Case B

As we have mentioned, Gal (2001) defines market size as the ratio of the size of the relevant market, that is, the output that would be demanded at a price just sufficient to cover minimum unit costs, to the size of a unit of production that is just sufficiently large to achieve lowest average costs of production MES.[26] Firms in a small market where demand is small relative to MES face cost disadvantages, and arguably limitations on the creation of indigenous research and development, technology acquisition and technical progress. Scherer et al (1975) provides estimates of the observed plant sizes in a variety of countries based on late 1960s data. This information is reproduced in Table 2. Asterisks indicate that the estimate is based on actual production levels. Figures without asterisks are based on employment information.

Table 2 illustrates that the problem of plants operating below MES can occur in practice. Plant sizes above 100% may indicate that, once MES is reached, plant scale can be increased to double or triple MES without causing unit costs to significantly increase.[27] In any case, observed plant sizes may reflect other restrictions (eg, interstate or inter-provincial trade barriers in brewing) or, where based on employment information, may simply reflect inefficiencies or employment arrangements.

The issue posed by diseconomies of scale is illustrated in Figure 2 where the firm’s average cost curve is drawn so that it reaches its minimum at a relatively large output level (denoted Q_MES). The demand curve is denoted D(P) and the output level that would be demanded at a price just sufficient to cover minimum average cost is given by Q*. The ratio of Q* divided by Q_MES gives an indication of market size. A value of one for this ratio indicates that the market is just large enough to support a single firm operating at minimum efficient scale. A value of two indicates that two firms of efficient size can be supported while values of less than one indicate that not even a single firm of minimum efficient scale can be supported.

Notes: Data from Tables 3.1 to 3.6 of Scherer et al (1975). Observed plant sizes reported are mid-points of a number of observations for each country – ie, actual observations on individual plant sizes in a country could be either higher or lower than the reported mid-point.

The magnitude of the cost disadvantage depends on the market size ratio, the price level, and how quickly the average cost curve rises.

The demand curve in Figure 2 (and the associated Q*) includes not only domestic demand but also all foreign markets that the firm or firms can supply at a small per unit tariff and/or transportation cost. That is, implicit in Figure 2 is the definition of a relevant geographic market.

Figure 2 – Graphical depiction of the allocative (b) efficiency problem

We may distinguish between final and intermediate goods when considering whether export markets should be included when identifying Q*. For example, consider the case of a book or a machine that can be used to make tools. It may be the case that the input (the text of the book or the machine) can be cost-effectively transported to foreign markets while at the same time it is not an economic proposition to transport the final output (the printed book or the tools made by the machine) across international boundaries.[28]

If the market for the intermediate good is international, the relatively small size of an individual country’s market cannot lead to technical inefficiency in the production of the intermediate good. For example, say Q_MES is 100 units of the intermediate good and the demand in the U.S. is 85, the demand in Europe is 35 and the demand is so small in New Zealand that it is not cost effective to justify the use of a single unit. Then, if indivisibilities are important, New Zealand may suffer a loss of economic welfare because the final output that is available in other countries does not reach New Zealand consumers. But this does not mean that there is allocative inefficiency in the production of the machine. In this example, 120 units would be produced at minimum average cost. Nor does it seem correct to call this allocative inefficiency in the production of the final good. Rather, the problem is that there is no economically viable production. If the relevant geographic market for the final good is international while the relevant geographic market for the intermediate good is restricted to the national market, this is enough to assure there is no allocative inefficiency at either level.[29] For example, consider wine. It may be the case that it is prohibitively expensive to transport the grapes internationally, but it is feasible to transport the more valuable finished product (wine or sterling silver). Then, in each local market, the production of the intermediate good (grapes) can expand until all scale economies have been exhausted. This could involve producing ten or one-hundred times the amount of grapes that the local population would consume as wine even at a zero price.

Scherer et al (1975) provide empirical information on cost effects of scale. These findings are reproduced in Table 3. They indicate quite significant cost differentials for firms that do not achieve scale economies. At the same time, it is worth noting that a small market is not a significant handicap for values of Q* which are “close” to Q_MES. This is because Q_MES is near the minimum of the average cost function and thus the rate of change of AC is small—ie, the AC function is “flat.” Or, to put the same idea somewhat differently, because marginal and average cost are equal at Q_MES, the effect of very small reductions on AC is “second-order small.”

While the specific values in Table 3 are arbitrary, a general conclusion holds: relatively small but significant deviations from Q_MES (eg, Q*/Q_MES of about 0.9) result in insignificantly small relative cost differentials that will hold up for any “U-shaped” cost function.

Source: Scherer FM (1974) “The Technological Basis of Plant Scale Economies in Twelve Manufacturing Industries,” Preprint I/74-6, International Institute of Management (Berlin, 1974). Reproduced in Scherer et al (1975).