Short-run Production Function Research Articles

A Short-run Indirect Production Function

A Short-run Indirect Production Function

A simulation study of capacity utilization to predict future capacity for manufacturing system sustainability

Capacity utilization (CU) measurement is an important task in a manufacturing system, especially in make-to-order (MTO) type manufacturing system with product customization, in predicting capacity to meet future demand. A stochastic discrete-event simulation is developed using ARENA software to determine CU and capacity gap (CG) in short run production function. This study focused on machinery breakdown and product defective rate as random variables in the simulation. The study found that the manufacturing system run in 68.01% CU and 31.99% CG. It is revealed that machinery breakdown and product defective rate have a direct relationship with CU. By improving product defective rate into zero defect, manufacturing system can improve CU up to 73.56% and CG decrease to 26.44%. While improving machinery breakdown into zero breakdowns will improve CU up to 93.99% and the CG decrease to 6.01%. This study helps operation level to study CU using “what-if” analysis in order to meet future demand in more practical and easier method by using simulation approach. Further study is recommended by including other random variables that affect CU to make the simulation closer with the real-life situation for a better decision.

Short Run Profit Maximization in a Convex Analysis Framework

In this article we analyse the short run profit maximization problem in a convex analysis framework. The goal is to apply the results of convex analysis due to unique structure of microeconomic phenomena on the known short run profit maximization problem where the results from convex analysis are deductively applied. In the primal optimization model the technology in the short run is represented by the short run production function and the normalized profit function, which expresses profit in the output units, is derived. In this approach the choice variable is the labour quantity. Alternatively, technology is represented by the real variable cost function, where costs are expressed in the labour units, and the normalized profit function is derived, this time expressing profit in the labour units. The choice variable in this approach is the quantity of production. The emphasis in these two perspectives of the primal approach is given to the first order necessary conditions of both models which are the consequence of enveloping the closed convex set describing technology with its tangents. The dual model includes starting from the normalized profit function and recovering the production function, and alternatively the real variable cost function. In the first perspective of the dual approach the choice variable is the real wage, and in the second it is the real product price expressed in the labour units. It is shown that the change of variables into parameters and parameters into variables leads to both optimization models which give the same system of labour demand and product supply functions and their inverses. By deductively applying the results of convex analysis the comparative statics results are derived describing the firm's behaviour in the short run.

Production Theory: Accounting for Firm Heterogeneity and Technical Change

The paper presents a new framework to assess firm level heterogeneity and to study the rate and direction of technical change. Building on the analysis of revealed short-run production functions by Hildenbrand (1981), we propose the (normalized) volume of the zonotope composed by vectors-firms in a narrowly defined industry as an indicator of inter-firm heterogeneity. Moreover, the angles that the main diagonal of the zonotope form with the axes provide a measure of the rates and directions of technical change over time. The proposed framework can easily account for n-inputs and m-outputs and, crucially, the measures of heterogeneity and technical change do not require many of the standard assumptions from production theory.

Supply and Demand for Cereals in Pakistan, 2010-2030

This paper presents the projections of future demand and supply for these two main cereals for 2010, 2015, 2020, 2025, and 2030. For projecting household demand, the Almost Ideal Demand System (LA-AIDS) is estimated for eight food items using the data of nationally representative household survey. The results are used to project the household demand under three different scenarios. These scenarios are: a business-as-usual situation (per capita income is assumed to grow at a rate of 3 percent per year), an optimistic situation (assumed growth rate of per capita income 4 percent per year), and a pessimistic situation (per capita income is assumed to grow by 2 percent per year). Cereal supply is projected using a short-run production function approach (with such variables as area and share irrigated fixed exogenously at observed levels). This projection is then used to estimate the levels of wheat and rice produced for 2009-2030, with the projections of the exogenous determinants of production based on linear time trend models. The results show that the demand for wheat and rice will more than double by 2030. The projections of supply show an increase in the output of wheat and rice by 2030. From 2008 to 2030, the demand for wheat will increase from 19 million tons to 30 million tons. Projection estimates of wheat supply based on the production function technique show that by 2030, wheat output will reach 28 million tons, and rice output will be 11 million tons. The demand for wheat is expected to be greater than its supply whereas production of rice will be higher than consumption.

