Transportation Economics/Costs

Costs

IntroductionEdit

Price, cost and investment issues in transportation garner intense interest. This is certainly to be expected from a sector that has been subject to continued public intervention since the ninteenth century. While arguments of market failure, where the private sector would not provide the socially optimal amount of transportation service, have previously been used to justify the economic regulations which characterized the airline, bus, trucking, and rail industries, it is now generally agreed, and supported by empirical evidence, that the move to a deregulated system, in which the structure and conduct of the different modes are a result of the interplay of market forces occurring within and between modes, will result in greater efficiency and service.

Many factors have led to a reexamination of where, and in which mode, transportation investments should take place. First, and perhaps most importantly, is the general move to place traditional government activities in a market setting. The privatization and corporatization of roadways and parts of the aviation systems are good examples of this phenomenon. Second, there is now a continual and increasing fiscal pressure exerted on all parts of the economy as the nation reduces the proportion of the economy’s resources which are appropriated by government. Third, there is increasing pressure to fully reflect the environmental, noise, congestion, and safety costs in prices paid by transportation system users. Finally, there is an avid interest in the prospect of new modes like high speed rail (HSR) to relieve airport congestion and improve in environmental quality. Such a major investment decision ought not be made without understanding the full cost implications of a technology or investment compared to alternatives.

This chapter introduces cost concepts, and evidence on internal costs. The chapter on Negative externalities reviews external costs.

SupplyEdit

In imperfectly competitive markets, there is no one-to-one relation between P and Q supplied, i.e., no supply curve. Each firm makes supply quantity decision which maximises profit, taking into account the nature of competition (more on this in pricing section).

Supply function (curve). specifies the relationship between price and output supplied in the market. In a perfectly competitive market, the supply curve is well defined. Much of the work in transportation supply does not estimate Supply-curve. Instead, focus is on studying behaviour of the aggregate costs (in relation to outputs) and to devising the procedure for estimating costs for specific services (or traffic). Transport economists normally call the former as aggregate costing and the latter as disaggregate costing. For aggregate costing, all of the cost concepts developed in micro-economics can be directly applied.

TE-Costs-SupplyCurve.png

Types of CostsEdit

There are many types of costs. Key terms and brief definitions are below.

  • Fixed costs (C_F): The costs which do not vary with output.
  • Variable costs (C_V): The costs which change as output levels are changed. The classification of costs as variable or fixed is a function of both the length of the time horizon and the extent of indivisibility over the range of output considered.
  • Total costs (C_T): Total expenditures required to achieve a given level of output (Q).
    • Total costs = fixed costs + variable costs. = a + bQ
  • Average costs: The total cost divided by the level of output.
    • Average Cost for a single product firm: C_A = C_T/Q,
      • Average fixed cost = a/Q
      • Average variable cost = b
    • Average Cost for a multi-product firm is not obvious (i.e. which output), two methods
      • Ray average cost: Fix the output proportion and then examine how costs change as the scale of output is increased along the output 'ray'. Like moving out along a ray in output space - thus 'ray' average cost; multiproduct scale economies exists if there is DRAC (declining ray average cost). (Fixity or Variability depends on the time horizon of the decision problem and is closely related to the indivisibility of production (costs).)
      • Incremental average cost: Fix all other output except one, and then examine the incremental cost of producing more ith output - thus, incremental average cost; product-specific scale economies exist if there is DAIC (declining average incremental cost).
  • Marginal (or incremental) cost: The derivative (difference) of Total Cost with respect to a change in output.
    • Marginal Cost MC = dC_T/dQ
    • Incremental Cost IC = \Delta C_T/ \Delta Q
  • Opportunity costs: The actual opportunities forgone as a consequence of doing one thing as opposed to another. Opportunity cost represents true economics costs, and thus, must be used in all cases.
  • Social cost: The cost the society incurs when its resources are used to produce a given commodity, taking into account the external costs and benefits.
  • Private cost: The cost a producer incurs in getting the resources used in production.

Shared costsEdit

The production of transport services in most modes involves joint and common costs. A joint cost occurs when the production of one good inevitably results in the production of another good in some fixed proportion. For example, consider a rail line running only from point A to point B. The movement of a train from A to B will result in a return movement from B to A. Since the trip from A to B inevitably results in the costs of the return trip, joint costs arise. Some of the costs are not traceable to the production of a specific trip, so it is not possible to fully allocate all costs nor to identify separate marginal costs for each of the joint products. For example, it is not possible to identify a marginal cost for an i to j trip and a separate marginal cost for a j to i trip. Only the marginal cost of the round trip, what is produced, is identifiable.

Common costs arise when the facilities used to produce one transport service are also used to produce other transport services (e.g. when track or terminals used to produce freight services are also used for passenger services). The production of a unit of freight transportation does not, however, automatically lead to the production of passenger services. Thus, unlike joint costs, the use of transport facilities to produce one good does not inevitably lead to the production of some other transport service since output proportions can be varied. The question arises whether or not the presence of joint and common costs will prevent the market mechanism from generating efficient prices. Substantial literature in transport economics (Mohring, 1976; Button, 1982; Kahn, 1970) has clearly shown that conditions of joint, common or non-allocable costs will not preclude economically efficient pricing.

  • Traceable cost (Untraceable cost): A cost which can (cannot) be directly assigned to a particular output (service) on a cause-and-effect basis. Traceable (untraceable) costs may be fixed or variable (or indivisible variable). Traceability is associated with production of more than one output, while untraceable costs possess either (or both) common costs and joint costs. The ability to identify costs with an aggregate measure of output supplied (e.g. the costs of a round trip journey) does not imply that the costs are traceable to specific services provided.
  • Joint cost: A cost which is incurred simultaneously during the production for two or more products, where it is not possible to separate the contributions between beneficaries. These may be fixed or variable. (e.g. cow hides and cow steaks)
  • Common cost: A cost which is incurred simultaneously for a whole organization, where it cannot be allocated directly to any particular product. These may be fixed or variable. (e.g. the farm's driveway)


External and Internal CostsEdit

External costs are discussed more in Negative externalities

Economics has a long tradition of distinguishing those costs which are fully internalized by economic agents (internal or private costs) and those which are not (external or social costs). The difference comes from the way that economics views the series of interrelated markets. Agents (individuals, households, firms and governments) in these markets interact by buying and selling goods are services, as inputs to and outputs from production. A firm pays an individual for labor services performed and that individual pays the grocery store for the food purchased and the grocery store pays the utility for the electricity and heat it uses in the store. Through these market transactions, the cost of providing the good or service in each case is reflected in the price which one agent pays to another. As long as these prices reflect all costs, markets will provide the required, desirable, and economically efficient amount of the good or service in question.

