Economies of scale

International trade theory recognizes three fundamental reasons for countries to trade: comparative advantage (to exploit differences in countries’ tastes, technologies, or factor endowments), economies of scale (to concentrate on fewer tasks in order to produce more efficiently), and imperfect competition (to expose firms to more competition). Comparative advantage has always been dominant in trade theory, although economies of scale also long played a secondary role. This changed in the late 1970s, when economists realized that the lion’s share of world trade consisted of the exchange of similar (manufactured) goods between similar (rich) countries.

A common reaction to this realization was that such trade could not be due to comparative advantage. But if similar countries trade similar goods, price elasticities (the sensitivities of demands and supplies of goods to price variations) are likely to be high since the traded products will likely be good substitutes. Similar countries would have similar relative prices in autarky (the absence of international trade), so comparative-advantage trade, establishing a world price between the two autarky prices, would imply a modest price change in each country. But, with high elasticities, this could still involve heavy trade. Likewise, dissimilar countries trading very distinct goods manufactures for primary products, for example could be expected to experience large price changes, but the resulting trade volumes could be small as price elasticities are likely to be low.

So, comparative advantage was not necessarily inconsistent with actual trade. Nevertheless, it was important to consider alternative possibilities because, although trade to exploit differences does not imply that the greater the differences, the greater the trade, it does imply, other things being equal, that the greater the differences, the greater the gains from trade. Thus onemight conclude that the smaller part of world trade that between dissimilar countries in quite different products is more important for policy. But if trade patterns are significantly due to something other than comparative advantage, this conclusion need not follow.

Increasing returns to scale (IRS) and imperfect competition supply alternatives. This article considers the former, often also referred to as economies of scale.

Types of Scale Economies

In practice, scale economies occur in great variety, so a classification of the more important attributes is useful.

Internal versus external (to the firm). Scale economies are internal if the individual firm can reduce average costs by operating at a higher scale (e.g., assembly-line operations and equipment made possible by large-scale production). They are external if the individual firm operates subject to constant returns to scale (CRS), but costs are lower the larger the industry in which the firm is located (e.g., welldeveloped infrastructure and a large supply of skilled workers consequent on a large industrial sector). Internal economies are inconsistent with a perfectly competitive equilibrium, and external economies are, well, externalities. Since the theory of comparative advantage assumes perfect competition and no externalities, trade due to economies of scale alone cannot be comparative-advantage trade.

National versus international. Economiesofscale may depend on the scale of operations within a nation (e.g., large plant size) or on the scale of operations globally (e.g., division of labor and free trade in intermediate goods). Either might be internal or external to the firm. An example of internal, international economies of scale is research and development (R&D) by amultinational firm that utilizes the results of the R&D in several countries.

Aggregative versus disaggregative. Increasing returns may be a property of manufacturing generally (e.g., the size of the industrial sector) or of individual manufactured goods (e.g., the number of red sedans).

These three considerations generate eight types of scale economies, each relevant in reality. Comparative- advantage trade can also be due tomany causes, but they all matter solely in terms of how they influence differences in relative autarky prices. This imparts an attractive formal unity to that theory’s predictions. Trade due to economies of scale is dramatically different: Basic implications are indeed very sensitive to the type of scale economy. Consider first national, aggregative, increasing returns external to the firm.

National, Aggregative Economies of Scale External to the Firm

IRS can furnish a basis for trade independent of comparative advantage. Consider a simple model with two identical economies with two-good Ricardian technologies. Good A is produced with CRS, with one unit of labor required in each country to produce one unit of A. The B sector has IRS external to the firm: B ¼k(LB)LB, where k(LB)¼k0(LB)a - 1 for a>1. The individual firm takes k as a parameter.

Two such identical countries will have equal relative autarky prices. But there is still a basis for trade: with IRS in the B industry it is not globally efficient for both countries to produce both goods.

