Scale economies and the “0.6 rule”

Abstract

One aspect of scale economies which has received more attention in the engineering than in the economics literature is the “0.6 rule”. This rule has its origins in the relationship between the increase in equipment cost ( C) and the increase in capacity ( V) given by C 1 / C 2 = ( V 1 / V 2 ) α where α denotes the scale coefficient. A value of α less than unity implies increasing returns to scale. The value of α = 0.6 used in the basic version of the rule refers to equipment such as tanks and pipes which, in principle, give significant economies of scale. It is often used as a rule of thumb to obtain the investment cost of a capacity level V 2 given the cost C 1 associated with the level of capacity V 1 . The purpose of this paper is to consider the rule within the overall context of scale economies and to examine its applicability for a specific industry, using data obtained from a major machinery supplier in the course of research on the choice of technique in cane sugar manufacturing in less developed countries. The information available consisted of price data at three levels of aggregation: individual pieces of equipment (of varying capacities), specific sub-processes, and aggregate equipment and total investment costs. In the latter two cases data covered a range of scales, from 1250 to 10,000 tonnes of cane per day (tcd) crushing capacity. At the factory level the scale coefficients were all clearly less than unity (for both equipment alone and for total initial investment). Remarkably, that for a rise in scale from 1250 to 10,000 tcd was indeed 0.60, but this single overall value conceals considerable variations in the calculated scale coefficients, and an increase in the size of the coefficient as scale increases. Thus a factory-size increase from 1250 to 2500 tcd has a scale coefficient of 0.37 whereas the corresponding value for an increase from 7500 to 10,000 tcd is 0.79. This pattern is consistent with the main finding that the major scale economies in this industry have at present been exhausted at around 5000 tcd for the type of countries included in the analysis. The pattern of results at the sub-process level is broadly similar, but there are considerable differences between the coefficients for different sub-processes. This picture is reinforced by the results for individual pieces of equipment, whose scale coefficients vary from 0.21 to 1.26. Clearly the 0.6 overall result is derived from a very considerable averaging process. Strictly speaking the rule applies to the costs of production of equipment whereas the raw data relate to manufacturer's quoted prices. The paper concludes by discussing a number of reasons why the coefficients vary across both equipment type and scale of production; in particular differences in price competition, length of production run, and the need for stand-by equipment. The findings of this study — evaluating the 0.6 rule at different levels of aggregation — suggest strongly that the rule's application to the analysis of investment costs should be regarded as no more than a very rough guide.