The interaction of economic agents, the costs and benefits they convey or impose on one another are fully reflected in the prices which are charged. However, when the actions of one economic agent alter the environment of another economic agent, there is an externality. An action by which one consumers purchase changes the prices paid by another is dubbed a pecuniary externality and is not analyzed here further; rather it is the non-pecuniary externalities with which we are concerned. More formally, "an externality refers to a commodity bundle that is supplied by an economic agent to another economic agent in the absence of any related economic transaction between the agents" (Spulber, 1989). [1] Note that this definition requires that there not be any transaction or negotiation between either of the two agents. The essential distinction which is made is harm committed between strangers which is an external cost and harm committed between parties in an economic transaction which is an internal cost. A factory which emits smoke forcing nearby residents to clean their clothes, cars and windows more often, and using real resources to do so, is generating an externality or, if we return to our example above, the grocery store is generating an externality if it generates a lot of garbage in the surrounding area, forcing nearby residents to spend time and money cleaning their yards and street.

There are alternative solutions proposed for the mitigation of these externalities. One is to use pricing to internalize the externalities; that is, including the cost which the externalities impose in the price of the product/service which generate them. If in fact the store charged its customers a fee and this fee was used to pay for the cleanup we can say the externality of ‘unsightly garbage’ has been internalized. Closer to our research focus, an automobile user inflicts a pollution externality on others when the car emits smoke and noxious gases from its tailpipe, or a jet aircraft generates a noise externality as it flies its landing approach over communities near the airport. However, without property rights to the commodities of clean air or quiet, it is difficult to imagine the formation of markets. The individual demand for commodities is not clearly defined unless commodities are owned and have transferable property rights. It is generally argued that property rights will arise when it is economic for those affected by externalities to internalize the externalities. These two issues are important elements to this research since the implicit assumption is that pricing any of the externalities is desirable. Secondly, we assume that the property rights for clean air, safety and quiet rest with the community not auto, rail and air users. Finally, we are assuming that pricing, meaning the exchange of property rights, is possible. These issues are considered in greater detail in Chapter 3 where the broad range of estimates for the costs of the externalities are considered.

Other termsEdit

  • Sunk costs: These are costs that were incurred in the past. Sunk costs are irrelevant for decisions, because they cannot be changed.
  • Indivisible costs: Do not vary continuously with different levels of output or must expenditures, but be made in discrete "lumps". Indivisible costs are usually variable for larger but not for smaller changes in output
  • Escapable costs (or Avoidable costs): A cost which can be avoided by curtailing production. There are both escapable fixed costs and escapable variable costs. The escapability of costs depends on the time horizon and indivisibility of the costs, and on the opportunity costs of assets in question.

Time HorizonEdit

Once having established the cost function it must be developed in a way which makes it amenable to decision-making. First, it is important to consider the length of the planning horizon and how many degrees of freedom we have. For example, a trucking firm facing a new rail subsidy policy will operate on different variables in the short run or a period in which it cannot adjust all of its decision variables than it would over the long run, the period over which it can adjust everything.

Long run costs, using the standard economic definition, are all variable; there are no fixed costs. However, in the short run, the ability to vary costs in response to changing output levels and mixes differs among the various modes of transportation. Since some inputs are fixed, short run average cost is likely to continue to fall as more output is produced until full capacity utilization is reached. Another potential source of cost economies in transportation are economies of traffic density; unit cost per passenger-kilometer decreases as traffic flows increase over a fixed network. Density economies are a result of using a network more efficiently. The potential for density economies will depend upon the configuration of the network. Carriers in some modes, such as air, have reorganized their network, in part, to realize these economies.

In the long run, additional investment is needed to increase capacity and/or other fixed inputs. The long run average cost curve, however, is formed by the envelope of the short run average cost curves. For some industries, the long run average cost often decreases over a broad range of output as firm size (both output and capacity) expands. This is called economies of scale. The presence of economies at the relevant range of firm size means that the larger the size of the firm, the lower the per-unit cost of output. These economies of scale may potentially take a variety of forms in transportation services and may be thought to vary significantly according to the mode of transportation involved.


Time horizon in economic theory

  • Short run: the period of time in which the input of one or more productive agents is fixed
  • Long run: the period of time in which all inputs are variable

actual length of the time horizon to use depends on

  • the type of decision: when do the costs and benefits occur ?
  • the expected life time of assets involved
  • the time horizon for major transportation projects tends to be lengthy relative to that in other industries

The relationship between short and long run costs is explained by the envelope theorem. That is, the short run cost functions represent the behavior of costs when at least one factor input is fixed. If one were to develop cost functions for each level of the fixed factor the envelope or lower bound of these costs would form the long run cost function. Thus, the long run cost is constructed from information on the short run cost curves. The firm in its decision-making wishes to first minimize costs for a given output given its plant size and then minimize costs over plant sizes.

In the diagram below the relationship between average and marginal costs for four different firm sizes is illustrated. Note that this set of cost curves was generated from a non-homogeneous production function. You will note that the long run average cost function (LAC) is U-shaped thereby exhibiting all dimensions of scale economies.


TE-Costs-LRACSRAC.png

Mathematically

C\left( Q \right)\equiv C_{s}\left( Q,K\left( Q \right) \right)

\frac{\partial C\left( Q \right)}{\partial Q}=\frac{\partial C_{s}\left( Q,K\left( Q \right) \right)}{\partial Q}+\frac{\partial C_{s}\left( Q,K\left( Q \right) \right)}{\partial K}\bullet \frac{\partial K\left( Q \right)}{\partial Q}

where: \frac{\partial C_{s}\left( Q,K\left( Q \right) \right)}{\partial K}=0 provides the optimal plant size.

Indicators of Aggregate Cost BehaviorEdit

Scale economies is the behavior of costs when the AMOUNT of an output increases while scope economies refers to the changes in costs when the NUMBER of outputs increases.

Economies of ScaleEdit

Economies of scale refer to a long run average cost curve which slopes down as the size of the transport firm increases. The presence of economies of scale means that as the size of the transport firm gets larger, the average or unit cost gets smaller. Since most industries have variable returns to scale cost characteristics, whether or not a particular firm enjoys increasing, constant or decreasing returns to scale depends on the overall market size and the organization of the industry.