The no-trade case, with each country doing what it had done in autarky, is a free-trade equilibrium. But it will not be a very stable one. For suppose the home economy produces more B, and the foreign economy less. Then k is greater than k*, the foreign analog, so home B firms can undersell their foreign rivals, while the two countries can still produce A on equal terms. Home B producers can increase their market share at the expense of their foreign competitors, so foreign resources move into the A sector. Thus k rises further and k* falls, increasing the home B advantage still more. This continues until a new equilibrium is reached with the home economy producing only B and/or the foreign economy producing only A. Indeed there is more than just a second equilibrium: since the two countries are identical we can find a third equilibrium by simply reversing the home and foreign roles.

The basic idea behind comparative advantage is that countries should do what they can do relatively well; this implies some particular role in the world economy. Scale economies on the other hand require countries to concentrate on a small number of tasks; who does what is secondary. Thus scale economies introduce a bias toward a multiplicity of equilibria.

The other equilibria might involve one country specialized inBand/or one specialized inA.Consider anequilibriuminwhich the home country specializes in B,with the (identical) foreign economy producing both goods. Since k > k*, foreign wages must be lower than home wages and also lower than wages in autarky, so foreign real income must have declined. Likewise, the home wage must have risen relative to autarky. Thus trade has benefited the home economy, buthasmade the foreignworse off.There is also a ‘‘mirror-image’’ equilibrium in which the roles of the two countries reverse. Thus potential international conflict is inherent. We might call this the Graham case since it corresponds to Graham’s (1923) argument for protection.

Suppose now that, instead, the dynamic adjustment ends with the foreign economy specialized in A and the home economy producing both goods. Since both countries produce A, wages must be the same internationally, in sharp contrast to theGrahamcase. Thus residents of both countries fare the same, and that common fate must be an improvement over autarky, since the home B sector has grown. There will again be another ‘‘mirror image’’ equilibrium, but unlike the previous case this is of no consequence, because everyone fares the same regardless of country of residence. With identical economies, a wageequalization equilibrium is associated with a large world equilibriumdemand forA, so that one country alone cannot satisfy it. But with dissimilar countries, it is easy to construct examples in which either the larger or the smaller country specializes in A, and in which both countries lose relative to autarky.

The final possibility is that both countries specialize. Then the international equilibrium is efficient, unlike the other cases, where too little B is produced. The various types of equilibria are not mutually exclusive. That is, if tastes, technology, and size imply multiple equilibria, the equilibria could be of different types. It is the possibility of wage equalization and (especially) Graham equilibria that produces the real value added that can come from consideration of IRS. These equilibria can produce positive andnormative implications in sharp contrast to those of comparative advantage and can therefore be used in support of quite different policy recommendations. They are of direct relevance to the old debates in developing countries over the wisdom of participating in the international trading system.

But this analysis of national external economies of scale is less than fully satisfying and has accordingly had to play a role very much subservient to that of comparative advantage. The indeterminacy of results due to the likelihood of multiple equilibria renders the theory cumbersome to use. Also, this investigation of scale economies wasmotivated in large part by a desire to address more directly a world in which the lion’s share of trade consists of the exchange of similar commodities between similar economies. But the influence of scale economies, enhancing the possibility of specialization, and perhaps causing initially similar economies to become very dissimilar, is to move the discussion in just the opposite direction. Additional methods of modeling scale economies are needed.

Disaggregative Economies of Scale

Consider nowthe samemodel as above, except that the B sector now consists of n distinct varieties, Bi, each with the technology described above. Note the following concerning international trade in such a model.

1. Wage equalization equilibria will again feature both countries producing some A, but no variety of B in common, so that both are equally well off with free trade. If one country specializes in A all trade will consist of the interindustry exchange of A for B, but if both countries produce somevarieties ofB there will also be an intraindustry exchange of B varieties. We would expect the latter to be relatively more important the more similar the two countries are: if the two are exactly alike, there will be an equilibrium with only intraindustry trade. 
2. Graham equilibria can still emerge whenever the two countries produce some variety of B in common but in different amounts. The country with the larger production must have the higher wage and therefore cannot be producing any A. However this now seems like a much less likely outcome than before, since a smaller B sector than in autarky need not condemn a country to a lower wage: it can just produce a smaller number of varietieswhile fully supplying the world demand for each. 

