THE THEORY OF IRRELEVANCE OF THE SIZE OF THE FIRM

Pak-Wai Liu

Department of Economics
Chinese University of Hong Kong

and

Xiaokai Yang

Department of Economics, Monash University and
Center for International Development, Harvard University

November 1999

JEL Code: D23, L11, L22, L23

Key words: size of the firm, division of labor, theory of the firm

Abstract
This paper formalizes Cheung, Coase, Stigler, and Young's theory of irrelevance of the size of the firm. This theory states that if division of labor develops within the firm, the average size of the firm and productivity go up side by side. If division of labor develops between firms, the average size of firms decreases as productivity goes up. Inframarginal analysis of the trade off between positive network effects of division of labor on aggregate productivity and transaction costs can predict recently popular business practices of down sizing, oursourcing, contracting out, focusing on core competence, and disintegration. We present evidence for a negative correlation between average employment of labor by firms and productivity.

1. Introduction
Many scholars have observed that average employment of labor by firms (average firm size) in many industries in both advanced countries and newly industrialized countries has declined. Data clearly show that in numerous developed countries, such as the U.S., U.K., France, Austria and Belgium, employment share of small and medium enterprises in their manufacturing industries exhibits a U-shape pattern. It declined initially in the 1960s and early 1970s but started to increase in the late 1970s and early 1980s. Among the newly industrialized countries, South Korea's manufacturing industries exhibit the same pattern as the developed countries, with a turning point in the early 1980s. In Taiwan, average firm size in manufacturing measured in terms of average employment increased from 7.3 persons per firm in 1954 to a peak of 28.2 in 1971 after which it followed a decline trend, reaching 24.2 in 1984. Similarly in the 1980s, manufacturing firms in Singapore were getting smaller in size on the average.

This inverted U-shaped trend is not confined to manufacturing industries. Liu (1992) shows that in Hong Kong, besides manufacturing, industries such as business services, import/export and restaurant exhibit a trend of declining average firm size. Table 1 shows the change in firm size of these four industries measured in two ways, the average number of employees per firm and the percent of employees engaged in firms with employees larger than 50. The trend since the late 1970s when data became available is generally downward. The decline in the average size of firms is associated with an increase in per capita real income and total factor productivity.

This trend of declining average firm size is contrary to the common perception that due to technological change and economies of scale, firm size should get larger over time. For instance, Kim (1989) shows from his model that because there are economies of scale arising from increasing returns due to specialization, firm size gets larger with specialization and the extent of the market. Our study provides an explanation of why firm size may get smaller over time on the basis of an analysis of the division of labor and transaction cost. We will show that the institution of the firm will emerge if the transaction efficiency for labor is higher than that for intermediate goods. By transaction efficiency we measures the fraction of the purchased good which disappears in transit due to transaction cost. Transaction competes for time and management. For instance, a producer of an intermediate good can either pay the search cost to find a supplier of the primary good used in its production or the managerial monitoring cost of in-house production of the primary good. We will show that given the emergence of firms, their size (measured by employment) decreases if the transaction efficiency for intermediate goods becomes higher than that for labor. The decrease in the size of firms is driven by two forces. First, each firm becomes more specialized if division of labor develops among firms, so that each firm's scope of activities is reduced. However, if division of labor and specialization are developed within each firm, the level of specialization of each worker in a firm and the scope of the firm may increase hand in hand. But if the transaction efficiency for intermediate goods is higher than that for labor, then organizing division of labor between more specialized firms will be more efficient than organizing division of labor within a firm since the former involves more transactions of intermediate goods while the latter involves more trade in labor, thus generating a decline in the size of firms.

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