The presence or absence of scale economies is important for the industrial structure of the mode. If there were significant scale economies, it would imply fewer larger carriers would be more efficient and this, under competitive market circumstances, would naturally evolve over time. Scale economies are important for pricing purposes since the greater are the scale economies, the more do average and marginal costs deviate. It would, therefore, be impossible to avoid a deficit from long run marginal [social] cost pricing.

Another note of terminology should be mentioned. Economics of scale is a cost concept, returns to scale is a related idea but refers to production, and the quantity of inputs needed. If we double all inputs, and more than double outputs, we have increasing returns to scale. If we have less than twice the number of outputs, we have decreasing returns to scale. If we get exactly twice the output, then there are constant returns to scale. In this study, since we are referring to costs, we use economies of scale. The presence of economies of scale does not imply the presence of returns to scale.

Scale measures long-run (fully adjusted) relationship between average cost and output. Since a firm can change its size (network and capacity) in the long run, Economies of Scale (EoS) measures the relationship between average cost and firm size. EoS can be measured from an estimated aggregate cost function by computing the elasticity of total cost with respect to output and firm size (network size for the case of a transport firm).

Returns to Scale (Output Measure)Edit

Increasing Returns to Scale (RtS)

f(tx_1, tx_2) > t f(x_1, x_2)

Decreasing RtS

f(tx_1, tx_2) < t f(x_1, x_2)

Economies of Scale (Cost Measure)Edit

Economies of scale (EoS) represent the behavior of costs with a change in output when all factors are allowed to vary. Scale economies is clearly a long run concept. The production function equivalent is returns to scale. If cost increase less than proportionately with output, the cost function is said to exhibit economies of scale, if costs and output increase in the same proportion, there are said to be 'constant returns to scale' and if costs increase more than proportionately with output, there are diseconomies of scale.

  • if cost elasticity < 1, or LRMC < LRAC -> increasing EoS
  • if cost elasticity = 1, or LRMC = LRAC -> constant EoS
  • if cost elasticity > 1, or LRMC > LRAC -> decreasing EoS

Economies of DensityEdit

There has been some confusion in the literature between economies of scale and economies of density. These two distinct concepts have been erroneously used interchangeably in a number of studies where the purpose was to determine whether or not a particular mode of transportation (the railway mode has been the subject of considerable attention) is characterized by increasing economies or diseconomies of scale. There is a distinction between density and scale economies. Density economies are said to exist when a one percent increase in all outputs, holding network size, production technology, and input prices constant, increase the firm’s cost by less than one percent. In contrast, scale economies exist when a one percent increase in output and size of network increases the cost by less than one percent, with production technology and input prices held constant.

Economies of density, although they have a different basis than scale economies, can also contribute to the shape of the modal industry structure. It can affect the way a carrier will organize the delivery of its service spatially. The presence of density economies can affect the introduction of efficient pricing in the short term, but generally not over the long term since at some point density economies will be exhausted. This, however, will depend upon the size of the market. In the air market, for example, deregulation has allowed carriers to respond to market forces and obtain the available density economies to varying degrees.


Returns to Density similar to returns to a capacity utilization when capacity is fixed in the short run. Since the plant size (network size for the case of transportation firms) is largely fixed in the short run, RTD measures the behavior of cost when increasing traffic level (output) given the plant size (network size). It is measured by the cost elasticity with respect to output.

  • if cost elasticity < 1, or SRMC < SRAC -> increasing EoD
  • if cost elasticity = 1, or SRMC = SRAC -> constant EoD
  • if cost elasticity > 1, or SRMC > SRAC -> decreasing EoD

Because of the presence of high fixed costs and cost of operating terminals (airports, stations, depots, etc), most transportation firms have increasing RTD.

Economies of Capacity UtilizationEdit

A subtle distinction exists between economies of density, which is a spatial concept, and economies of capacity utilization, which may be aspatial. As a fixed capacity is used more intensively, the fixed cost can be spread over more units or output, and we have declining average cost, economies of scale. However, as the capacity is approached, costs may rise as delays occur. This gives a u-shaped cost curve.

While economies of scale refer to declining average costs, for whatever reason, when output increases; and economies of density refer to declining costs when output increases and the network mileage is held constant; economies of capacity utilization refers to declining costs as the percentage of capacity which is used increases, where capacity may be spatial or aspatial.

While density refers to how much space is occupied, capacity refers to how much a capacitated server (e.g. a bottleneck, the number of seats on a plane) is occupied, and may incorporate economies of density if the link is capacitated, such as a congesting roadway. However if a link has unlimited (or virtually unlimited) capacity, such as intercity passenger trains on a dedicated right-of-way at low levels of traffic, then economy of density is a more appropriate concept. Another way of viewing the difference is that economies of density refers to linear miles, while economies of utilization refer to lane miles.

Economies of ScopeEdit

Economies of Scope

Typically, the transport firm produces a large number of conceptually distinct products from a common production facility. In addition, the products of most transportation carriers are differentiated by time, space and quality. Because a number of distinct non-homogeneous outputs are being produced from a common production facility, joint and common costs arise. The presence of joint and common costs give rise to economies of scope. There has been some confusion in the multi-product literature among the concepts of sub-additivity of the cost function, trans-ray convexity, inter-product complementarity and economies of scope. Sub additivity is the most general concept and refers to a cost function which exhibits the characteristic that it is less costly to produce different amounts of any number of goods in one plant or firm than to sub divide the products or service in any proportion among two or more plants. Trans-ray convexity is a somewhat narrower concept. It refers to a cost function which exhibits the characteristic that for any given set of output vectors, the costs of producing a weighted average of the given output vectors is no greater than the weighted average of producing them on a stand alone basis. Economies of scope refers to the cost characteristic that a single firm multi-product technology is less costly than a single product multi-firm technology. It, therefore, is addressing the issue of the cost of adding another product to the product line. Inter-product complementarity is a weak test of scope economies. It refers to the effect on the marginal cost of one product when the output of some other product changes. It, therefore, is changing the amount of output of two or more products and not the number of products. Whether scope economies exist and the extent to which they exist depend upon both the number of products and the level of each output. There have not been definitive empirical estimates of economies of scope for transportation modes which are based on reliable data and undertaken in a theoretically consistently fashion.

Thought Question: Most firms produce multiple products. Why do multiple product firms exist ?

It must be cheaper to have one firm to produce multiple products than have separate firms produce each type of product.

Economies of scope arise from shared or jointly utilised inputs, e.g., imperfectly divisible plant which if used to produce only one product would have excess capacity (freight and passenger services using same airplane, forward-back haul production using a truck or rail car, etc.).