A Journey from the Short-Run Production Function to the Derivation of the Corresponding Total Variable Cost Function and Everything in Between

This paper derives all the formulae of interest of a short-run production function. For a perfectly competitive firm, this paper derives real profit maximizing labor, output, and real operating profit. For a given nominal wage rate of labor, it derives the corresponding total variable cost function. This paper finds that the outputs corresponding to the point of inflection and Stage I do not correspond with the outputs that minimize the marginal cost and the average variable costs respectively. All the derived formulae are either directly or indirectly in terms of marginal product function maximizing labor.

A short-run production function for electricity generation in China

Process industries, such as chemicals, aluminium, steel, pulp and paper, and thermal electricity generation, are important basic industries for economic growth in an economy such as the Chinese one. In order to promote improved efficiency and growth-inducing structural change, it is of paramount importance to model the development of such industries in a relevant way. It will then be necessary to go outside the smooth textbook production theory and turn to models incorporating typical features of process industries, such as embodied technical change, a sharp difference in substitution possibilities before and after investing, and a dynamic change at the industry level driven by entry and exit of plants and embodied technical change. The purpose of the paper is to give an introduction to the key production function concept of a short-run industry production function, and to show how this concept is the key to understanding industry dynamics. An empirical application is made on data for Chinese coal-fired electricity generation plants for one year. However, this will only be the first stage in a full-blown dynamic analysis. Combined cross-section and time-series data for plants are then required.

Employment and Environmental Protection

One of the most pressing problems in an economy intransition is that of unemployment. Hitherto the`costs' of this unemployment have either focused onthe value of the lost production, or on the costs tothe government of supporting the unemployed. From asocial viewpoint this is inappropriate. In this paper,we discuss the costs of unemployment in terms of theirimpacts on human welfare, particularly the healtheffects. On the positive side, as inefficient industries areshut down and as production responds to marketpressures, wasteful government subsidies are reduced,as is the level of environmental pollution. Clearly,therefore, there is a trade-off between theenvironmental and economic benefits on the one handand the welfare costs of unemployment on the other.In this paper, a simple model is developed to analyzethis trade-off. A single firm has a short-runproduction function in which output is dependent onthe level of employment. The present position ischaracterized by `inefficiency' in that the firm ismaking a loss and overproduction is taking place.Environmental damage is a function of the level ofoutput. The efficient production point is known, asare the efficiency prices.The problem to be solved is to minimize the costs ofmoving to the efficient point. The papercharacterizes the efficient dynamic path and givessome illustrations of such a path for the coal sectorin Russia, for given values of the efficiency losses,the environmental costs of using coal and the costs ofunemployment.

The Interplay between Micro-Frontier and Sectoral Short-Run Production Functions

We apply Leif Johansen's dynamic production function framework to the development of the Finnish brewery industry over a 30-year time span, 1955 to 1984, based on micro data (plants). The relationship between the micro-frontier and short-run industry production functions is analysed, particularly with respect to the evidence of embodied technical progress. The empirical analysis reveals striking differences in the time pattern of productivity growth of the two functions, illustrates the importance of capacity expansion for technical progress at the frontier, and clarifies the distinction between embodied and disembodied technical progress.

Modeling Short-Run Cost and Production Functions in Computerized Business Simulations

This article develops an algorithm to model short-run cost and production functions using Sheppard's lemma in computerized business simulations. The algorithm is derived using duality theory to maintain consistency between the production technology and cost relationships of the firm. The short-run cost function is shown to depend on: variable factor prices, the production rate, and the level of the fixed factors. Sheppard's lemma is applied to derive the cost minimizing input demand levels based on the characteristics of the short-run cost function. A recommended system of equations is presented and discussed to simulate the theoretical model of the firm. A numerical example is given to illustrate how the parameters of the equation set can be estimated and how the functions behave. The system is shown to be flexible and may be applied to model a wide array of cost structures.

