Short-run Cost Function Research Articles

Understanding the costs of urban rail transport operations

There is considerable variation in the average cost of operations across urban rail transport (or metro) systems. Since metros are typically owned and operated by public authorities, there is a public interest case in understanding the key drivers of their operational costs. This paper estimates short-run cost functions for metro operations using a unique panel dataset from twenty-four metro systems around the world. We use a flexible translog specification and apply dynamic panel generalised method of moments (DPGMM) estimation to control for confounding from observed and unobserved characteristics of metro operations. Our empirical results show that metro systems with a high density of usage are the most cost-efficient. We also find that operational costs fall as metro size increases. These results have important implications for the economic appraisal of metro systems.

Cost efficiency and electricity market structure: A case study of OECD countries

The OECD electricity sector has witnessed significant institutional restructuring over the past three decades. As a consequence, many power generation utilities now act as unregulated companies that technically compete to sell power on an open market. This paper analyses the performance in term of cost efficiency for electricity generation in OECD power sector while accounting for the impact of electricity market structures. We employ the short-run cost function in which capital stock is treated as a quasi-fixed factor input. Empirical models are developed for the cost function as a translog form and analysed using panel data of 25 countries during the period 1980 to 2009. We show that it is necessary to model latent country-specific heterogeneity in addition to time-varying inefficiency. The estimated economies of scale are adjusted to take account of the importance of the quasi-fixed capital input in determining cost behaviour, and long run constant returns to scale are verified for the OECD generation sector. The research findings suggest there is a significant impact of electricity market regulatory indicators on cost. In particular, public ownership and vertical integration are found to have significant and sizable increasing impacts on cost, thereby indicating policy lessons on the desirable ways to implement structural electricity generation reforms.

A note on the envelope theorem

The purpose of this note is to discuss the envelope relationship between long run and short run cost functions. It compares the usually presented relationship with one of different form and implications, resulting from a simple production function and constant prices. It points out in particular that the tangency condition between the short and long run total cost functions does not necessarily hold always. The note also shows that a given value of the fixed factor might support in the long run a whole range of levels of output.

A Note on the Envelope Theorem

The purpose of this note is to discuss the envelope relationship between long run and short run cost functions. It compares the usually presented relationship with one of different form and implications, resulting from a simple production function and constant prices. It points out in particular that the tangency condition between the short and long run total cost functions does not necessarily hold always. The note also shows that a given value of the fixed factor might support in the long run a whole range of levels of output.

Pseudoconvexity properties of average cost functions

It is well known that short run cost functions of firms are convex functions when production functions are concave [14]. Average cost minimization as a classical economics problem has been studied in fundamental textbooks [14,4,7,8] and in the literature [2,3,9,12,13,1]. However, it seems that less attention so far has been paid to the study of properties of the average cost function and its minimization methods. The aim of this paper is to fulfill this gap. First, we show that average cost functions are pseudoconvex. Second, we develop an algorithm for solving the average cost minimization problem. We implement the algorithm to solve a real carpet manufacturing problem in Mongolia.

KONSTRUKCE NÁKLADOVÝCH FUNKCÍ V PODMÍNKÁCH RIZIKA A NEURČITOSTI

In economics, a cost curve is a graph of the costs of production as a function of total quantity produced. In a free market economy, these curves are used by the entities to find the optimal point of production, where they make the highest profits. There exist several different types of cost curves, while each of them is relevant to a different area of economics. In the article, authors are focused on solution of cost-functions modelling, both short-run cost function and long-run cost function under circumstances of risk and uncertainty. Considerations about factors of risk and uncertainty are based on an irrefutable fact that companies are not separate entities taken out of surrounding environment; entities operate in global world where many random factors are influencing the processes in companies while the number of these random factors is ad infinitum. The fact that estimation of cost functions' parameters are realized from past data is the basis of the considerations about planning of future scope of production based on these functions. Especially for the long-run cost functions it is impossible to leave out all the random influences. Their quantification is derived from aposteriori probabilistic approach according to Bayesian Theorem.

Feed prices and production costs on Spanish dairy farms

This paper analyses the impact of livestock feed prices and pasture quality on the long and short-term costs of milk production in a region of Spain (Navarre). The empirical results are obtained from the estimation of a flexible short-run cost function, followed by the approximation of long-run equilibrium based on the quasi-fixed factors adjusted to their optimal levels. The results reveal a high sensitivity of milk production costs to changes in livestock feed prices due to two reasons. One is that, as milk production expands, it tends to become technologically more intensive. The other is that, in the current structure of dairy farming, land input is suboptimal, particularly in the case of large farms and areas of poor pasture. The results reveal that short-run substitution between feed and livestock is a potential strategy for farms to respond to feed price increases. They also suggest that structural policies designed to strengthen the dairy sector’s competitiveness should vary according to agro-climatic conditions. In areas of poor pasture, herd growth might be used as a long-term measure to increase competitiveness through economies of scale; while the alternatives for farms in better-endowed regions also include extensification of dairy production.

