5. FIRM PRODUCTION AND COST IN TRANSPORTATION – THE SHORT RUN



5.1. Theory



Short run – level of capital fixed
}In the short run at least one factor of production is fixed (we assume capital)
}In the short run, a discussion of returns to scale is no longer relevant, since all inputs cannot
change in the same proportion.
}Adding more workers to a fixed amount of capital reduces MPL = law of diminishing returns.

Short run cost curves
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Short run cost curves
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Short run market supply
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The relationship between short run and long run costs
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5.2. Short run variable costs in the railroad industry under regulation



Rate setting
}Railroad regulation in the USA after 1887 required railroads to charge just and reasonable rates
and specifically banned a variety of pricing practices (discrimination tariffs, preference tariffs,
long hails tariffs, pooling).
}All rates and fares had to be publicly available
}Regulator: Interstate Commerce Commission (ICC)

Research questions
}The presence of large fixed costs leads to an important question regarding a railroad’s optimal
strategy for competing with other intercity modes for freight traffic.
}Is the railroad industry characterized by short-run increasing returns to density and, if so, can
railroads significantly reduce their average variable costs by more efficiently utilizing fixed
factors of production?
}Braeutigam et al. (1984) explored these and some other questions in a study on the short-run cost
structure for a large Class I railroad during a 35-month period from January 1976 through November
1978.

Specification
The short run total variable costs depend upon output, input prices, the fixed factor of
production, and technology. In their analysis of rail costs, Braeutigam et al. (1984) specified the
following translog empirical total variable cost model:

Definition of variables
}Output – this is measured as the Number of Carloads of freight that the rail carrier moved each
month.
}Input prices – in the short run, the variable factors of production are fuel (f), labor (l) and
equipment (e).
}Operating characteristics – the only operating characteristic included in this model is Average
Speed of service (ospd).
}Fixed factors of production – among the various factors of production – including track, switches,
land and buildings – that are fixed in rail operations, miles of track is the largest component and
is used in this study to measure the diverse fixed factors.

Hypotheses
1.Rail firm technology is expected to exhibit increasing returns to capital stock utilization: εo/k
> 1 → α1 = 1/εo/k is positive and less than one.
2. An exogenous increase in Average Speed will decrease total variable costs. α5, therefore, is
expected to be negative.
3.Cost minimization imply: 0 < αi  < 1  (i = 2, 3, 4) and           α2 + α3 + α4 = 1
4.An increase in Effective Miles of Track, the fixed factor of production is expected to reduce
total variable costs, which implies that α6 will have a negative sign.

Estimation results



Short-run Elasticities



Comments
}The identified translog empirical cost function does not include a constant term.
}

5.3. Profit margins in the airline industry



Introduction
}In their work on the US airline industry, Morrison and Winston (1985) developed and estimated an
empirical model of airline carrier short-run profitability, measured by annual rate of return for
the period 1970-88. Their empirical model is given as follows:
}

Specification



Hypotheses
1.An increase in input costs reduces profitability. Thus is expected that α2 > 0, α3 < 0, α4 < 0,
α5 < 0.
2.It is expected that more hub enplanements and development of computer reservation system (CRS)
will increase profitability. CRS may not impact profitability immediately, but will do so over
time. It is expected, that:    α6 > 0, α7 > 0, α8 > 0, α7 < α8.
3.Average Length of Haul, Average Load Factor and Route Density are expected to increase
efficiency. It is expected:    α9 > 0, α10 > 0, α11 > 0.
4.The last set of variables reflects the characteristics of top management. The coefficients on
each of these variables are expected to be positive.

Estimation results



Estimation results



Comments
}The results indicate that a carriers network, rather than its size is more important to financial
success.
}Management matters in a carrier’s profitability.

5.4. Urban bus transportation cost and production



Introduction
}An often stated economic argument for the justification of a single bus system, a market structure
that chracterizes most urban mass transit systems in the USA, is the presence of large economies of
scale.
}Source of scale economies: costs of administrative staff, economies of capital stock utilization,
traffic density and generalized economies of scale.
}Viton (1981) analyzed the cost and production structure of bus systems operating in the United
States and Canada

Specification
Viton specified a translog empirical cost model in which short-run total variable cost was assumed
to depend upon a bus system’s produced output, defined as vehicle/miles (millions), input prices
for labor (pl) and fuel (pf) and a fixed factor of production (buses), which is defined as the
number of buses in the bus system. Specifically, the empirical cost model is:

Hypotheses
1.Bus transit systems operate under increasing returns to capital utilization → α1 < 1.
2.α2 > 0, α3 > 0     α2 + α3 = 1
3.An increase in a bus system rolling stock is expected to decrease short-run total variable costs:
α4  < 0.

Estimation results



Utilization economies



Optimal bus fleet size



Long run economies



Comments
1.In the short run bus companies will have trouble covering their variable costs of service.
2.Bus systems in general appear to be overcapitalized.
3.Even with optimal fleets, smaller bus systems require subsidies.

