Efficient Production Function Research Articles

Nonprofit public libraries and technical efficiency: An application of data envelopment analysis to technology-based outputs

Nonprofit public libraries (NPPLs) with technically efficient production functions attain greater program and service outputs per registered user in comparison to peers with less efficient production functions. An output-oriented nondiscretionary data envelopment analysis (DEA) model with variable returns-to-scale is used to assess the technical efficiency of 339 NPPLs in the United States (US) in attaining electronic-, physical-, and Internet-based program and service outputs. Based on the output-oriented DEA analysis, 46% of the NPPLs are technically efficient in producing program and service outputs per registered user. On average, US NPPLs are moderately inefficient in attaining their program and service outputs. The DEA analysis also reveals that the inefficient NPPLs should increase their electronic, physical, and Internet service levels per registered user to achieve technical efficiency as annual input levels are held constant.

Operational and Efficient Production Functions: Measuring Efficiency in Abyek Cement Factory

In this paper, Leontief linear production functions with one product, and one activity are used to derive the production function of Abyek Cement Factory. The mathematical closed form of production function and also, profit, cost, and demand functions for production factors are obtained for the cited factory.
 We tried to calculate Operational Production Function of Abyek Cement Factory. It was realized that Leontief linear production function is applicable, and its mathematical form can properly express the economic structure of production in a cement factory.
 The efficient production function for this factory is also derived in this research. This function exhibits the costs incurred due to the inefficient production of the factory during different years. According to the findings, it was concluded that if the Abyek Cement Factory produces efficiently through employing optimal amounts of factors of production, it can reduce costs by 21 to 52 percent without any change in production level. Calculations were done for both short-term and long-term periods.
 JEL: D22, L11, L61

Efficient Cobb-Douglas Production Function

In this paper, we present a function for the share of factors of output, which is in complete agreement with primary production theories in microeconomics. We follow some assumptions for production function, and also payment to each factor equals their marginal products, and we create a new production function which is called the efficient production function. We then try not only to remove the significant defects in Cobb-Douglas production function but also by accept the presented theory. We conclude that the need for most previous approaches have caused problems and even the developed functions have not been able to solve the problem. The presented model in complete agreement is also supported by the empirical findings for the United States (U.S.) economy.

The Economic Impact of Increased Congestion for Freight-Dependent Businesses in Washington State

Congestion in the transportation system necessitates select businesses to operate on a less efficient production function. A survey of freight-dependent businesses in Washington State was used to calculate the costs of congestion and economic impact of increased congestion. As these businesses spend more to provide goods, responses suggest consumers would pay 60% to 80% of the increased cost. Primary areas of increased cost were identified as additional trucking and inventory costs. Results identify an additional $8.7 billion in consumer costs for a 20% congestion increase. The economic impact is a loss of $3.3 billion in total output and over 27,000 jobs.

Weight restrictions in DEA: misplaced emphasis?

Measuring productive efficiency is an important research strand within fields of economics, management science and operations research. One definition of efficiency is the proportional scaling needed for observations of inefficient units to be projected onto an efficient production function and another definition is a ratio index of weighted outputs on weighted inputs. When linear programming is used to estimate efficiency the two definitions give identical results due to the fundamental duality of linear programming. Empirical applications of DEA using linear programming showed a prevalence of zero weights leading to questioning the consequence for the efficiency score estimate based on the ratio definition. Early literature on weight restrictions is exclusively based on the ratio efficiency. It was stated that variables with zero weights had no influence on the efficiency score, in spite of the alleged importance of the variables. This has been one motivation for introducing restrictions on weights. Another empirical result was that often there were too many efficient units. This problem could also be overcome by introducing weight restrictions. Weight restrictions were said to introduce values for inputs and outputs. The paper makes a critical examinations of these claims based on defining efficiency relative to a frontier production function.

A postmodern turn to estimating performance frontiers

Extremal approaches in Management Science (MS) to estimating efficient production functions owe their conceptual modelling origins to earlier, theoretical work in agricultural and production economics. The primary metaphor in this paradigm has been one of material production. This work departs from the main body of the DEA literature, in that it proposes a modelling framework that: acknowledges explicitly the social construction of many production functions; identifies the modernist conceptual traps of many implementations; explores some alternatives to the modelling of ephemeral social production that are framed in relation to postmodern sensibilities.