This can be represented graphically as in the diagram on the right. In production space an isoquant would link two outputs and would have the interpretation of an isoinput line, that is, it would be the combination of outputs which are possible with a given amount of inputs. If there were economies of scope, the line would be concave to the origin, if there were economies of specialization it would be convex and if there were no scope economies it would be a straight line at 45 degrees.

Let q = (q_1,...,q_n), n = number of different outputs.

Economies of scope exists if

  c(q_1) + ... + c(q_n) > c(q_1,...,q_n).

That is, it is cheaper to have one firm produce all outputs than to have n separate firms produce each output q_i, where c(q) is the cost for a firm to produce output q.


Scope economies are a weak form of 'transray convexity' and are said to exist if it is cheaper to produce two products in the same firm rather than have them produced by two different firms. Economies of scope are generally assessed by examining the cross-partial derivative between two outputs, how does the marginal cost of output one change when output two is added to the production process.


Changes in CostEdit

Costs can change for any number of different reasons. It is important that one is able to identify the source of any cost increase or decreases over time and with changes in the amount and composition of output. The sources of cost fluctuations include:

  • density and capacity utilization; movements along the short run cost function
  • scale economies; movements along the long run cost function
  • scope economies; shifts of the marginal cost function for one good with changes in product mix
  • technical change which may alter the level and shape of the cost function

Characterizing Transportation CostsEdit

All modes of transport experience:

  • economies of vehicle size up to a point
  • increasing returns in provision of way and track capacity
  • economies of longer distance travelled
  • rapidly rising average cost with increased speed;
  • exponentially increasing energy consumption with speed
  • difficultly in identifying the costs associated with particular traffic because of indivisibilities in production and heterogeneity of output
  • declining unit costs over a range of output because of indivisibilities,
    • e.g. the backhaul problem, increase in traffic on the backhaul will reduce the average costs of the round trip operation
    • indivisibilities in production give rise to "kinked" average cost curves and discontinuous marginal costs

CostingEdit

Costing is the method or process of ascertaining the relationship between costs and outputs in a way which is useful for making decisions (managerial, strategic, regulatory policy etc.). There are numerous examples where detailed cost information is necessary for carriers' management decisions and government's regulatory decisions. Also there are many carrier and government decisions requiring information about the behaviour of aggregate costs of a firm.

Carrier Management DecisionsEdit

Requiring disaggregate cost info:

  • rates and rate structure decisions;
    • rate setting
    • shipper-carrier negotiations
  • financial viability of specific services; e.g.,
    • rail passenger operations,
    • rail branch lines
  • decision to launch a specific service
  • application of subsidies
  • compensation for running rights;
    • passenger trains
    • leased right of way

Requiring aggregate cost info:

  • carrier network plan
  • plan for mergers and acquisitions
  • strategic plan
  • major investment decisions

Policy DecisionsEdit

Requiring disaggregate cost info:

  • enforcing pricing regulation
  • decisions on public subsidies
  • branchline abandonment decision - "short-line" sales
  • user charges for government-owned infrastructure

Requiring aggregate cost info:

  • decision on price and entry regulation;
    • natural monopoly question - scale and density economies
    • effect of regulation on efficiency;
      • allocative efficiency
      • X-efficiency
  • approval of mergers and acquisition - scale and density economies
  • decisions on transport infrastructure investment
  • licensing of competitive services

Aggregate Cost AnalysisEdit

Econometric cost functions are estimated to study the behaviour of aggregate costs in relation to the aggregate output level (economies of scale) and output mix (economies of scope). The aggregate cost function also allows one to estimate the changes in productive efficiency over time. This allows inference about the effect of regulation on productivity of an industry

Which CostsEdit

Economic theory suggests that costs are a function of at least factor prices and outputs. In practice, calculating costs, prices, or outputs can be tricky. For example, how should capital costs be determined ?

Capital costs may occur over one year but it is likely to be used over a long period of time. So we should use the opportunity costs which includes depreciation and interest costs. The capital stock of a firm will vary year to year.

Accountants tend to use historical costs which do not account for inflation. The point is that in the real world get all sorts of complications.

Prices and OutputsEdit

For prices and outputs, a firm may use many inputs and provide many different outputs. Transportation outputs are produced over a spatial network. An appropriate definition of outputs is the movement of a commodity/passenger from an origin to a destination - a commodity/passenger trip. A trip from A to B is different from a trip from C to D (or B to A) even if the same distance. Ideally, a transport cost model should account for this multiproduct nature. But cannot specify thousands of outputs -some aggregate is necessary. Often. lack of data requires aggregation to a single output measure like ton-kilometres or passenger-kilometres.

Attribute VariablesEdit

To account for the multidimensional heterogeneous nature of outputs, one can use attribute variables such as average length of haul or average stage length. They will vary by firms. Operating characteristics such as average shipment size, average load factor, etc., also affect costs. For example, if plane or truck is not full, there is unused capacity; adding a commodity trip may incur little marginal cost; longer distances can lower AC by spreading terminal costs or takeoff fuel costs.

EstimationEdit

Cost function Estimation requires decisions on:

  • short run vs. long run cost function
    • short run cost functions from time series data;
    • long run cost functions from cross-section data;
  • variable vs. total cost function;
    • variable cost functions are estimated by fixing some inputs such as physical plants (rail roadbed and track; aircraft fleet, etc)
  • the choice of functional form
  • the choice of output measure;
    • single vs. multiple output measures
    • revenue output vs. available output
  • the choice of the level of aggregation of cost accounts
  • the choice of attribute variables to account for heterogeneous nature of outputs being produced over time or across different firms in the sample data.

Difficulties with CostingEdit

  • multi-dimensionality and heterogeneous nature of outputs
  • indivisibilities in production
  • costs may not occur at the same time as the outputs being produced. eg. capital costs may over one year but it is likely to be used over several years, and some expenses occur some time after the increases in outputs (expenses occur less frequently than changes in (train) trips), etc
  • ambiguity in cost standards
  • difficulty of relating past to future
    • input price changes
    • changes in production technology
    • changes in operating conditions

Disaggregate CostingEdit

Disaggregate costing can be used to estimate the variable cost of a block of traffic, or traffic on a particular line,etc. it is useful for setting rates, investment decisions, subsidy determinations, etc. by companies themselves or government

Deductive (economic) vs inductive (engineering) approaches are used in transportation modeling, and analysis. The deductive approach uses modeling and prior relationships to specify a functional relationship which is then examined statistically. An inductive approach is based on a detailed understanding of physical processes.

