategies hasbeen to more or less ignore costs under the rubric of "charging what thetraffic will bear" following so-called value-of-service pricing privileges. Inunsophisticated form, gross revenue maximization might be construed as the

objective. In more sophisticated versions the objective becomes profit maximization to be achieved by following the practices of a price-discriminatingmonopolist. Technically this would mean a price that equates marginal revenueto marginal costs for several separate classes of users.2 In practice, however,effort seldom is devoted to estimating the marginal costs needed to fullyimplement profit maximization or some approximation thereto. Even in less

sophisticated versions it should be obvious that these pricing procedures, withtheir emphasis on price discrimination or differentiation, are not likely to be

administratively simple: markets must be identified and segregated and a

complex structure of many prices has to be established and maintained. Thiscan be particularly difficult over time. Nevertheless, multiple price strategiesof this type are almost certainly the most prevalent approach to establishingrailroad, airline and truck tariffs in the world today. Furthermore, the influence of such pricing can also be seen in many highway, airway and waterwayuser charges.

2 J. R. Meyer, M. J. Peck, J. Stenason, and C. Zwick, The Economies ofCompetition in the Transportation Industries, Harvard Univ. Press,1959, Chapter VII.

SURVEY OF PRICING STRATEGIES 35

One obvious simplification of a tariff system involving price discrimination(implicit or explicit, haphazard or systematic) aimed at monopoly profit maximization is single-price profit maximization. That is, retain the objectivefunction of profit maximization but limit the number of prices to one. Thisapproach would be more akin to that practiced (probably of necessity) bythose sellers with some market power but dealing with more homogeneousindustrial products. Perhaps because of the inherent geographical, service andcommodity heterogeneity of much transport, simple single-price profit maximization has rarely, if ever, been applied in transport markets.

If complex, multiple price systems have dominated the private (or pseudo-private, e.g. originally private and then nationalized) sectors of transport, verysimple average cost pricing, admittedly with much adornment in some cases,has probably dominated the approach of public agencies to establishing tollsor user fees for highways, airports, airways, bridges and similar facilities. Ina sense, average cost pricing avoids the more complex distributional, con

ceptual and estimation questions by not asking them. Average cost pricingis simplicity itself: price is set equal to the total cost of a facility divided bythe total number of users. An average cost pricing policy (as can be demonstrated, for example, by formulating it as a linear programming problem)maximizes output for a facility (with a well-behaved, i.e. downward sloping,demand curve) subject to the constraints that total revenue equals total cost

and only one price is charged.

Slightly more complex formulas (than total cost divided by number of

users) might be used for estimating average costs but the end result wouldbe much the same under most conceivable average cost pricing schemes. Ofcourse, the cost of a facility might be expected to be a function of the volumeof services provided or demanded and these in turn normally would be sensitive to price. Thus, under an average cost pricing scheme, price itself is afunction of cost and a certain simultaneity or interdependency is introducedinto the pricing and capital budgeting procedure.8 As a rule (though not asa necessity), with average cost pricing only one price, common to all, is

charged. Accordingly, an average-cost pricing scheme usually has all of theadministrative and other simplicity associated with single price schemes.

Simple Efficiency Solutions: Marginal Cost Pricing

As an alternative to conventional average-cost user fees, application ofmarginal cost pricing principles to transportation has been advocated, inseveral different forms. In essence, the principles applicable to marginal cost

3 The system could be described by the following: equations:

cP = —

q

q = Mp)c = f2(q,q0)

where p represents price, q quantity and c the total costs of the facility,and qQ is a parameter of the facility size.


pricing decisions in transport are the same as those that could be advancedfor any sector of the economy. The justification usually would be to improveutilization of resources.

A most instructive application of marginal cost pricing is in public utilitiessince this sector shares certain common service and regulatory characteristics

with transport and has experienced the most elaborate and extensive use ofmarginal cost principles. At any rate, full implementation of marginal costpricing implies a capital budgeting as well as a pricing regime. Specifically,under a strict regime of marginal cost pricing, "an investment must be undertaken if the total revenue, derived from the stream of output added to thenetwork and sold throughout the year at the variously prevailing (short-run)marginal-cost prices, exceeds the cost for the year of using the additional

capacity: the cost of the capital (interest and 'true' depreciation) plus the sumof the additions to the stream of variable costs incurred throughout the yearin its utilization."*

Administrative and other practical difficulties can arise if the "variouslyprevailing marginal cost prices" are quite different at different periods of timeor for different classes of users and if homogeneous classes (by time or user)are not easily identified or segregated. In transport (and public utilities aswell) the short-run costs generally pertain to conditions at only one or a few

points in the operating cycle. The long-run costs, of course, relate to the

aggregate effect throughout the cycle. This means that equality between shortand long-run costs can only be met by aggregation (as in the above quotation),even with an optimum facility. In other words, a situation wherein the long-run marginal cost curve, the short-run marginal cost curve, and "the" demand

curve all have a common intersection point realistically occurs at only one or

a few points in time for most transport facilities (e.g., at one hour of the dayduring a particular year and season). Or, given an optimum system with a

certain long-run marginal cost, traffic flow demand variation will cause theflow and thus the short-run marginal costs to fluctuate throughout the oper

ating cycle— thus ruling out the practical possibility of any simple marginalcost pricing solution in which equal short and long-run marginal costs are

found at all points in time.