Resource and Waste Taxation in the Theory of the Firm with Recycling Activities

The management of solid waste has become an urgent problem in nations with a great population density. Accordingly, waste reduction through source reduction and recycling has become increasingly important. Our purpose is to show how prevention, recycling and disposal of waste could be part of a theory of the firm. We first derive efficient production functions from production processes with waste as a by-product. Waste obtained as new scrap can partially be recycled by using additional inputs in order to cut back the purchase of virgin material. Waste not completely recyclable will leave the firm as disposal which also entails cost to the firm. We use the dual cost function approach to develop a theory of the firm under solid residual management. Since the producer does not bear the full cost of disposal, there will be a bias toward virgin materials and away from recycling. The goal of the government is to stimulate the firms to recycle with respect to the preservation of exhaustible resources. An incentive to recycle is a tax on resources or on waste. In order to determine the tax levels the government maximizes welfare subject to the dynamic constraint for decumulation of land fill for waste deposits. This gives the user cost and its time profile for taxing waste disposal or virgin material. In a comparative statics analysis we compare the effect of taxes on waste vs. virgin material on effort to produce in a resource saving manner, on the quantity of recycled material, on output, and on the reduction of waste. Since the impact of environmental regulation on employment is important, our model detects seven effects on labor demand as part of resource conservation policy. We finally carry out a comparative statics analysis of waste intensive firms operating in different market structures. Of interest is the impact of a resource or waste taxation on market volume, on the number of firms, on resource saving effort, and on profit.

Robustly efficient parametric frontiers via Multiplicative DEA for domestic and international operations of the Latin American airline industry

Previous studies of (parametric) aggregate frontiers have attempted to capture stochastic features of the random variables (i.e. inputs and outputs) by assuming a ‘risk’ situation (where the probability distributions of the random variables are known). The purpose of this paper is to present and test a new method invented by Charnes, Semple, Song and Thomas for the usual situations of uncertainty (where the probability distributions of the random variables involved in the technical inefficiencies are unknown) to build up global efficient production functions in the context of operations in the Latin American airline industry. This method develops an empirical efficient production function via a ‘Robustly Efficient Parametric Frontier’ (REPF) in a two-stage approach. As in the Charnes et al. development using a Multiplicative-DEA model, the marginal tradeoffs of the efficient production function are immediately available instead of being harassed by discontinuities of derivatives and numerical instabilities.

Estimating Efficient Production Functions under Increasing Returns to Scale

AN earlier paper by one of us (Farrell, 1957) developed, inter alia, a method for estimating efficient production functions from observations of the inputs and outputs of a number of individual production units. The method consisted essentially in plotting these observations as points in a space of a suitable number of dimensions, forming the convex closure of this set of points and taking the appropriate part of the surface of this convex closure as the estimate of the efficient production function. In the case where n inputs are used to produce a single output under conditions of constant returns to scale, if output is represented by X and the inputs by xl, x2, ..., Xw then each firm can be represented as a point in n-dimensional space with coordinates (xl/X, x2/X, ..., x./X). This set of points is then augmented by the points at infinity on each of the n axes, and the convex closure of the augmented set is formed. The surface of this convex closure, omitting the facet at infinity, is our estimate of the efficient production function. The earlier paper was primarily concerned with this simple version of the method. Not only was it used for the basic exposition but a large part of the paper was devoted to applying it to observations on American agricultural production. The paper did, however, discuss at a formal level the relaxation of the assumptions of single product and constant returns to scale, and in Section 2.3 showed how the method could be generalized to the case of m outputs X1, X2, ..., Xm by treating each observation as a point in n + m-dimensional space with coordinates (X,, X2, ..., Xm, x1, x2, ..., xn). A broadly similar procedure which would accommodate the possibility of decreasing returns to scale was indicated in Section 2.4. Underlying the use of the method in all these cases is the assumption that the efficient production function to be estimated is convex. In no case does this assumption hold necessarily, but it is one frequently made in economics, and will probably hold in most actual situations. Certainly there is nothing in the nature of multiple outputs or decreasing returns to scale that is inconsistent with the convexity assumption. This happy state of affairs ceases to obtain as soon as we consider a situation with increasing returns to scale, because this essentially involves a non-convex production function; indeed they are in practice probably the most important example of nonconvex production functions. The estimation of efficient production functions under