Inductive Approaches

  • Use of Engineering Relationships

Economic Approaches

  • Average Cost Calculation using Accounting Info
  • Statistical Costing

Engineering CostingEdit

Engineering costing focuses on the amount of each input required to produce a unit of output, or the technical coefficients of production. combining such coefficients with the costs of the inputs yields the cost function for the particular output.

There are two approaches to engineering costing:

  • to derive the technical coefficients from physical laws or precise engineering relationships.
  • to empirically establish the technical relationship by controlled experiment.
  • advantage
    • Accuracy ? Precision?
  • shortcomings:
    • data- and time-intensive costly
    • nonstochastic
    • must have well defined production processes

Accounting CostingEdit

  • compiles the cost accounts categories relevant to the output or service in question, and use that information to estimate the costs associated with a specific movement.
  • advantages:
    • relatively cheap
    • convenient
  • shortcomings:
    • data/information must exist
    • the recorded values of assets may not be a reliable indicator of the actual opportunity costs of those assets
    • the cost accounts may not distinguish fixed vs. variable costs Y over estimation of the marginal cost.
    • the accounts are classified by the types of expenses, not by output type, it is difficult to uncover the true relations between cost and outputs
    • the aggregation in the accounts may prevent identifying the costs which can be related to the production of particular outputs


Statistical CostingEdit

Statistical costing employes statistical techniques (usually multiple regression analysis) to infer cost-output relationships from a sample of actual operating experiences. It makes use of accounting information.

Basic steps in statistical costing are:

(1) Decompose and identify the intermediate work units associated with the specific traffic. For example, costing 500 tons of coal from point a to b, intermediate work units may consist of line haul, switching, terminal activities, administration, etc. Explanatory variables for these activities would include ton-miles, car-miles, yard-switching miles, train-hours, gallons of fuel, etc.

(2) Establish relationship between factor inputs and the intermediate process. This can be done by direct assignment of an expense category to the work unit, if causal relation is clear. Often, expenses are common to several types of traffic, so estimate statistical relationship with regression analysis.

For example, regression of track and roadway maintenance (TRM)

TRM = f(\text{ton-miles, yard-switching minutes, train switching minutes, road miles})

(3) Apply the marginal/unit costs of the intermediate work units estimated in step (2) to the work units identified in step (1).

(4) Sum all expenses in step (3) to calculate the total avoidable cost of a block of traffic.


Evidence on Carrier CostsEdit

How do the long run concepts of economies of scale and economies of scope and the short run concepts of economies of density and economies of capacity utilization influence costs? Why are they important to our discussion of transport infrastructure pricing? These questions will be addressed in the following section.

Air CarriersEdit

A considerable number of studies, Douglas and Miller (1974) [2], Keeler (1974) [3], Caves, Christensen and Tretheway (1984) [4], Caves, Christensen, Tretheway and Windle (1985)[5], McShan and Windle (1989)[6], and Gillen, Oum, and Tretheway (1985, 1990)[7][8], have been directed at determining the functional relationship between total per-unit operating costs and firm size in airlines. All studies have shown that economies to scale are roughly constant; thus, size does not generate lower per-unit costs. However, generally, the measures of economies of density illustrate that unit cost would decrease for all carriers if they carried more traffic within their given network. In other words, the industry experienced increasing returns to density. The results also indicated that the unexploited economies of density are larger for low density carriers. Caves, Christensen, and Tretheway (1984) have shown that it is important when measuring costs to include a network size variable in the cost function, along with output, which would allow for the distinction between economies of scale and economies of density. McShan and Windle (1989) utilize the same data set as that used by Caves et al., and explicitly account for the hub and spoke configuration that has developed in the US since deregulation in 1978. They estimate a long run cost function which employs all the variables included in Caves et. al., and found economies to density of about 1.35. The hubbing variable indicates that, ceteris paribus, a carrier with 1% more of its traffic handled at hub airports expects to enjoy 0.11% lower cost than other similar carriers.

Intercity BusesEdit

Gillen and Oum (1984)[9] found that the hypothesis of no economies of scale can be rejected for the intercity bus industry in Canada; there are diseconomies of scale at the mean of the sample (0.91). Large firms were found to exhibit strong diseconomies of scale, and small and medium sized firms exhibit slight departures from constant returns. No cost complementarities are found to exist between the three outputs, namely, number of scheduled passengers, revenue vehicle miles of charter, tour and contract services, and real revenue from freight. These results, however, may be biased since no network measure was included in the estimating equations. The scale economy measure will, therefore, contain some of the influence of available density economies.

Since deregulation of the intercity bus industries in the US and the UK., the number of firms has been significantly reduced. In the absence of scale economies, the forces leading to this industry structure would include density economies. We have, for example, observed route reorganization to approximate hub-and-spoke systems and the use of smaller feeder buses on some rural routes. The industry reorganization is similar to what occurred in the airline industry. The consolidation of firms was driven by density and not scale economies. One significant difference between these two industries, however, is airline demand has been growing while intercity bus demand is declining.

Railway ServicesEdit

The structure of railway costs is generally characterized by high fixed costs and low variable costs per unit of output. The essential production facilities in the railway industry exhibit a significant degree of indivisibility. As with other modes, the production of railway services give rise to economies of scope over some output ranges. For example, track and terminals used to produce freight services are also used to produce passenger services.

Caves, Christensen and Tretheway (1980)[10] have found that the US railway industry is characterized by no economies of scale over the relevant range of outputs. However, their sample does not include relatively small railroads, firms with less than 500 miles of track. Griliches (1972)[11] and Charney, Sidhu and Due (1977)[12] have found economies scale for such small US railroads. Friedlaender and Spady (1981) [13] suggested that there may be very small economies of scale with respect to firm size. Keeler (1974)[14], Harris (1977)[15], Friedlaender and Spady (1981) and Levin (1981)[16] have all shown that there are large economies of traffic density in the US railroad industry. They show that, allowing all factors of production except route mileage to vary, a railway producing 10 million revenue ton-miles per mile of road, for example, will have substantially lower average costs than will a railway producing only 5 million revenue ton-miles per mile of road. Harris (1977) estimated that approximately one-third of density economies were due to declining average capital costs, and two-thirds due to declining fixed operating costs, such as maintenance, and administration. Friedlaender and Spady (1981) estimate a short run cost function with five variable inputs, one quasi-fixed factor (structures) and two outputs which take the form of hedonic functions, accounting for factors such as low density route miles and traffic mixes. The study found no economies of scale. Caves, Christensen, Tretheway and Windle (1985) have examined economies of scale and density in the US railroads. Their basic result demonstrates that there are substantial economies of density in the US railway operations.

