4. FIRM PRODUCTION AND COST IN TRANSPORTATION The long run 4.1. Theory Productivity curves Scan 28. 7. 2015 21.25.pdf Scan 28. 7. 2015 21.27.pdf Isoquants Elasticity of substitution The elasticity of substitution is defined as: and interpreted as the percentage change in he capital/labor ratio that results from a 1% increase in the marginal rate of technical substitution. Returns to scale }sT = MPLL + MPKK }where s is a return to scale parameter (RTS). For s=1, the firm is operating under constant RTS; s >1 implies increasing RTS and s < 1 decreasing RTS. } }s = MPL(L/T) + MPK(K/T) = MPL/APL + MPK/APK = ET,L + ET,K } }RTS in production is the summation of individual output elasticities with respect to labor and capital. Long run costs curves Scan 28. 7. 2015 21.29.pdf Returns to scale and long run costs where EC,T is the elasticity of total cost with respect to output EC,T = ∆C/∆T * T/C The relationship between economies of scale and cost elasticity Former equation tells us that, for constant input prices, there is an inverse relationship between production RTS and elasticity of total cost with respect to output: Therefore, analysis of firm cost s provides economically relevant information on a firm’s production technology without having to separately estimate a firm’s production function. Input demands and Shephard’s lemma Elasticity of substitution and long run costs Alternative measures of cost elasticities in transport }Economies of scale }Economies of capital stock utilization }Economies of traffic density and generalized economies of scale The long run market supply function Assuming that there are F firms in the industry and summing over each of these firms gives the long run market supply function: Changes in long run market supply Estimating long run cost functions Scan 28. 7. 2015 21.31.pdf Leontif (fixed proportions) cost function Cobb Douglas cost function Scan 28. 7. 2015 22.51.pdf Leontief and Cobb-Douglas isoquants Flexible cost functions (translog) Flexible cost functions (translog) Intercity freight movements in the US Motor carriers costs and production technology under regulation }Economic regulation of motor carrier activities during 1935 – 1980 }Two types of cargo: truckload (TL) carriers and less than truckload carriers (LTL) }LTL find it advantageous to invest in terminal facilities (no need in TL sector) }Underlying technologies and costs different in TL and LTL sector }Two analyses of motor carrier cost and technology in regulated environment. }The first study focus upon TL sector, while the second upon LTL sector 4.2. Regulated truckload carriers Specification McMullen and Stanley (1988) estimated a translog flexible cost function for specialized commodity (TL) motor carriers. In abbreviated form, their empirical cost function is: Hypotheses 1.The truckload sector operates under constant returns to scale → α1 = 1 2.An increase in the price of any input increases all else constant, long-run total costs. Thus, we expect: α2 > 0; α3 > 0; α4 > 0; α5 > 0. From Shephard’s lemma: α2+α3+α4+α5 = 1 3.Average load per vehicle reflects increased capacity utilization; longer hauls are expected to have lower costs and higher insurance is a proxy for high value or perishable goods. Therefore we expect: α6 < 0; α7 < 0; α8 > 0. 4. 4. 4. Estimation results Estimation results Interpretation 1.Firms are operating under increasing rather than constant RTS 2.Each of the price coefficients is positive and significant. 3.The results for firm operating characteristics are mixed. Elasticities Discussion 1.What are long-run total costs? 2.Increasing RTS under regulation and constant RTS after deregulation? 3.The elasticities of substitution are neither equal to zero or one, therefore use of flexible cost function is appropriate (unlike Leontif or Cobb-Douglas) 4.The relationship between output and long run total cost reflects a movement along the long run total cost curve. Changes in any of the other variables reflects change in the location of the curve. 5. 4.3. Regulated general freight carriers Introduction }The results presented for the TL sector characterize specialized commodity motor carriers firms as operating under increasing RTS and whose underlying technology enables firms to substitute between their owned inputs and purchased transportation. }Would we expect to see similar cost and technological characteristics for general freight services? – No, since general freight services require a network of origin and destination terminals. Hypotheses }H0: LTL and TL motor carriers have identical cost structures and production technologies }H1: LTL and TL motor carriers have different cost structures and production technologies } } } Estimation results Interpretation }In contrast to specialized commodity carriers, firms in the LTL sector operate under constant RTS }What is the effect of deregulation? }The share of labor is much higher in LTL sector due to more handling }Operating characteristics in both sectors have same signs but different magnitudes Elasticities Final comments 1.At the sample mean, the TL sector operated under increasing RTS, whereas LTL sector under constant RTS. 2.On average capital, fuel and purchased transportation were more important in the production of TL than LTL transportation services. On the other hand, labor played a more important role in providing LTL services. 