The highway speed-volume relationship revisited

The highway speed-volume relationship has been studied by a number of authors, and is an important issue in urban transportation. Estimates of the relationship may be used to examine congestion externalities, calculate optimal tolls, and calibrate traffic simulation models. A recent paper in this journal by Fare, Grosskopf, and Yoon [2; hereafter referred to as FGYI views highways as a production process, with flow of cars and highway scale representing inputs, and speed representing the output. FGY then present a functional speed-flow relationship grounded in production theory. In addition to the basis in production theory, FGY observe that their function is consistent with the law of variable proportions. FGY state that, unlike most other specifications that have been employed, their function is able to describe the characteristic speed-volume relationship where speed increases with volume over a range of low volume, attains a maximum, then decreases with volume. Unfortunately, as shown below, the parameter estimates presented by the authors are incorrect, due to the authors’ use of faulty software. In addition, FGY incur some minor problems in their application, which are also addressed below. Nonetheless, with some minor adjustments, the production theory approach to the speed-volume relationship remains appealing and useful. FGY begin with a general, short-run production function of the form G = g(x, N), where G represents common speed of vehicles, x > 0 represents fixed highway scale, and N E R, is defined as the flow of cars in a lane past a fixed point. This short-run production function is required to satisfy several properties of production functions listed by FGY. In Eq. (2.3) of their paper, FGY present the function

Energy Efficiency and Capital Embodied Technical Change The Case of Mexican Cement Manufacturing

This paper analyses energy efficiency in the Mexican cement industry by studying disaggregated data at the plant and production unit level. A short-run production function is examined to look at the substitution possibilities between labour and energy with given equipment, but these are found to be limited (as expected). Instead, reduction of energy use per unit of output is mainly due to capital embodied technical progress: the most important improvements in plant efficiency are related to investments in new pieces of specific equipment. Average energy intensity of the branch as a whole is, therefore, mainly explained by capacity expansion. Finally, the importance of factor prices and the relevance of our results to other industries are discussed.

Highway traffic flow and the uneconomic region of production

In this paper highway traffic flow is formulated as a short-run production function in which traffic volume is the output and traffic density is the variable input. Given this formulation, the ‘uneconomic’ region of production is relevant. Often it is the case that traffic density will exceed the point at which traffic volume is at a maximum; i.e., the marginal product of the variable input is negative.

The distribution approach to the aggregation of production functions

We shall argue below that the distribution approach to the aggregation of production functions provides an useful framework to analyse the production structure of an economy and enhances our understanding of it. The distribution approach was initiated by Houthakker (1956), elaborated by Johansen (1972) and extented by Sato (1975). Apart from summarising the main features of the distribution approach developed by these authors in a consistent framework, we also add new insights. Some of these insights stem from our earlier research, e.g. the interpretation of the aggregate short-run production function and the estimation of the capacity distribution. However, the extension of the analysis to economy-wide aggregation has not been presented before. The same holds for the role capital plays according to the distribution approach in both the short-run and in the long-run production function.An important feature of the distribution approach is that the production structure of an economy is seen as the result of both management decisions and technological possibilities. Moreover, the approach enables us to identify production units and their production functions at any desired micro level. As a consequence, the influence of technological change on the production structure can be analysed extensively. The same holds for changes in output prices and factor prices, through their influence on management decisions.

Productivity measurement with adjustments for variations in capacity utilization and other forms of temporary equilibrium

One of the most persistent puzzles addressed by recent productivity research is the substantial decline in measured productivity growth during the 1970's. In this paper we trace a substantial part of the measured decline to the fact that traditional methods of productivity measurement assume that producers are in long-run equilibrium when in fact they may be in short-run or temporary equilibrium. We utilize the Marshallian framework of a short-run production or cost function with certain inputs quasi-fixed to provide a theoretical basis for accounting for temporary equilibrium. Within this theoretical framework it is the value of services from stocks of quasi-fixed inputs which should be altered rather than the quantity. The empirical application to U.S. manufacturing data 1958–81 shows that, depending on the measurement procedure, one can attribute somewhere between 18% and 65% of the traditionally measured decline in TFP growth between 1965–73 and 1973–81 to the effects of temporary equilibrium.