The application of short-run marginal cost pricing principles has beenwidely advocated for transport in circumstances where congestion can ordoes create a divergence between privately perceived costs and the marginalsocial costs of using a facility. The usual proposal is to set tolls so that thetotal price perceived by users is equal to the short-run marginal cost of usingthe facility; the increments in cost to which prices are adjusted are normallyattributed to increased congestion created by more intensive use of the facilityat certain times (of the day, week or year). Since the incremental level ofsocial or congestion cost would be a function of facility design and capacity,an interdependence would exist between the solution to the normal supply

4 Fred M. Westfield, "Practicing Marginal-Cost Pricing —A Review," TheJournal of Business, Vol. XXXIX, No. 1, Part 1, (January 1966), p. 68.


and demand problem and the capital budgeting process.5 This, however, isconventionally overlooked in congestion cost pricing proposals.6 Their objective, rather, is not so much to recoup the investment or even indicate theappropriate investment level but to induce "better" or "more optimal" use ofthe existing facility by prohibiting its use in circumstances where the pricepaid (or perceived) falls short of the marginal costs of such use. One or moreprices may be appropriate in a congestion cost pricing scheme depending onthe number of operating periods in which average variable or privately perceived costs fall noticeably beneath marginal social costs. Aside from somepractical administrative difficulties of such flexible pricing proposals, it shouldbe noted that marginal cost pricing criteria for transport services is theoretically sound only if all other services and enterprises in other sectors of theeconomy are also selling output under a marginal cost rule and if properinvestment practices accompany marginal cost pricing. Also, to followmarginal cost pricing principles in transport while other sectors pursue othertypes of pricing policies might induce distortions or inefficiencies as seriousas those originally meant to be overcome.

An interesting aspect of marginal cost pricing of this limited, short-runvariety, is that under normal methods of application it could be expected toproduce a profit or surplus as long as capacity were in short supply. Shortagesof capacity could be expected, of course, in economically developing situations.Profits obtained from a short-run marginal social cost pricing solution areanalogous to monopoly profits in the sense that they would be largely eliminated if the transport facility were provided within the private sector of amarket economy and entry was relatively easy. (They would not be the sameas conventional monoply profits because quantity would be determined bythe intersection of average revenue and marginal cost rather than of marginalrevenue and marginal cost as in the monopoly case). It has therefore beensuggested that profits obtained by a public agency from following a short-runmarginal social cost pricing scheme should be invested in expansion of thefacility. Putting aside the question of exactly how the financing is done, itis clear that expansion of facilities yielding such surpluses generally will beconsistent with a "fully implemented" marginal cost pricing scheme.7

Whether or not the long-run equilibrium or fully implemented situationwould result in a profit or loss when pursuing a marginal social cost pricingscheme would depend on whether the additional units of capacity are subject

The first equation in the system of footnote (3) would now be

"The costs of providing the highway network are irrelevant for optimalutilization," A. A. Walters, "The Theory and Measurement of Privateand Social Cost of Highway Congestion," Econometrica, Vol. 29, No. 4(October 1961), p. 685.H. Mohring, "Relation Between Optimum Congestion Tolls and PresentHighway User Charges," Traffic Congestion as a Factor in Road UsersTaxation, Highway Research Record No. 47, Washington, D.C., (1964) ;and "Urban Highway Investments," Measuring Benefits of GovernmentInvestments, (Robert Dorfman, editor), The Brookings Institution, Washington, D.C. (April, 1965).


to increasing, decreasing or constant returns. (That is, whether each additionalunit of capacity costs less to provide than its predecessors or vice versa). Ifthe incremental cost of additional capacity were declining (increasing returns

prevail) the full equilibrium at which demand, short-run marginal cost andlong-run marginal cost (including the cost of providing additional capacity)were all equal would result in a loss. With decreasing returns the situation

would be just reversed; as in the usual short-run marginal cost pricing solutionwith insufficient capacity, a surplus of funds would be generated in the sensethat revenues from user charges would exceed the total cost of providing the

facility. Only in the case of constant returns will the long-run equilibriumobtained from a marginal social cost pricing regime yield revenues exactly

equal to those required to finance the equilibrium level of plant or capacity—and even then only if an aggregation scheme is found to make the short-runsub-class or inter-temporal solutions over the operating cycle consistent withthe long-run solution.