Evidence on Infrastructure CostsEdit

As early as 1962, Mohring and Harwitz[17] demonstrated that the financial viability of an infrastructure facility, under optimal pricing and investment, will depend largely upon the characteristics of its cost function. To quote Winston (1991)[18]: “ If capacity and durability costs are jointly characterized by constant returns to scale, then the facility’s revenue from marginal cost pricing will fully cover its capital and operating costs. If costs are characterized by increasing returns to scale, then marginal cost pricing will not cover costs; conversely, if costs are characterized by decreasing returns to scale, marginal cost pricing will provide excess revenue.”

The objective of this section is to provide a summary of the theoretical and empirical literature on the cost characteristics of modal infrastructure. The discussion will deal with the following types of infrastructure: airports, highways, and railways.

In developing a set of socially efficient prices for modes of intercity transport, it is not just the carrier’s cost structure which is important. Airports, roadways and harbors all represent public capital which is used by the carriers in the different modes to produce and deliver their modal services. This capital must also be priced in an efficient way to achieve the economic welfare gains available from economically efficient pricing. As with the carriers, the ability to apply first best pricing principles to infrastructure and still satisfy cost recovery constraints will depend upon the cost characteristics of building and maintaining the infrastructure.

As with carriers, the cost characteristics for infrastructure providers include scale economies, scope economies, density economies and utilization economies. Scale economies refer to the size of a facility; for example, is it cheaper to build three runways than it is to provide two runways? If so, there are economies of scale in the provision of runways. Scope economies encompass similar concepts as with carriers. Small, Winston and Evans (1989)[19] refer to scope economies in highways when both capacity and durability are supplied. Capacity refers to the number of lanes while durability refers to the ability to carry heavier vehicles. A similar concept would apply to airports: small and large aircraft, VFR and IFR traffic, and to harbors: large ships and small ships. Although rail infrastructure is currently supplied by the same firms operating the trains, there have been moves to separate infrastructure and carrier services. This separation will mean the track and terminals will have to be priced separately from carrier services.

Density economies should also, in principle, be evident in the provision of infrastructure. It is, for example, possible to expand outputs and all inputs for highways while holding the size of the network fixed.

Utilization economies refer to the short run cost function. They describe how quickly average and marginal costs will fall as capacity utilization approaches capacity. Although not of direct interest, they are important to consider in any cost estimation since failure to consider capacity utilization can bias upward the measures of both long run average and marginal costs.

AirportsEdit

Economists have typically assumed that capacity expansion is divisible. Morrison (1983)[20], in his analysis of the optimal pricing and investment in airport runways, has shown that airport capacity construction is characterized by no economies of scale, and, therefore, under perfect divisibility of capacity expansion, the revenue from tolls will be exactly equal to the capital cost of capacity investment (Mohring and Harwitz, 1962). Morrison’s results, however, were based on a sample of 22 of the busiest airports in the US and did not include any small airports. In the literature, there is no empirical evidence on the cost characteristics of capacity construction of new small airports or capacity expansion of existing small airports (e.g. one runway).

HighwaysEdit

In general, highways produce two outputs: traffic volume which requires capacity in terms of the number of lanes, and standard axle loading which require durability in terms of the thickness of the pavement. Prior to determining economies of scale in this multi-product case, the measure of economies of scale for each output, or the product specific economies of scale, must be examined. Small, Winston, and Evans (1989) reported the existence of significant economies of scale associated with the durability output of roads, the ability to handle axle loads. This is because the pavement’s ability to sustain traffic increases proportionally more than its thickness. They also found evidence that there are slight economies of scale in the provision of road capacity; i.e. the capacity to handle traffic volume. However, they reported diseconomies of scope from the joint production of durability and capacity because as the road is made wider to accommodate more traffic, the cost of any additional thickness rises since all the lanes must be built to the same standard of thickness. They conclude that these three factors together result in highway production having approximately constant returns to scale. In other words, the output-specific scale economies are offset by the diseconomies of scope in producing them jointly.

RailwaysEdit

An important difference between rail and other modes of transportation is that most railroads provide the infrastructure themselves and the pricing is undertaken jointly for carrier services and infrastructure. However, in a few cases, ownership and/or management of the trackage has been separated from carriers. Sweden is a good example but even in the US there have been joint running rights on tracks. This creates a situation whereby one firm may be responsible for the provision of trackage and another for carrier services. It is, therefore, legitimate to ask if there are any scale economies in the provision of railway infrastructure. There are no empirical estimates but it may be possible to use some of the Small, Winston and Evans (1988) work for roads to shed some light on the issue.

Small et al. argue road infrastructure produces two outputs, durability and capacity. The former refers to the thickness of roads and the latter to their width. They found economies with respect to durability, but this is less likely to occur with a rail line since there would be a relatively broad range of rail car axle loading for a given level of durability of rail, ballast and ties. Thus, there may be some minor economies. The authors found diseconomies of scope from the joint production of durability and capacity for highways. These diseconomies are less likely to be evident in rail due to the broad range of durability noted above and the ability to restrict usage to specific tracks. On balance, it may be there are generally constant or minor economies in the provision of rail line infrastructure. The output specific scale economies seem to be minor as do the diseconomies of producing them jointly.

Factors affecting Transportation CostsEdit

Transportation costs seem to be rising, There are many factors which might explain this. These are listed below. This list is no doubt incomplete, but may serve as a point of discussion.