Overhead labour and bounded substitutability

In this paper we argue that due to the presence of quasi-fixed overhead labour, the aggregate short-run production function of the industry has the property of bounded substitutability. That is, when employing overhead labour, the industry will only be able to earn a positive quasi-rent for a bounded interval of aggregate labour intensity.

Technical Progress and Structural Change in the Swedish Cement Industry 1955-1979

The purpose of this article is to provide a deeper empirical insight into the structural change of an industry which is more relevant than that obtained by an analysis based on the traditionally estimated average production function. The main contribution is a long run analysis of technical progress and structural change by means of the short run industry production function introduced by Johansen [13], and based on micro data for individual production units. For that purpose we have developed Johansen’s approach into an operational framework for discrete capacity distributions including a special algorithm for the computation of the short-run industry production function. (This abstract was borrowed from another version of this item.)

The distribution approach to the aggregation of putty-clay production functions

The point of departure of the distribution approach is the efficiency distribution of the production units in an industry. From this distribution the full-capacity production function and the short-run aggregate production function of the industry are derived. The long-run production function of the industry then is derived from the full-capacity function and the short-run production function. Hence, in the context of the distribution approach the relation is analysed between the short-run, full-capacity and long-run aggregate production functions of the industry and the efficiency distribution (and related capacity distribution) of the production units in that industry. Finally, the distribution approach is applied for the case of the Japanese cotton spinning industry.

Another possible source of wage stickiness

A number of hypotheses have been advanced to explain wage stickiness. This article explores another reason why wage stickiness might be in an employer's interest: the relationship between productivity and the wage rate. If the wage enters the short-run production function, a cost-minimizing firm will leave its wage offer unchanged, no matter how its output varies, if and only if the wage enters the production function in a labor-augmenting way.

The Short-Run Demand for Workers and Hours: A Recursive Model

The short-run relationship between employment and output has generated a wealth of literature since the early 1960's (Hultgren (1960, 1965), Kuh (1960, 1965a, 1965b), Neild (1963), Raines (1963), Wilson and Eckstein (1964), Brechling (1965), Ball and St Cyr (1966), Soligo (1966), Brechling and O'Brien (1967), Dhrymes (1967), Ireland and Smyth (1967, 1970), Masters (1967), Smyth and Ireland (1967), Fair (1969), Nadiri and Rosen (1969, 1973). A substantial part of this work has involved the construction and estimation of employment equations the composition of which is derived primarily from an (inverted) short-run production function. The choice of statistical surrogate for employment has strong implications for the structure of the estimating equations and yet, remarkably, relatively little attention has been paid to this aspect of the problem. In most of the studies employment has been approximated either by the number of men in employment or by man-hours. Both formulations assume implicitly that men and average hours are perfect substitutes for one another; that is they are functionally related to the same set of exogenous variables, adjust at an equal rate to their own lagged values and exhibit similar reactions over the cycle to each and every influence. Such assumptions, however, are bold and several writers have seen the need to provide a separate specification for equations depicting the demand for the number of workers and their rate of utilization (see Kuh (1956b), Brechling (1965), Fair (1969), Nadiri and Rosen (1969, 1973) from above and also Brechling (1974) and Ehrenberg (1971)). Three major reasons may be given which would warrant such a separation: (i) Hours may be viewed as comprising the principal short-run means of adjusting labour to output changes while men are adjusted to meet longer-term movements in output, capital stock, etc. (ii) Men and hours may themselves be interdependent (recursively) given the different time scales mentioned above. (iii) Certain exogenous influences may affect the demand for men in different (and possibly opposite) ways from their effect on hours. The main purpose of this paper is to present and test a simple theory which takes explicit account of the interdependence between the employee and utilization decisions. The functional form of our model is developed in Section 2 with particular variable constructions and results presented in Section 3. Where possible, it will be interesting to compare our results with those of Brechling (1965) since the early development of our model follows closely along lines suggested by Brechling and, like him, our data refer to British manufacturing industries. Brief conclusions appear in Section 4.