Of course, with average (rather than marginal) cost pricing the facilitywould always be just self-sufficient, e.g., a loss would not appear even if increasing returns prevailed. Whether or not average cost pricing is to beconsidered superior to marginal cost pricing is, in essence, the old problemof marginal vs. average cost pricing that has played such a prominent role inthe economics and transportation literature for many years. Actually, a decision on whether to use short-run marginal cost pricing in situations where

congestion exists involves more or less the same considerations (of income

redistribution, means of financing, etc.), albeit somewhat reversed becausea surplus rather than a deficit is generated by short-run marginal cost pricingin such situations (since marginal costs lie above average costs).

At least one additional pricing rule is thus implicit in these longer-runconsiderations. This would be to set the charge initially (e.g., before equilibrium capacity is achieved) at a level equal to what is needed to cover theincremental cost of the last additional unit of capacity that would be providedunder the rule that such increments of capacity should be made available as

long as people are willing to pay the incremental cost of their supply. Thisis to be contrasted with the alternative of immediately or presently settingthe charge equal to the short-run marginal cost, and continuously varying the

price to keep it synchronized with changes in marginal costs as suggested bya strict marginal approach.

It should be noted that if capacity at a given point in time is less than thetotal capacity that would be justified in the long run (which would seem tobe the conventional case in situations of economic development) early adoption of long-run equilibrium prices (whether based on average or marginalcosts), would imply that demand in the short-run greatly exceeds existingdesign capacity. A major consequence would be that marginal social congestioncost could be expected to be very high. Indeed, if the long-run solution priceswere a very great deal beneath the prices at which marginal cost and demandwould be equilibrated under existing capacity (which would seem to be quiteprobable particularly if increasing returns do characterize the provision oftransport capacity) it might be deemed wise to use some alternative rationingscheme (e.g., physical controls) at least temporarily. In general, physical

SURVEY OF PB ICING STRATEGIES 39

controls can be viewed as an alternative means of coordinating decentralizedor individualistic decisions to restrict demand to a level consistent with mar

ginal cost pricing. The need for some such controls would seem to be almostundeniable if the level of demand generated by the use of the long-run solution prices were so beyond the available capacity that this led to "a backward

bending supply" situation or, more properly, shock wave effects that resulted

in a reduction in the effective capacity of the facility during peak congestion

periods.

Efficiency Solutions with Multiple Uses: Prices Based on User Cost Estimates

A natural, and fairly widely advocated, extension to the long-run marginalcost approach in transport is to separate facility costs into different categoriesassociated with different classes of users. Charges might then be set equal (asin average cost pricing) to the quotient of these different categories of cost

divided by the number of users in the category.

It is this approach that underlies much highway costing and taxation withinthe U.S. today. That is, highway costs are assigned to different vehicularclasses (e.g., heavy trucks, medium trucks, light delivery vehicles and passengerautomobiles) according to the extent to which they require special or particular facilities. The usual procedure is to define those additional costs thatseem required to meet the particular demands of a particular class of usersand to assign to those users both these costs and a portion of "basic" facilitycosts as well.8 The basic facility might be defined as that facility required tomeet light vehicle traffic or to permit minimum required access to abuttingproperty. The premise is that heavy vehicles need the fundamental facilityas well as all the additional engineering specifications added on to meet their

specific or singular needs. Thus, different classes of vehicular users would beordered according to the complexity or extent of the demands for capacitythat they create or for which they are solely responsible. For example, theheaviest vehicles using a road would bear a proportion of previous incrementsneeded to create a basic facility for their needs as well as the cost of especiallyheavy pavement or especially wide shoulders (etc.) that would be needed fortheir purposes only. The same "incremental cost" principle applied to peakand off-peak users could result in the users of the peak hour capacity being

assigned all the costs of extra length or extra capacity used intensively onlyduring the peak hours plus a proportion of the base road or capacity that isneeded through most hours of the day.9 The underlying rationale for these

procedures again would be the usual or general grounds of welfare economics

that prices for resources used should be fairly closely correlated with the

marginal costs of these resources. Practical applicability obviously depends on

8 A description of these cost assignments and procedures can be foundin J. JL Meyer, M. J. Peck, J. Stenason and C. Zwick, op. cit., pp. 65-85.