  1. Standards
    1. Standards have risen - Society now demands safety, features, environmental protection, access for the disabled, and quality that drive up the cost. Engineering design is often 20% of project costs. Does the firetruck really need to do a 360 degree turn on the cul-de-sac, or can it back out?
    2. Smith's Man of System - The man of system . . . is apt to be very wise in his own conceit; and is often so enamoured with the supposed beauty of his own ideal plan of government, that he cannot suffer the smallest deviation from any part of it. He goes on to establish it completely and in all its parts, without any regard either to the great interests, or to the strong prejudices which may oppose it. He seems to imagine that he can arrange the different members of a great society with as much ease as the hand arranges the different pieces upon a chess-board. He does not consider that the pieces upon the chess-board have no other principle of motion besides that which the hand impresses upon them; but that, in the great chess-board of human society, every single piece has a principle of motion of its own, altogether different from that which the legislature might chuse to impress upon it. If those two principles coincide and act in the same direction, the game of human society will go on easily and harmoniously, and is very likely to be happy and successful. If they are opposite or different, the game will go on miserably, and the society must be at all times in the highest degree of disorder. -- Adam Smith, The Theory of Moral Sentiments, 1759
    3. Gold-plating - Adding needless or useless features to projects. The costs of gold plating are several. Money spent on project X cannot be spent on project Y. This is the monetary opportunity cost of misallocation. Land devoted to project X cannot be devoted to project Y. More land also means greater distances to traverse. This is a spatial opportunity cost. There is a tension between the risk of gold plating (focus on benefits to the exclusion of cost) and of corner cutting (focusing on costs to the exclusion of benefits). But there is available to us a balance, building something which maximizes the difference between benefits and costs, not just looking at benefits or costs. Insufficient attention is placed on the trade-off, too much on the ends by advocates of one side or the other.
    4. Design for forecast.
    5. The State Aid system and associated standards - Funds are collected at the state and federal levels for transportation and then a portion of that money is transferred back to local governments for transportation. Along with the money comes requirements that dictate how that money is to be used. These include engineering requirements for things such as lane width, degree of road curvature and design speed and planning requirements for things like maintaining a hierarchical road network.
    6. Doing construction on facilities still in operation. - Aside from the rare bridge, it is unnecessary to keep facilities opening and operating while doing construction. This reduces construction space, reducing time, increases set-up/break-down costs, and otherwise adds to total costs. Construction is much faster (and thus cheaper) if rebuilding could be done on a closed facility. See the w: Tube Lines as the classic example of the high cost of doing construction only at night and weekends, but keeping the line in operation. The system as a whole must be reliable, meaning I can get from here to there, but that does not mean every segment must be open 24/7/365. One reason the reconstruction of the I-35W bridge was so fast as that they contractors did not need to worry about existing traffic, (and it was design/build).
    7. Environmental Impact Statements (Reports) lead to "lock-in"
    8. Open government/costs of democracy - The planning process is required by law to bring in as many stakeholders as possible. This has (potentially) led to transportation investment being sought and justified for non-transportation concerns. Transportation investment is now used for social, moral and economic goals that are not directly related to mobility.
    9. Climate change adaptation is increasing the costs of projects.
  2. Scale economies
    1. There are in-sufficient economies of scale - When everything is bespoke, there is no opportunity for standardization and economies of scale. While many rail against cookie-cutter design, it is only with cookie-cutters that we get lots of cookies.
    2. Thin markets - There is no online department store for public works. I cannot go online and buy a transit bus or an interchange. The internet has not driven down prices in this field the way it has in so many others. As a result a few vendors can collude or orchestrate higher prices than would be faced in a more competitive market.
    3. Peaking - Transportation agencies attempt to provide high levels of peak capacity to accommodate the demand that results from un-priced roads and highways. This is very costly capacity to provide. If tolls were charged that reflected true costs people would drive less, especially during peak hours. It would therefore cost much less to provide the economically optimal amount of peak system capacity.
  3. Change of scope
    1. Projects are scoped wrong - We have investments that don't match actual demands. And this is not just for megaprojects. We have big buses serving few passengers. We have overgrown highways. We have a fear of building too small and having congestion or crowding so we build too big.
    2. Project creep - Side-payments in project development: noise walls hither and thither, etc. Side-payments are a required part of the politics of getting something built.
    3. "Starchitecture",
    4. Fragmented governance leads to large and meandering projects rather than centralized projects. Politicians have to "share the wealth" of projects. This is perhaps a cause of "project creep."
  4. Principal-agent problems
    1. Other people's money - Public works agencies are spending Other People's Money, and so are less motivated to get value for dollar than an individual consumer on their own. This principal-agent problem prevails in lots of organizations, but especially so in public works where the bias is not to have a failure. There was an old saying in business, no one ever got fired for buying IBM. The same holds in public works, where rocking the boat with new or innovative technologies is not sufficiently rewarded.
    2. Benefits are concentrated, costs are diffuse - As a result, the known beneficiaries lobby hard for projects, but not just to build it, but to build it in a way that is expensive. Costs are diffuse, it is seldom worth the taxpayer's time to oppose a project just because of its costs, which are spread among millions of other taxpayers. See: w:The Logic of Collective Action.
    3. Decision-makers are remote - Remote actors cannot have precise information about local conditions, and in the absence of a free market in transportation (there is generally one buyer, who is generally a government agency), prices are not clear. As a result these remote actors misallocate because they are misinformed. This notion derives from the w: Economic calculation problem See w:The Fatal Conceit.
    4. Benefit cost analysis is only as good as the integrity of the data and the analysts.
    5. B/C analysis is not used to affect project outcomes.
    6. Planners and engineers are paid as percentage of total project cost.
    7. Formula spending reduces the incentive or need to worry much about costs. This is obviously related to many of the other hypotheses already considered but I think deserves it's own number.
    8. Lack of user fee funding - projects funded out of user fees are more likely to be efficient, partly because the agencies or private parties receiving those fees know the fees are limited and partly because they want to spend them in ways that will generate more fees (which means in ways that benefit users enough that the users are willing to pay for them).
    9. Federal funds favor capital-heavy technologies and investments. - Federal funding programs create perverse incentives that lead to very costly capital projects. Almost any project looks good if somebody else is paying for most of it. For example every year billions of dollars are spent on passenger rail projects that would never be funded were it not for generous Federal grants. Just look at the high speed rail program or the FTA New Starts program. There are examples on the highway side too, such as bridges to nowhere and freeways in rural areas with little traffic. These Federal programs, no matter how well intentioned, tip the local decision making process in favor of expensive capital projects and discourage consideration of lower cost options and policy reforms.
    10. Public ownership - Most of the transportation system is owned, planned, and managed by public agencies. These entities have many objectives but efficiency and cost-effectiveness are rarely a high priority. The public sector does some things well but it doesn't usually do them very efficiently. As a result transportation revenues are not always efficiently converted to transportation user benefits.
    11. Multi-jurisdiction - Because transportation involves a large number of public agencies with overlapping or intertwined responsibilities planning is complex and inefficient. Projects end up with all the bells and whistles needed to satisfy the agencies and constituencies that could block a proposal. Local elected officials often load up regional plans with pet projects that do little to improve transportation system performance. There is a whole science to how public agencies bargain with each other and interact, unfortunately the results are rarely optimal from a cost-effectiveness perspective. The principal/agent problem is part of the reason for this, but only a part. In nearly every metropolitan area in the United States institutional structure results in transportation plans and policies that fall far short of the cost-effectiveness that could be achieved.
    12. Graft.
    13. Poor commissioning - Contracts determining who does what on a project are poorly written, and affect outsourced projects.
    14. Separation of design and build - Different firms are responsible for engineering and construction, creating high communication costs.
    15. Union work rules (not wages) that inhibit productivity gains through new technologies.
    16. Public-private partnerships trade additional up front costs for faster construction.
  5. Project Duration
    1. Paralysis by analysis - The bureaucratic requirement to do analysis delays projects and adds costs
    2. Lack of upfront funds - Delays projects adds to ultimate costs.
    3. Lack of consensus - Political requirements for consensus add delays.
    4. Mismanagement and graft add to delays.
  6. Other
    1. The highest demand areas for maintenance and new stock occur in places that are expensive.
    2. Envy - is a much bigger problem in public works than in personal life. - I pay taxes for those things, why does Jurisdiction X get an LRT when my neighborhood/district doesn’t? It’s a recipe for political hostages at budget time, as few political leaders have any reason to say "You know, the benefit cost on a project in my district just shows the project makes no sense." It’s leads to two problems: projects that make no sense to serve some notion of geo-political equity, and project creep because if Jurisdiction X’s light rail stations had public art and golden knobs and a fountain, then my district’s light rail should have those and more. Combined with the Other People’s Money problem, this type of envy is a recipe for project creep.
    3. Materials are scarcer (and thus more expensive).
    4. Stop/start investment.
    5. w:Ratchet effect - Interest groups are attracted to a particular public issue and pressure the legislative body to increase spending on that issue, but make it impossible to decrease spending on the issue.
    6. w:Baumol's cost disease - The rise of wages in jobs without productivity gains is caused by the necessity to compete for employees with jobs that did experience gains and hence can naturally pay higher salaries.
    7. Transit investment isn't realizing any productivity gains from labor. - Every dollar spent on public transportation yields 70% more jobs than a dollar spent on highways. This is used to bolster the argument that we should spend more on transit, but instead suggests we are much better at building roads than at building transit. As labor is a large proportion of total cost, transit investment has not realized productivity gains that have occurred in road building. This could be explained in part by lack of competition, low levels of total investment haven't brought new producers into the market, or a number of other reasons. I don't think the relatively high number of jobs per dollar spent necessarily means that transit investment is more virtuous. It may just be more inefficient. This is a problem with treating transport investment as industrial policy.
    8. Utility works are uncharged.
    9. Experience and Competence - The US has no experience with high-speed rail, so there is no domestic expertise.
    10. Ethos, training and prestige - Transportation engineering is more prestigious in other countries.
    11. Government power - Governments have more power to implement in other countries.
    12. Legal system - Legal systems are more amenable to infrastructure construction, including liability, bonds, and insurance.