3.For both sectors, all inputs were substitutes in production. However demand for purchased transportation was more elastic in TL, whereas labor, capital and fuel were more easily substitutable in LTL. 4.Technological differences reflected by firm operating characteristics differed between the two sectors. 4.4. Airline cost and production under regulation Introduction }After WWII, rapid growth in airline passenger traffic }From the beginning of government involvement in the airline industry, an explicit aim was to foster the industry’s growth }The main provision of the regulation dealt with market access, route restrictions, rate-setting and subsidization. Control of entry/exit }The regulators tightly controlled entry into and exit from the market }The carriers that provided intercity air service in 1938 were granted operating authority and between 1938 – 1975 there was no new allowance to entry }Exit from the industry was as difficult as entry because air carriers were mandated to provide adequate service }Over time firms found, that mergers were the quickest way to effectuate entry and exit. }Of the 16 trunk lines granted authority, 11 remained at the beginning of 1970. Route and rate restriction }The regulation aimed to stabilize the indsutry by equalizing profitability across firms. }There was a regulation of non-stop services and opening new markets (new routes) }Rates were requied to be just, reasonable and non-discriminatory }Rates were deemed to be too high if they led to inordinately high rates of return on investment and unjustly low if they affected the financial health of a competing carrier. } } Subsidization }Although the regulation severely restricted entry and exit into the major trunkline routes, it experimented with entry info feeder markets, giving temporary operating authority to local carriers to provide subsidized short-haul service from smaller communities to the larger markets served by the trunk carriers }During time, temporary authority became permanent and sometimes overlapped with the more profitable trunkline routes in order to stem the growing level of subsidies paid to local carriers. }As a result, in the period after permanent certification, local carriers evolved into a group of larger regional carriers that competed with trun carriers. } US providers of air transport services, 1970 Specifications of costs for regulated air carriers }Becuse differences in the markets, the size if aircraft used, average stage length and average load, local carriers may face different cost strucutres, and hence technologies, than trunk carriers }Consistent with this is the belief that the trunk carriers operate under constant RTS, whereas the local carriers operate under increasing RTS. }If true, the implicationis that larger size of operations of trunk carriers gives them competitive advantage and that local carriers will be able to reduce unit costs if allowed to increase their scale of operations. Specification }Caves, Christiansen and Tretheway (1984) estimated a general model of total airline costs based upon trunk and local carriers operating from 1970 through 1981, a total of 208 observations. }The empirical cost model is a flexible translog model which includes translog transformations of Output, Prices of inputs, operating characteristics and network characteristics. Hypotheses 1.Air carriers operate under constant RTS 2.There exist increasing returns to traffic density where the size of the carrier’s network is held fixed. 3.The coefficients of the input prices will be positive. 4.It is expected that increases in Average Stage Length and Average Load will decrease long run total costs. } Estimation results Estimation results Elasticities Trunks versus local carriers under regulation Policy implications }It is possible for the smaller local carriers to compete with the much larger trunk carriers? }The uit costs of local carriers are 44% higher than those of trunk carriers. }The reasons are density of service and stage length. }The implication from these results is that local carriers want to exploit economies of traffic density and economies of distance. 4.5. 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. }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 (2) }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 (3) }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 Shepard‘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. }In addition to economies of scale, transportation firms also experience economies of traffic density, economies of capital utilization, and economies of network size. } Summary (4) }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 (5) }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 of 1935, which regulated firm entry, rates, routes, and goods carrier. Many of these regulations were significantly relaxed in the Motor Carrier Act of 1980. } Summary (6) }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 (7 – 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. 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. (…) } Summary (7 – 2/2) }(…) 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. }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 (8) }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, increase costs proportionately. Air carrier operations were relatively capital intensive, with 48 % of total cost expended on capital. 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 (9) }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. }