9 J. R. Meyer, J. F. Kain and M. Wohl, The Urban Transportation Problem, Harvard University Press, 1965, pp. 70-74.


ability to identify costs in some causal sense with particular segments ofusage.10

This approximate long-run marginal cost approach primarily has been usedwhere rather flat or invariant charges are applied to broad categories of usersto recoup facility costs, e.g., a simple combination of fuel taxes and licensefees. In such instances, estimation of the average incremental cost using theabove procedures provides a rough check on the "equity" of the user charges.For example, such checks have been used to provide some notion of whetheran existing scheme of user taxes results in any disproportionate burden beingassigned to one class of users rather than another and whether this disproportion is of sufficient extent to suggest that major distortions may be occurring in the choice of different transport modes.11

This extended and approximate long-run marginal cost approach, it shouldbe noted, is based on the premise that in most instances there would be ademand for a basic facility even if the heavier or more advanced and complexdemands were eliminated. It also recognizes that a reluctance often exists toassign all the costs of a fully developed or expanded capacity to only themarginal users or those requiring the most complex facilities. Since, for example, off-peak demands require one-half to two-thirds of the total highwaycapacity in many circumstances, it is considered inequitable by some toassign all the costs of the total capacity to peak period users only. If there issome presumption, as often appears to be the case, that only by combiningthe demands of different users that one can justify the financing of a moreelaborate facility that "benefits all," this suggests, in turn, that total costsmight be apportioned in some measure to all users.

Indeed, modifications in "approximate long-run incremental cost prices" toreflect "benefits received" are often suggested in situations where differentlevels of capacity tend to have a great deal of complementarity or interdependence for different classes of users. For example, the provision of a sixlane instead of a four lane highway is likely to confer benefits upon highwayusers during off-peak periods as well as peak periods by permitting highertravel speeds, a somewhat safer trip (everything else equal), etc. Similarly,providing 12 foot rather than 9 or 10 foot lanes on a highway (e.g., becauseone expects truck and heavy vehicles as well as private automobiles) normallywould result in the private automobiles enjoying a better level of service atmost times of the day and in most circumstances. A blend of long-run marginal cost and benefit-oriented prices does, in fact, characterize the approachto setting user fees on many public facilities. In such circumstances, the user

10 J. R. Meyer and G. Kraft, "The Evaluation of Statistical Costing: Techniques as Applied in the Transportation Industry," The American Economic Review, Vol. LI, No. 2, (May, 1961), pp. 313-334; J. R. Meyer,"Some Methodological Aspects of Statistical Costing: as Illustrated bythe Determination of Rail Passenger Costs," The American EconomicReview, Vol. XLVIII, No. 2, (May, 1968), pp. 209-222; and A. R. Ferguson, "A Marginal Cost Function for Highway Construction and Operation, The American Economic Review, Vol. XLVIII, (May, 1958), pp.223-238.

11 Meyer, Peck, Stenason and Zwick, op. cit., and Meyer, Kain and Wohl,op. cit.


fees, even if basically oriented to long-run marginal costs, can acquire at leastsome of the appearances and characteristics of value-of-service tariffs.

Complex Differentiated Pricing Schemes

Problems of rationing peak demand and providing for "financial viability"(in circumstances of increasing returns), as well as simple concepts of whatis "equitable" or "just" in redistributing the burden of financing transportationfacilities, has led to the proposal of several more complex differentiated or"discriminatory" pricing schemes for transport facilities.

Probably the most basic of these is one borrowed from public utility pricing.In this scheme price would be used as a means of equilibrating facility use(or coming as close to equilibrium as possible) in different periods of time.The basic notion is simple enough: use of the facility should be maximizedsubject to the constraints that users pay the incremental costs directly assignable to their consumption and that total revenues equal total costs (or, atleast, the long-run marginal costs) of the facility or system.12 Thus, if totaldemand during the period of peak use was greatly in excess of that duringthe off-peak (specifically, so much in excess that the total demand in theoff-peak even at a price that just covered direct operating costs were insufficient to generate total off-peak demand in excess of the peak perioddemand) all (or the long-run marginal) costs of providing the basic facilitycapacity would be charged to peak period users.

Complications arise if a "shifting peak" occurs. This would be a situationin which the off-peak demand exceeded the peak period demand at an off-peakprice equal to direct operating costs. The usual solution suggested for theshifting peak case is, however, rather simple: basically, charges are set duringthe peak and off-peak periods so as to equilibrate demand in the two differentperiods subject (usually) to the "constraint" of covering all (or the long-runmarginal) costs. Derivation of the appropriate charges for this "shifting peak"case is greatly facilitated if inter-personal price differentiation is ruled out,that is, only inter-temporal price differentiation is permitted.13 Another veryserious practical problem in implementing peak and off-peak pricing schemesis that of defining the appropriate time periods for analysis. Not only is theexistence or non-existence of a shifting peak sensitive to such definitions butthe actual prices charged to different consumer groups can vary with thesedefinitions.

