Transportation Economics/Costs
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Costs
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[edit] Production Theory
Theory of production. an analysis of how a firm, given the given technology, transform its inputs (x) into outputs (y) in an economically efficient manner. Production function, y = f(x), is used to describe the relationship between outputs and inputs.
[edit] Supply
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.
[edit] Types of Costs
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.
Avoidable costs: The part of costs that can be avoided by reducing production.
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.
Fixed costs: The costs which do not vary with output.
Variable costs: 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: Total expenditures required to achieve a given level of output.
Total Costs = Fixed Costs + Variable Costs. = a + bQ
Average costs: The total cost (TC) divided by the level of output (Q).
Average Cost AC = TC/Q,
Average fixed cost = a/Q Average variable cost = b
Marginal (or incremental) cost: The derivative (difference) of Total Cost with respect to a change in output.
Marginal Cost MC = dTC/dQ
Incremental Cost IC =
[edit] Average Cost for A Multiproduct Firm
For a multi-product firm, computing average cost 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).
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).
[edit] Fixed
- Traceable
- Untraceable
- Joint
- Common
[edit] Variable
- Traceable
- Untraceable
- Joint
- Common
Fixity or Variability depends on the time horizon of the decision problem and is closely related to the indivisibility of production (costs).
[edit] Indivisibility
Do costs vary continuously with different levels of output or must expenditures be made in discrete "lumps"? Indivisible costs are usually variable for larger but not for smaller changes in output
[edit] Escapability
Can certain costs 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.
[edit] Traceability
Is it possible to identify precisely a certain level of expenditures with specific services provided? Traceability is associated with production of more than one output, while untraceable costs possess either (or both) common costs and joint costs. Untraceable costs can be fixed, variable or indivisible variable. 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.
[edit] Time Horizon
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 a 'longer' run, the period over which it can adjust everything.
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
In the long run there are no fixed costs. 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.
Mathematically
where: 
provides the optimal plant size.
[edit] Indicators of Aggregate Cost Behavior
[edit] Economies of 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, 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).
[edit] Returns to Scale (Output Measure)
increasing RtS
f(tx1, tx2) > t f(x1, x2)
decreasing RtS
f(tx1, tx2) < t f(x1, x2)
[edit] Economies of Scale (Cost Measure)
increasing EoS cost elasticity < 1, MC < AC
constant EoS cost elasticity = 1, or MC =AC
decreasing EoS cost elasticity > 1, or MC>AC
Economies of scale 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.
[edit] Economies of Scope
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.
Let q = (q1,...,qn), n = number of different outputs.
Economies of scope exists if
c(q1) + ... + c(qn) > c(q1,...,qn).
That is, it is cheaper to have one firm produce all outputs than to have n separate firms produce each qi.
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 below. 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.
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.
[edit] Economies of Density
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. When scale or scope economies are calculated the size of the network is considered fixed. Economies of density refers to the change in costs when the size of the network is allowed to vary. Thus density economy measures contain both scale and network variation.
This is 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.
increasing EoD if cost elasticity < 1, or MC < AC
constant EoD if cost elasticity = 1, or MC = AC
decreasing EoD if " > 1, or MC > AC
Because of the presence of high fixed costs and cost of operating terminals (airports, stations, depots, etc), most transportation firms have increasing RTD.
[edit] Changes in Cost
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:
- 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
- density economies; shifts in the cost function as the spatial organization of production changes
- technical change which may alter the level and shape of the cost function
[edit] Characterizing Transportation
[edit] Cost
- 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
- for all modes, the average cost rise rapidly with the increased speed;
- for all modes, energy consumption increases exponentially with speed
- indivisibilities in production and heterogeneity of output make it difficult to identify the costs associated with particular traffic
- indivisibilities cause declining unit costs over a range of output,
- e.g. the backhaul problem, increase in traffic on the backhaul will reduce the average costs of the round trip operation
- the indivisibilities in production give rise to "kinked" average cost curves and discontinuous marginal costs
[edit] Production
Production is characterized by multidimensional (heterogeneous) outputs.
- quantity: most common measures of outputs;
- tonne-kilometres
- passenger-kilometres
- spatial dimension - origin-destination and direction
- time dimension - transit time, peaking and seasonality
- quality of service - speed, reliability, etc.
Examples of the use of the production approach for system design considering both inputs and outputs are illustrated in the following table:
| Inputs | Outputs |
|---|---|
| dimensions | surface area/volume carrying capacity |
| size, speed | transport capacity (e.g. vehicles per hour) |
| system capacity, infrastructure quality | traffic flow |
| capacity, vehicle movements | O-D trips |
| runways, terminals | passenger and aircraft movements |
[edit] Inputs and Outputs
output is "service" rather than product,
- not storable - economics of peak/off-peak
- users participate in the production (passenger)
inputs supplied by carriers, users, and public
- carriers: terminal activities, line haul activities, etc.
- users: the value of time, etc.
- public: infrastructure
[edit] Lumpiness
Investments are often lumpy, and some are sunk;
indivisibility of investments - complex costing and pricing
sunk investment - can constitute an entry barrier
[edit] Jointness and Commonness
Occur in the presence of joint or common production.
In Joint production, it is unavoidable to produce multiple outputs in fixed proportions, e.g. fronthaul-backhaul problem; joint cost allocation problem. Joint costs are where the multiple products are in fixed invariant proportions.
In common production, multiple outputs of varying proportions are produced using same equipment or facility - cost saving benefits, e.g. freight and passenger services using a same airplane, or using a same train. Common costs are where multiple services can be produced in variable proportions for the same cost outlay
[edit] Activities
Carriers have a structure that can be decomposed into two primary activities (Terminal and Linehaul)
[edit] terminal activities
loading, unloading and sorting of goods (and, perhaps, pick up and delivery) the concept of speed can be important for terminals distance to be travelled is only of limited relevance terminal activities may differ depending upon the type of cargo.,e.g. increasing returns to scale for bulk loading facilities, while it is not clear where or not there are increasing returns to scale for facilities handing diverse product types.
[edit] linehaul activities
indivisibility of output unit on the supply side due to: lumps of capacity and nonstorability of output (mismatch between demand and production quantity) joint production of backhaul capacity common production; e.g., short haul markets served in conjunction with a longer haul market.
[edit] Costing
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.
[edit] Carrier Management Decisions
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
[edit] Policy Decisions
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
[edit] Efficiency
X-Efficiency is the effectiveness with which a given set of inputs are used to produce outputs. If a firm is producing the maximum output it can given the resources it employs, it is X-efficient.
Allocative efficiency is the market condition whereby resources are allocated in a way that maximizes the net benefit attained through their use. In a market under this condition it is impossible for an individual to be made better off without making another individual worse off.
Technical efficiency refers to the ability to produce a given output with the least amount of inputs or equivalently, to operate on the production frontier rather than interior to it.
[edit] Aggregate Cost Analysis
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
[edit] Which Costs
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.
[edit] Prices and Outputs
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.
[edit] Attribute Variables
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 effect 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.
[edit] Estimation
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.
[edit] Difficulties with Costing
- 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
[edit] Disaggregate Costing
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
[edit] Engineering Costing
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
[edit] Accounting Costing
- 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
[edit] Statistical Costing
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(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.
[edit] Considerations
the appropriate degree of aggregation of accounts traffic
data observational unit
casual (explanatory) variables to be used for each expense category
specification of functional form linking expenses and the intermediate work units associated with the specific traffic