Short-run and long-run cost curves
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5.5. Summary



Summary (1)
}Given the existing technology, a firm's production function is the maximum amount of output that a
firm can produce from a given quantity of inputs. If all inputs to the firm are variable, the firm
is in the long run; if some inputs are fixed, the firm is in the short run.
}

Summary (2)
}The elasticity of substitution, defined as the percentage change in an input ratio due to a
percentage change in the marginal rate of technical substitution, reflects the ease with which a
firm can substitute among inputs in the production process. If a proportional increase in all
variable inputs raises output (less than, more than) proportionately, then the firm is operating
under constant (decreasing, increasing) returns to scale.
}

Summary (3)
}A firm minimizes its cost of production by using inputs up to the point at which the marginal rate
of technical substitution equals the input price ratio. A firm's total cost function is the minimum
cost necessary to produce a given amount of output. A firm's minimum efficient scale is that level
of output corresponding to the minimum point on a firm's average cost curve. At this point, the
firm is operating under constant returns to scale.
}

Summary (4)
}Knowing a firm's cost function provides information on the firm's underlying production
technology. The inverse of the elasticity of total cost with respect to output measures a firm's
economies of scale. By Shephard's lemma, the elasticity of total cost with respect to input price
is the conditional optimal share of the input's expenditures in total costs. The long-run total
cost function also provides information on the elasticity of substitution among inputs.
}

Summary (5)
}In addition to economies of scale, transportation firms also experience economies of traffic
density. economies of capital utilization, and economies of network size.

Summary (6)
}Empirically, there exist several cost function models to characterize transportation activities.
The most restrictive is the Leontif cost function model, which assumes constant returns to scale
and no substitutability among inputs. The Cobb—Douglas cost function model allows for nonconstant
returns to scale and input substitutability, but the elasticity of substitution is constrained to
equal one. The least restrictive cost function model is the translog cost function, which allows
for nonconstant returns to scale and places no restrictions on substitutability among inputs.

Summary (7)
}The motor carrier industry comprises two basic sectors, the truckload or specialized commodity
carrier and the less-than-truckload or general freight carrier sector. By having to consolidate and
break-bulk shipments, the less-than-truckload sector has a different production technology than the
truckload sector.
}Economic regulation of the motor carrier industry began with the Motor Carrier Act 1935, which
regulated firm entry, rates, routes, and goods carried. Many of these regulations were
significantly relaxed in the Motor Carrier Act of 1980.
}
}

Summary (8)
}A case study of the truckload sector of the motor carrier industry under economic regulation found
that truckload firms operated under increasing returns to scale, which is inconsistent with the
competitive nature of this sector but consistent with regulatory-based economies of network size.
This sector was less labor intensive and relied more on purchased transportation. Input demands for
labor, capital, and fuel in this sector were inelastic. But the demand for purchased transportation
was elastic. The elasticities of substitution indicated that all inputs were substitutes. The
greatest opportunities for input substitution occurred with purchased transportation.
}

Summary (9 – 1/2)
}A case study of the less-than-truckload sector under regulation confirms that differences in
production technology exist between this sector and the truckload sector. Less-than-truckload firms
operated under constant returns to scale, holding network size constant. However, there was also
evidence of generalized returns to scale in this sector, which indicated that a proportional
increase in output and network size increased costs less than proportionately (…)

Summary (9 – 2/2)
}(…) This sector was more labor intensive than the truckload sector and relied much less on
purchased transportation. Firms’ costs in this sector were sensitive to shipment size, length of
haul, and value of commodity shipped. Factor demands, including purchased transportation, were
inelastic. Similar to the truckload sector, all inputs were substitutes. However, in contrast to
the truckload sector, there were greater substitution possibilities among fuel, capital, and labor
inputs, but fewer opportunities for substitution between each of these inputs and purchased
transportation.
}

Summary (10)
}Economic regulation of the US airline industry began with the Civil Aeronautics Acts of 1938,
which controlled firm entry and exit, route operating authority, and fares. Economic regulation
continued until passage of the Airline Deregulation Act in 1978.
}

Summary (11 – 1/2)
}A case study of trunk and local airline costs during the 1970s indicated that air carriers
operated under economies of density. Further, during this period, air carriers operated under
general constant returns to scale; that is, a proportional increase in output and network size, all
else constant, increased costs proportionately. Air carrier operations were relatively capital
intensive, with 48% of total costs expended on capital. (…)

Summary (11 – 2/2)
}(…) In the form of lower costs, air carriers benefited from high average loads and longer stage
lengths. Factor inputs were price inelastic, and relatively few possibilities appeared to exist for
input substitution between capital and labor or capital and fuel. Labor and fuel were complements
in production.
}

Summary (12)
}A comparison of trunk and local air carriers during the transition to deregulation indicated that
local carriers experienced unit costs that were more than 40% higher than those of trunk carriers.
This can be attributed to significant differences in traffic density between the two sectors, as
well as to the longer stage length of the trunk carriers.
}