Another differentiated or multiple price policy that has been suggestedrepresents a modification of the marginal social (i.e. congestion) cost approachdiscussed previously. Instead of setting the charge directly equal to the

marginal costs (at the point of intersection with demand), the discrepancybetween marginal social costs and average costs (privately perceived) wouldbe used as a means of determining the proportional allocations of a facility's

12 Marcel Boiteaux, "Peak-Load Pricing," Chapter 4 in James C. Nelson(ed.) Marginal Cost Pricing in Practice (1964), pp. 59-83; and Peter O.Steiner, "Peak Loads and Efficient Pricing," Quarterly Journal of Economics, (November 1957), pp. 585-610.

13 James M. Buchanan, op. ext.


total cost14. For example, the procedure would allocate to the users of eachtime period the cost of the basic facility according to that period's percentageof the total extra congestion or delay cost (which would be much the sameas the toll in short-run marginal cost pricing) incurred over a total operatingcycle (e.g., a work day in the case of urban facilities). Thus, the denominatorof the allocation ratio would represent the sum of extra congestion or delaycost incurred during a complete operating cycle while the numerator wouldrepresent the proportion of these costs attributable to a specific group of usersassociated with one specified period of the cycle. It can be shown that thiscongestion cost proportionality allocation also results in an allocation proportional to the tolls in short-run marginal cost pricing or roughly proportionalto benefits (net of any consumer surplus received by different classes of users).Furthermore, these prices normally would have more or less (but not identically) the same proportional relationships as- the short-run marginal costs sothat if different sub-classes of users had approximately the same cross-elasticities with other sectors of demand there would be about the samechoices made between sub-classes of use for the facility (e.g., peak or off-peakuse would be as relatively attractive or unattractive as with short-run marginal cost prices). However, congestion costs are a function of facility designand capacity so that the charges created by this proportionality approachcould differ significantly from the long-run equilibrium relationships if capacity were in short or over supply.

A somewhat similar procedure, specifically assigning facility costs in proportion to short-run marginal costs subject to a breakeven constraint, has alsobeen suggested as a solution to the budgetary or financing problem when

increasing returns prevail.15 Again, more or less the same arguments can bemade in defense (or rebuttal) of the economic logic. Indeed, many of those

advocating proportional mark-ups of this type often do so as much for pragmatic or practical reasons as for reasons of achieving economic efficiency.Thus, the breakeven or budget constraint is introduced because it is considered advantageous in imposing or creating incentives for management toachieve something approaching a minimum cost of production, especially ifthese incentives are considered to be all too easily lacking in the absence ofsuch constraints.

The same problem of determining an appropriate set of mark-ups or pricesin circumstances where strict marginal cost prices are ruled out by the neces

sity of meeting a budget constraint can also be investigated in the context ofa second best situation, e.g., wherein part of the economy meets the normal

competitive assumptions while part does not. In this approach the tolls areset so as to move as high as possible in terms of total utility or welfare achievement taking into account stipulated market imperfections. Almost by definition,

prices determined in this fashion would be superior conceptually (at least in

14 William Vickrey, "Pricing as a Tool in Coordination of Local Transportation," Transportation Economics —A Conference of the Universities-National Bureau of Economic Research (New York, 1965), pp. 275-296.

15 M. Allais, "Le Probleme de la Coordination des Transportes et la TheorieEconomique," Bulletin des Ports et Chaussees et des Mines, (October1947) and reprinted in Revue d'Economie Politique, 1948, No. 2, pp. 212271.


a static framework) to those determined by any of the cruder pricing rulesdiscussed previously; on the other hand, determination of these "second-bestprices" would also require considerably more information. The informationrequirements, though, may be partially mitigated by the fact that if the optimaltransfer rules (defined from the standpoint of second best optimality) canbe defined for distribution of business profits then prices determined bypursuit of simple profit maximizing rules on a decentralized basis will stilllead to a welfare (Pareto) optimum.16 Of course, determination of this optimaldistribution of the transfers of business income will also require a considerableknowledge, almost certainly in excess of that required to apply the simplermark-up or proportionality pricing rules.

