Manufacturing Progress Functions

Abstract

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.