Short-run Cost Function Research Articles

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.

Capacity utilization and depreciation-in-use

In this paper, the effect capacity utilization has on the depreciation of capital goods is studied, starting from a quadratic approximation to a normalized short-run cost function. Expressions for the optimal rate of capacity utilization, the demands for labour and energy, and for investment are obtained. Investment is a function of past capital stock, expected future capital stock, expected future relative prices and expected future depreciation rates. Expectations are modelled via instruments. The model is tested using US total manufacturing quarterly data. Depreciation dependent upon usage is found to be both statistically and economically significant.

Estimating cost functions for rail rapid transit properties

Using data from North American rail transit properties, short and long run cost functions are estimated using a neoclassical economic model. Various special econometric techniques are employed to estimate the relationships from a heterogeneous data set. The estimated cost functions are then used to forecast the cost experience of the BART system in San Francisco.

On the Short-Run Cost Function

IN this communication, we consider the variables included in the short-run cost function, its various forms under different conditions, and the concept of fixed costs. By the short-run cost function we mean the array of values of total cost that will be incurred in producing different volumes of output with given plant and equipment. The layout and mode of utilization of the given plant may of course be adjusted; and the whole complex of business organization and staffing is regarded as variable., The plant is regarded as producing a single product or a complex of products produced in constant proportions. We presuppose a 'matured' technique in which the economies of learning have been worked through.' For economy in presentation we deal only with the total cost function though our conclusions apply to the whole family of its derivatives. Consider first the nature of the variables whose behavior is described by the function. The determination of the output variable or its correlative rate of plant-utilization is relatively simple. But the same cannot be said for the cost variable. In principle this variable should comprehend all costs which arise out of producing and marketing the output in question or servicing and supporting the productive and marketing organization while it is engaged in carrying on productive operations. We disregard the tendency, stimulated in part by high income taxes, to camouflage net income in kind as productive expenses. Even then we must recognize that productive activities, particularly those on the staff or management level, may be designed to yield their fruits over a succession of output periods. The resulting costs need to be allocated by essentially arbitrary decision to particular parcels of product. Formulas of allocation have been quite crude and under stress chiefly of taxation have tended to assign allocable costs wherever possible to the particular period in which the costs were incurred or obligated.' More troublesome for theoretical purposes are the so-called implicit costs which involve more or less arbitrary charges against current output on account of imputed future shrinkage in asset value or capabilities. Thiis if natternq of unstable emnlovment will imDair working

Manufacturing Progress Functions

M OST economic cost studies have been concerned primarily with the relation of cost to rate of output. Shortrun costs are usually said to be those associated with variation in the utilization of fixed plant or other facilities, whereas longrun cost encompasses changes in the size and kind of plant. Strictly, then, the distinction is based upon the degree of adaptation of all input factors to rate of output.1 However, cost may vary because of changes in technical knowledge.2 Economists have explicitly excluded all irreversible changes in technology. Most longrun cost theories, for instance, are timeless; one future point in time is selected at which output rate and facilities are permitted to change. That such a cost function, particularly its height, will be affected by improvements in technical knowledge is beyond doubt. It is convenient to clarify the issue of the different cost functions by referring to production functions, which express the net relation between the input of variable productive factors and output during a given production period, under the assumption of a given plant and technical knowledge. From the production function we can derive a static shortrun cost function, which also assumes a given plant and technical knowledge. Longrun cost permits changes in the size and kind of plant, but assumes stability in technical knowledge. Thus, a longrun cost function is related to points on different production functions, each point involving a different plant while using the same technical knowledge. There can be a cost function which permits changes in technical knowledge but not in plant and other facilities. In a sense this is a dynamic cost function. If direct labor is the cost we consider, we shall speak about a (unit) learning or progress function. This expresses the net relation between the amount of direct labor needed to produce one product-unit and the cumulative units produced in a given facility. The progress function thus permits us to estimate the amount of direct labor needed to manufacture the nth unit, from n, the cumulative number of the product-unit. The function is related to a number of points on different production functions involving successive changes in technical knowledge in a given facility. In this study we will analyze data of a large United States machine builder, who has been one of the largest machine tool 3 manufacturers for about three-quarters of a century. Since the end of World War II the company has also manufactured textile and construction machinery. Of its twenty products, seven have been selected for an empirical analysis. They are either new products or new models. Machine i is a new semi-automatic machine tool and machines 2-5 are new automatic machine tools which differ greatly in the functions they perform, weight, labor requirement, etc. Machine 6 is a textile machine and machine 7 is a multipurpose construction machine. Production is carried out in one large plant. During the period under consideration, I946-50, the monthly direct labor force varied from 930 to 3,600 men. The production process is very complicated, calling for high professional skills. It is divided into machining of parts and their assembly. Each month top management decides on a production schedule which instructs the production manager to have ready for shipment by a *The author would like to express his gratitude to the Bureau of Business and Economic Research of the University of California for financial support of this study. 1J. Dean, Managerial Economics (New York, I951), p.