Options, Super-Peaks and Some Eclectic Pricing Strategies

Another suggestion for recouping (at least some) costs of transport facilitiesis implicit in what one might call the "option approach" to the pricing ofpublic services.17 In its most dramatic form it relates to the so-called"unexercised option." The argument is that in many cases people would bewilling to pay a price for just the possibility of someday using a facility; inshort, just holding an option to possibly use a facility is of value to someusers. Commonly cited examples of such consumption items are nationalparks and hospitals. A relevant situation common to transport systems mightbe where regular or normal demands, which change over time according todifferent cycles or frequencies, happen to coincide and create an extra largedemand for transport services at a particular time, as distinguished from anormal daily peaking and off-peak situation. Some of these "super peaks,"of course, might be foreseen as occurring seasonally during the year. Exampleswould include yearly peaks on recreational routes during the outdoor recreation season, or shopping travel peaks at Christmas, Easter, and just beforeschool opens in the fall. Other super peaks occur more randomly and maybe caused by weather conditions. Probably the classic example, in fact, ofan occasional or random super-peak in transport is that of urban commuterswho might never want to use transit regularly but still desire enough transit

capacity available for their occasional use if needed, say, in bad weather orif the private automobile is under repair. In a strict sense, it is these randomor irregular peaks to which the option concept would seem to apply best.That is, these extra large demands or "super peaks" require services or systemoutputs over and above those outputs or services normally required and predictable. The question arises of what pricing scheme might be followed torecover costs of these extra "super peak" services or capacity (assuming, atleast for the moment, that government subsidy is ruled out).18

16 M. Boiteaux, "Sur la Gestion des Monopoles Publics Astreints a l'equilibreBudgetaire," Econometrica, (January 1956), pp. 22-40. A very thoroughEnglish language summary and exposition of the Boiteaux article canbe found in Dreze, "Post-war Contributions of French Economists."American Economic Review, Vol. LIV, No. 4, Part II (Supplement),June 1964.

17 Burton A. Weisbrod, "Collective-Consumption Services of Individual-Consumption Goods," Quarterly Journal of Economics, Vol. LXXVIII,No. 3, (August 1964), pp. 471-477.

18 For a discussion of some of the pros and cons of using subsidy for thispurpose see Meyer, Kain and Wohl op. cit., pp. 347-348.


The impact of occasional or optional users is to be distinguished from thatcreated by uncertainty attached to the demand of regular users. This type ofuncertainty or stochastic demand situation can be extremely troublesome forpublic utilities because of sharply rising marginal costs at or beyond capacity.Such problems have been analyzed for public utilities using operational research techniques closely analogous to those used in some of the simplerinventory analyses.19 The major outcome of that discussion, not too surprising

ly,

has been a discovery that on simple statistical principles if the demandsof different users are imperfectly correlated the overall standard deviationapplicable to the totality of all demands will be less than the simple sum ofthe standard deviations of the individual demands. Thus, as in the inventorycase, accumulation or concentration of many individual demands at one pointor at one productive facility will induce increasing returns to scale eventhough the basic cost of the service without uncertainty is subject to constantreturns (or, in the inventory case, the holding costs are linearly and homogeneously related to the size of the inventory).20

Stochastic demand variations attributable to regular users of a transportsystem (as differentiated from occasional users) has not been as major a concern to transport as to public utility analysts or policy makers. The most costlyforms of insufficient transport capacity are likely to be associated withpassenger transport for which demand is generally thought to be binary ornon-continuous in character, i.e., a person is assumed to either appear or notto appear as a demander of passenger transport facilities. The general tendency in transport analysis, as pointed out earlier, is to analyze the impactof these variations in passenger transport demand in terms of congestioncost.21 Freight demands do register, of course, along a continuum and regularusers on occasion can evidence considerable variability in their demands. However, if the probability of not being served within a given period of time is

not extremely large, the cost associated with temporarily insufficient capacityfor freight demands is likely to be expressed in a short delay which in turn

is not likely to be too costly. Furthermore, the fact that the need for promptand reliable freight services is likely to be greater for some commodities thanfor others suggests that with minimal organizational control the commoditieswith the high priority for such services normally can be accommodated withreasonable promptness. Indeed, for many rail transport systems there is often

a large category of low cost bulk commodities (e.g. coal, grains, ores and

lumber) for which prompt service is not important and in some cases is

actually not sought because of the implications for increasing storage costsat the points of delivery.

As for the optional or occasional user of transport, they essentially exercise

19 For an application to public utility pricing see M. Boiteaux, "La Terri-fication au Cout Marginal et les Demandes Aleatoires," Cahiers duSeminaire d'Econometric, (1951) (1).

20 An excellent summary of the underlying inventory theory applied to a

broad context of circumstances can be found in E. S. Mills, "Price, Output and Inventory Policy," New York, 1962.