ReferencesEdit

  1. Spulber, D. (1989), Regulation and Markets, The MIT Press Cambridge, Massachusetts.
  2. Douglas, G. and J. Miller (1974), Economic Regulation of Domestic Air Transport: Theory and Policy, Brookings Institution, Washington, D.C.
  3. Keeler, T. (1974), “Railroad Costs: Returns to Scale and Excess Capacity”, Review of Economics and Statistics, 56, 201-208.
  4. Caves, D., L. R. Christensen, and M. W. Tretheway (1984), “Economies of Density versus Economies of Scale: Why Trunk and Local Service Airline Costs Differ”, Rand Journal of Economics, 15 (4), Winter, 471-489.
  5. Caves, D., L. R. Christensen, M. W. Tretheway, and R. Windle (1985), “Network Effects and the Measurement of Returns to Scale and Density for U.S. Railroads”, in Analytical Studies in Transport Economics, Daughety (ed).
  6. McShan, S. and R. Windle (1989), “The Implications of Hub-and-Spoke Routing for Airline Costs and Competitiveness”, Logistics and Transportation Review, 35 (3), September, 209-230.
  7. Gillen, D.W., T.H. Oum, and M.W. Tretheway (1985), Airline Cost and Performance: Implications for Public and Industry Policies, Centre for Transportation Studies, University of British Columbia, Vancouver, B.C., Canada.
  8. Gillen, D.W., T.H. Oum, and M.W. Tretheway (1990), “Airline Cost Structure and Policy Implications: A Multi-Product Approach for Canadian Airlines”, Journal of Transport Economics and Policy, Jan, 9-33.
  9. Gillen, D.W. and T.H. Oum (1984), “A Study of Cost Structures of The Canadian Intercity Motor Coach Industry”, Canadian Journal of Economics, 17(2), May, 369-385.
  10. Caves, D., L. R. Christensen, and M. W. Tretheway (1980), “Flexible Cost Functions for Multi-product Firm”, Review of Economics and Statistics, August, 477-481.
  11. Griliches, Z. (1972), “Cost Allocation in Railroad Regulation”, Bell Journal of Economics and Management Science, 3, 26-41.
  12. Charney, A., N. Sidhu, and J.Due (1977), “Short Run Cost Functions for Class II Railroads”, Logistics and Transportation Review, 17, 345-359.
  13. Friedlaender, A. F. and R. H. Spady (1981), Freight Transport Regulation: Equity, Efficiency and Competition in the Rail and Trucking Industries, MIT Press, Cambridge, Mass.
  14. Keeler, T. (1974), “Railroad Costs: Returns to Scale and Excess Capacity”, Review of Economics and Statistics, 56, 201-208.
  15. Harris, R. (1977), “Economics of Traffic Density in the Rail Freight Industry”, Bell Journal of Economics, 8, 556-564.
  16. Levin, R. (1981), “Railroad Rates: Profitability and Welfare Under Regulation”, Bell Journal of Economics, 11, 1-26.
  17. Mohring, Herbert D. and I. Harwitz (1962), Highway Benefits: An Analytical Framework, Northwestern University Press, Evanston, Illinois.
  18. Winston, C. (1991), “Efficient Transportation Infrastructure Policy”, Journal of Economic Perspectives, 5 (1), Winter, 113-127.
  19. Small, K., C. Winston, and C. Evans (1989), Road Work: A New Highway Pricing and Investment Policy, Brookings Institute, Washington, D.C.
  20. Morrison, S. (1983), “Estimating the Long Run Prices and Investment Levels for Airport Runways”, in T. Keeler (ed), Research in Transportation Economics. Vol.1, 103-131.
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