Economies of scale and scope in the Danish hospital sector prior to radical restructuring plans

ObjectiveThe Danish hospital sector faces a significant rebuilding program driven by recent regional reform and guidelines for acute admission hospitals. Within the next 5–10 years, the number of public hospitals offering acute admission will be reduced from 35 to approximately 20 larger hospitals. As the administrative data may be biased during the middle of a restructuring process our objective was to analyze whether the configuration of Danish public hospitals was subject to economies of scale and scope prior to the restructuring plans. MethodsWe estimated a quadratic cost function using panel data on the total costs for somatic treatment, casemix adjusted DRG-production values, and other cost drivers for the three years before the 2007 reforms. A short-run cost function was used to derive estimates of a long-run cost function by applying the envelope condition. Next, we estimated economies of scale and scope. ResultsWe identified moderate-to-significant economies of scale and scope. This indicates that the Danish hospital sector was characterized by unexploited gains from consolidation. ConclusionsOur results suggest that the proposed plans have the potential to result in hospitals that are more efficient. However, post-restructuring studies elsewhere show that the strategy of horizontal integration has failed.

A Microeconometric Model of a Short Run Cost Function with Unobserved Heterogeneity

Unobserved plant level heterogeneity and discrete production processes can produce problems for estimation. A structural model of discrete production decisions by heterogeneous plants is constructed and, as a case study, estimated for the U.S. Portland cement industry. A new estimator is proposed to handle the discrete production process – for which the ordered probit is a special case. Data on firm survival and exit are used to adjust all input requirement coefficients for unobserved heterogeneity. The structural model is successfully estimated. Differences between many estimated coefficients and independent estimates from external sources are statistically insignificant.

Cost structure and capacity in the Norwegian pelagic fisheries

The parameters of the short-run cost function are estimated for three vessel types taking part in the Norwegian pelagic fisheries: purse seine vessels, trawlers, and coastal vessels. The generalized translog functional form is used. Estimates of returns to scale are calculated and the results indicate that there are substantial economies of scale in all vessel classes. It is further investigated whether excess capacity varies with vessel size and age. The analysis suggests increased quotas per vessel to avoid rent dissipation. With the total allowable catch given, the number of participating vessels must be reduced.

Cost Functions and Efficiency Estimates of Midwest Bus Transit Systems

Short-run variable cost functions are estimated with the use of a sample of 68 bus systems in the U.S. Midwest operating in the 1996 to 2002 period. Variable costs are specified as functions of outputs, input prices, bus stocks, and network size. Various output, input price, network, capacity, and disturbance specifications are examined. The cost functions are estimated with the use of ordinary least squares, switching regression, seemingly unrelated regression, and stochastic frontier cost models. The results indicate constant returns with vehicle outputs, increasing returns with passenger outputs, inelastic input demands, and substantial technical efficiencies that vary by firm and by state.

Cost Functions and Efficiency Estimates of Midwest Bus Transit Systems

Short-run variable cost functions are estimated with the use of a sample of 68 bus systems in the U.S. Midwest operating in the 1996 to 2002 period. Variable costs are specified as functions of outputs, input prices, bus stocks, and network size. Various output, input price, network, capacity, and disturbance specifications are examined. The cost functions are estimated with the use of ordinary least squares, switching regression, seemingly unrelated regression, and stochastic frontier cost models. The results indicate constant returns with vehicle outputs, increasing returns with passenger outputs, inelastic input demands, and substantial technical efficiencies that vary by firm and by state.

Capacity Utilization of the Rice Milling Industry and Interlinkage in the Rice Market in Ghana

Most large-scale millers in the Kumasi area, central Ghana, provide interest-free or low interest loans to farmers under the agreement that the farmers will bring their paddy to the millers. This paper examines the effect of this interlinkage on the efficiency of rice milling. A quadratic short-run cost function was estimated by controlling for self-selection bias using the results of first-stage Probit regression, and capacity utilization was calculated in relation to money lending. The results show that if a miller provides a loan to farmers, the operating rate will increase by 24% and the total cost will decrease by 17%.

R&D, technology and productivity growth in Italian agriculture, 1963-1991

This paper investigates the role of gross investments in Research and Development (R&cD) and, in extension, in generating technical change by adding a variable representing the knowledge stock in a cost function of Italian agriculture. It is a short-run cost function thus regarding only variable factors while other conventional inputs are considered fixed. The chosen functional form (translog) belongs to the family of flexible functions and allows an estimation of the technology parameters without imposing any restriction on the factor substitution matrix both in the short and in the long run. Moreover, it is possible to measure the biases and the rate of technical change as well as the rate of return to R&D -extension public expenditure. The model can provide empirical evidence of the positive and relevant impact of these investments on Italian agricultural productivity net of scale effect and capacity utilization.