21 Boiteaux has made some suggestions for treating the public utilitystochastic demand problem in terms that are somewhat analogous tothose applied to congestion cost situations in transport. See in particularthe suggestions in M. Boiteaux, op. ext.


an explicit or implicit option for excess or standby capacity during a particularperiod. Structuring a pricing policy which retrieves the costs of requisitestandby capacity from the holders of these options could aid in a rationalallocation of resources. Difficult problems of identification may arise, however,and in any case those who value an option for standby capacity yet neverhave an occasion to use it could avoid most schemes of user charges. Still, thepricing implication would appear to be that occasional or latent users, ifidentifiable, should be charged most or all of the costs of creating any additional capacity to meet their special needs. Specifically, the option pricingapproach would suggest that a set of surcharges be created over and beyondthe basic and peak period charges assigned to other users in the system byanyone of the pricing methods already discussed (e.g. a tripartite tariff mightbe established for urban systems with off-peak users paying the lowest fare,regular peak-hour users a somewhat higher tariff, and occasional peak-hourusers the highest rate).22

In general, two methods are usually available for accommodating demandfor stochastic super peaks. One is simply to provide the requisite excess orstandby capacity, e.g., capacity stored or held in reserve until called intouse by the extra large demand. This approach implies that levels of servicequality, at least for the regular users, are to be kept relatively constant, evenduring the super peak periods.

The second approach would be to maintain relatively constant capacitylevels and absorb super peak demands through increased congestion . in thefacility or system and corresponding deterioration in service comfort andquality. Each of these two general solutions has ramifications of cost incidenceand pricing structure design depending upon identification of the optionalconsumer or user, and the technological context of the capacity to be supplied.

In the first case, the solution by excess capacity, two important sub-casescan be specified. If the excess capacity is truly excess or standby, i.e. if it isnot used at all except during super peak periods (e.g. old surplus buses keptparked in a lot except during exceptional demand periods), and if optionalpeak demand users can be identified, it would seem reasonable to allocatetotal costs of the standby capacity strictly to the optional super-peak consumers. The regular user would be concerned with the basic charge for thenormal capacity of the system and would not be affected by any charges forexcess capacity. Such a system, it should be noted, has much in common with"average incremental cost" pricing or peak period utility pricing.

However, if the technology of the extra super-peak capacity is such thatit is "fixed" or is subject to joint use by both optional, occasional users andregular ones, then the allocation of the costs of the super-peak capacity increment can become somewhat more involved. A common view is that ifadditional capacity to serve super peak users also improves the quality ofservice to regular users, the regular user should in turn expect to pay someof the cost of the additional capacity. On the other hand, referring back

.to

the discussion of peak period pricing, it could be argued that if the super

22 There would seem to be some notions of this built into the famous "tarifvert" of Electricity de France (James Nelson, op. cit.)


peak demand supplied by joint-use or fixed capacity is firm, or non-shifting,relative to the "regular peak," the super-peak users should be charged allthe costs of the extra capacity. If

,

however, a shifting peak exists betweenregular and super-peak users (the seemingly more likely case), prices shouldbe computed according to the demand and cost parameters of the particularcase (to equalize use in different periods). Thus, if the situation is one with

a firm peak, capacity charges are assessed to the super peak or optionalusers. Regular or non-optional users need cover only direct operating costs.

If a shifting-peak exists, however, then a portion of the capacity cost is

charged to more than one class of user, the exact proportion varying with theparticular parameters of the specific case. As before, the scheme would be tomaximize use of the particular facility subject to the constraints that directcosts and total cost be covered by prices charged. Of course, if the alternativeof marginal cost pricing were employed instead in super peak cases, a surplusof revenues over costs normally would be generated just as in the short-runmarginal cost pricing solution.

In the second case, it may often be necessary or feasible to absorb largedemands with constant capacity, simply b

yreducing the quality of service

provided and overloading the system during the super peaks. Under suchcircumstances, no capacity charges need be retrieved. Still, it may be desirable to charge the optional users to reflect the extra costs they impose on the

regular users. Short-run marginal congestion cost pricing has an obvious andintuitive appeal in such a case. (Of course, this may lead to an increment in

capacity and thus to treatment as the first case.) Schemes for charging consumers of transport services according to each user's proportional contributionto total congestion cost might also be deemed appropriate. The result wouldbe higher prices to optional or super peak users, and possibly lower ones for

off-peak users (e.g., if the "profits" generated by the congestion prices wereused to reduce the basic cost burden of the regular users).

Summary and An Overview

Obviously, transport pricing strategies come in several varieties. The totalnumber of "pure" strategies is

,

however, reasonably limited. To a first approximation only six or seven might be identified. Option pricing, for example,involves no new concepts in a strict sense; rather, it is a synthesis of otherbasic pricing strategies applied to particular circumstances. Similarly, theseveral different manifestations of long-run marginal cost pricing involve nonew concepts beyond that inherent in all long-run marginal cost pricingstrategies, namely that price should be set equal to the long-run equilibriumposition at which the demand curve and long-run marginal cost curveintersect.