International Economies of Scale

External economies have often been identified with an increased division of labor made possible by a larger market: Adam Smith’s pin factory and the Swiss watch industry are the prominent hoary examples. Less common are examples having to do with a larger volume of public information generated by a larger industry. In principle none of these requires an industry to be physically located in one place. A dispersed industry can realize a great division of labor if intermediate components can be shipped fromplace to place; public information can be dispersed within the industry if communication is efficient. What matters, under these conditions, is the global size of the industry, not its geographical concentration.

This suggests that returns to scale may depend on the size of the world industry, not the national industry. This is what ismeant by international returns to scale. Suppose that resources are used to produceA and m. A production is characterized, as in the above one-factor models, byCRS;mis an index of the scale of operations of the national B industry, subject to IRS. With national returns to scale, national B production B is related to m by B ¼km where k ¼k(m), k0 >0:

With international returns to scale, on the other hand, we have instead B þB*¼ k(mþm*) where k ¼k(mþm*), k0 >0: Here an asterisk refers to the foreign country.

At first glance it might seem that we have complicated matters enormously. National productionpossibility frontiers between final goods are not even defined, because productivity in each country’s B industry depends on the size of the other country’s B industry. But the situation becomes almost transparent as soon as we focus on patterns of resource allocation rather than on goods.

To see this, consider the world productionpossibility frontier betweenAandB.Apointon it can be found by maximizing world B production for a given feasible volume of world A production, that is, by choosing m, m* to maximize: B þB*¼k(mþm*)[mþm*] subject to: T(m)þT*(m*)¼some specified value: T and T* denote the home and foreign productionpossibility frontiers between A and m. Clearly, B þB * will be maximized by maximizing mþm*: This problemhas exactly the same solution as that of choosing m, m* to maximize: mþm* subject to: T(m)þT*(m*)¼some specified value and the solutions to problems of the latter sort are just the comparative advantage predictions. Efficient patterns of world activity in A and B correspond to efficient patterns in A and m, ignoring the scale economies.

Productive efficiency is as with CRS, and firms behave competitively because the economies are external to them. The result is that the complex tendencies associated with Graham equilibria when scale economies are national disappear when they become international.

The second major implication of international IRS is that they imply a theory of the intraindustry exchange of intermediate goods between relatively similar economies. The essential idea behind international IRS is that a dispersed industry can realize the benefits of a large division of labor if intermediate goods can be shipped within the industry. Thus themore nearly equal in sizemand m* are, the greater the volume of intraindustry trade in B components.

All trade will be interindustry if the disparity between countries is great enough for the A exporter to specialize completely in A. Small international differences reduce the incentive for interindustry trade but cause the integrated B industry to be divided relatively evenly between countries, thereby inducing intraindustry trade. In the limiting case where the countries are identical, theywill both be self sufficient in A. But they can gain from trade by establishing a single, rationalized B industry; all trade will be intraindustry.

Applications of Scale Economies

Economies of scale can be a basis for trade, just like comparative advantage. But they can give a very different picture of the consequences of such trade. This has clearly emerged from recent work in the area.

The notion of international economies of scale, developed by trade theory, has been used to rejuvenate the theory of economic growth, as in thework of Romer (1986). If the division of labor is limited by the extent of the market, it is reasonable to suppose that indivisibilities in the production of intermediate goods is the reason why. So there is a role for imperfect competition with regard to the latter.

Imperfect competition and scale economies have been investigated in the context of both consumer goods, by Krugman (1979), Lancaster (1980), and Helpman (1981), and producer goods, by Ethier (1982a). As this literature does involve imperfect competition, it is beyond the scope of the present entry. More recently, scale economies have been central to the literature on trade with heterogeneous firms, as in the work of Melitz (2003).

Though scale economies were in trade theory fromthe beginning, their rolewas basically tangential until the late 1970s. Now it is central. See also comparative advantage; intrafirm trade; intraindustry trade; monopolistic competition; New Trade Theory; Ricardian model

WILFRED J. ETHIER