Production-planning horizon, production smoothing, and convexity of the cost functions

One of the productions planning models economists have used for the past four decades is the production-smoothing model. The model's conclusion is simple: if cost functions are convex, under certain conditions, firm's production plans may show smaller variability than the firm's sales. This is a result of the first-order condition for cost minimization over the production-planning horizon. In a 1986 paper Blinder raised doubts regarding the ability of the production-smoothing model to explain the observed data. Some researchers (e.g. Ramey, Journal of Political Economy 99(2) (1991) 306) explained the inconsistency between the theory and the data by providing evidence that the cost functions are non-convex. In this paper, I point out that the shapes of the cost functions depend on the length of the time horizon under consideration. It is possible that while short-run cost functions are upward sloping, long-run cost functions may be downward sloping. Because the planning horizon for firms facing seasonal demand has been shown to be one seasonal cycle, the short-run cost function, whose shape determines the firm's production plan over the horizon, need to be estimated using single planning horizon data, i.e., a single seasonal cycle. Researchers who use long time series data are, in effect estimating long-run cost functions, the slopes of which may be non-positive. I show, further, that convexity of the production cost function is neither necessary nor sufficient condition for production smoothing to be an optimal plan.

Measuring embodied technical change in the US local telephone industry

This study attempts to measure the rate of embodied technical change by using a short-run variable cost function that contains arguments for labour and capital quality. In this short-run variable cost model, the expansion of the amount of physical capital increases variable costs due to more maintenance outlays, and then it leads to improvements in capital quality. When a measure of competition is included as a proxy for organizational efficiency, improvements in labour and capital quality explain more than two-thirds of productivity growth. The degree of returns to scale and the shadow cost of capital input in the embodiment cost model are presented as well. The study is based on pooled time-series and cross-section data of eight US local exchange carriers.

Utilization of optimal capacity in Indian manufacturing, 1974–1996

This paper attempts to estimate a consistent series for the economic capacity utilization of the Indian non-electrical machinery manufacturing sector. The economic or optimum capacity is defined as the output where the short-run average total cost is minimized. Using an iterative version of Zellner's seemingly unrelated regression estimation technique, a translog short-run cost function is estimated, imposing the conditions for economic optimizing behaviour of firms to calculate the optimal output. Such a measure assumes that variations in capacity utilization (CU), defined as the ratio of actual to optimal output, are the systematic results of rational optimization procedures, depending on price and cost conditions of firms. A comparison of the new series with the conventional engineering measures of CU shows that the widely used ‘installed CU’ figures clearly underestimate the true economic utilization levels, mainly due to definitional problems.

A comparison of hospital scale effects in short-run and long-run cost functions.

Numerous estimates of economies of scale in the hospital setting have been obtained since the early 1980s from both flexible long-run and short-run cost functions. Although the theoretical superiority of the latter approach is widely recognized, it has been previously suggested that the two cost specifications yield quite similar econometric findings regarding scale effects. This paper utilizes a new data set consisting of 91 Greek NHS hospitals in order to empirically examine this proposition by comparing economies of scale estimates derived from both translog total and variable cost functions. The results indicate that the use of long-run equations might seriously mislead policy makers and that constant returns to scale prevail in Greek public hospitals.

Are bureaucrats efficient? An application to the provision of AFDC

The question on how bureaucrats behave in the provision of a public service has been the subject of a considerable amount of research, most of which has been largely theoretical and inconclusive, especially on the issue of efficiency. This paper builds a bureaucratic theoretical model and provides empirical evidence by examining the workings of a government bureau, supplying a public service, namely Aid to Families with Dependent Children (AFDC), at the state level. It builds and estimates a generalized short run cost function that allows for systematic relative price inefficiency and does not require cost minimization subject to market prices as a maintained hypothesis. The model tests cost minimization as a testable special case. The estimating procedure allows us to test for a number of other features of the technology that are of interest such as productivity growth, marginal costs, returns to scale, technical change, and factor demands.

Uncertain demand, the structure of hospital costs, and the cost of empty hospital beds

In this paper we reformulate the theory of cost and production to take account of uncertain demand facing a firm. In the reformulated theory the duality between cost and production no longer obtains, and demand distribution parameters enter the cost function as well as the traditional outputs and input prices. We then estimate a short run cost function for a hospital facing uncertain demand using data from a national sample of over 5000 hospitals for the years 1983–1987. The traditional cost model is strongly rejected in favor of the reformulated model. This model is used to calculate the cost of empty hospital beds, controlling for the effect of uncertain demand on the structure of hospital costs. The cost of an empty hospital bed is calculated as $36,443 in 1987 dollars. We estimate that a one percent decrease in the number of hospital beds would decrease hospital costs by slightly over one-third of one percent. Increasing the occupancy rate from the average 1992 level (65 percent) back to the average 1980 level (76 percent) is estimated to save the average hospital over $2 million, or 9.5 percent of costs.