This is not to say that these derivative pricing schemes may not be worthyof very careful consideration under many circumstances. For example, proportional mark-ups of either short or long-run marginal cost prices might be

worthy of investigation in circumstances where financial integrity and maintenance of managerial incentives for efficiency are deemed particularly necessary.When demands fluctuate widely over time, pricing schemes seeking betteruse of capacity, that is peak and off-peak price differentiation schemes, should


be useful. Both proportional mark-ups and peak and off-peak pricing are,

though, basically derivative from marginal cost pricing principles.

Simple profit maximization without price discnnination can also be construed as a derivative strategy in the sense that it is simply monopolisticpractice constrained by a limit, namely one, on the number of prices thatcan be charged for any reasonably homogeneous service. As noted, transportmarkets tend to present many opportunities for market segregation and differentiation so that profit maximization pursued without price discriminationtends to suggest some form of self-imposed or other constraint on normal

monopolistic urges. Still, in the broader context of a developing or non-

stationary economy, such pricing might have sufficient implications for savings-investment rates or other objectives of public policy as to merit specialattention.

Of the pure strategies, the two most common are simple average costpricing and value of service pricing. Value of service pricing, as noted, isin concept basically a form of price discriminating monopolistic behavior andits economic implications are best understood in terms of the correspondingconceptual model. Value of service pricing rarely appears, moreover, in perfectly pure form. Indeed, value of service pricing might best be analyzedas a form of constrained price discriminating monopoly and derives much ofits historical popularity from the fact that it lends itself well to the achievement or financing of non-economic goals, particularly in the context of transport regulation. Typically, the monopoly profit derived from large mark-upson certain transport markets has been used to finance losses on other transportactivities serving specified social or political goals. In short, constraints areplaced on prices in the unprofitable "social service" sectors. In the contextof private transportation companies operating under government regulation,as in the United States, this means that the regulatory authorities often cooperate with the private transportation companies in achieving high mark-upsand profits in certain sectors of the transportation business in order to financelosses imposed by these pricing constraints in other sectors. In much thesame vein, simple average cost pricing can be modified to achieve non-economic goals of public policy; as a rule, these modifications tend to createa price structure consistent with a value of service tariff schedule.

The two transport pricing strategies most often advocated by economists,at least in recent years, have tended to be either short or long-run marginalcost pricing. The choice between these two depends very much on practicalconsiderations. In fact, if one can hypothesize almost continual and highlyflexible adjustment of prices to changes in cost, perfect competition and theinstitution of policies or reforms to insure that changes in prices are wellunderstood and forecast by those consuming transport services, it is ratherdifficult to argue against short-run marginal cost pricing on conceptualgrounds. Short-run marginal cost prices tend to have the best immediate resource allocation implications (always assuming that competition is reasonablywell approximated on a consistent basis across the entire economy) and provide quite good guides for investment decisions over time.

The argument for long-run marginal cost prices, by contrast, is that tariffschedules do not adapt with the flexibility or speed required to derive max


irhum benefits from short-run marginal cost pricing. The empirical argumentfor the existence of some lethargy in transport market adjustments wouldseem to be quite strong, given that transport almost invariably operates eitherunder direct government ownership or regulation. The process of adjudicatingor adjusting transport prices to other objectives of political or public policyalmost invariably consumes time. There are, moreover, reasons for doubtingthat the consumers of transport services have perfect foresight in forecastingpotential changes in prices under a short-run marginal cost pricing regime;accordingly, it is quite possible that wrong locational choices and other decisions can be made.

The only challenger to short or long-run marginal cost pricing on conceptualgrounds would be the optimal second best prices (i.e. the prices which whenapplied to transportation would maximize total society welfare taking intoaccount the market imperfections existing in the rest of the economy). Torepeat, marginal cost pricing principles derive their optimality properties onthe premise that they are reasonably universally observed. Such an assumption is rather heroic and likely to be less than perfectly satisfied within mostmodern industrial economies. The important empirical questions are, ofcourse, whether the extra information needed to implement optimal secondbest pricing is ever really available and whether the imperfections in the restof the economy are of sufficient extent or of a character as to really createa substantial loss by pursuing marginal cost pricing within transport.

It should be reasonably clear that choice of a pricing strategy normallydepends at least to some extent on subjective preferences and objectives ofpublic policy. This is true even within a relatively limited and static viewof technologies and demand structures. Among the range of issues to beconsidered are development objectives, administrative questions (as for ex

ample government ability to tax and the possible influence of price structureon savings and investment rates), and policies possibly aiming at income redistribution between regions or social groups. In short, generalization aboutwhat constitutes and optimal pricing strategy is likely to be quite difficult ifnot impossible. Nevertheless, an effort to at least make more orderly the

process of identifying goals and deciding between alternative pricing strategiesseems worthwhile.

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