Scale economies, product differentiation, and the pattern of trade

American Economic Association Scale Economies, Product Differentiation, and the Pattern of Trade Author(s): Paul Krugman Reviewed work(s): Source: The American Economic Review, Vol. 70, No. 5 (Dec., 1980), pp. 950-959 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/1805774 . Accessed: 11/01/2013 09:04 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review. http://www.jstor.org This content downloaded on Fri, 11 Jan 2013 09:04:30 AM All use subject to JSTOR Terms and Conditions Scale Economies, Product Differentiation, and the Pattern of Trade By PAUL KRUGMAN* For some time now there has been con- siderable skepticism about the ability of comparative cost theory to explain the ac- tual pattern of international trade. Neither the extensive trade among the industrial countries, nor the prevalence in this trade of two-way exchanges of differentiated prod- ucts, make much sense in terms of standard theory. As a result, many people have con- cluded that a new framework for analyzing trade is needed.' The main elements of such a framework-economies of scale, the pos- sibility of product differentiation, and im- perfect competition-have been discussed by such authors as Bela Balassa, Herbert Grubel (1967,1970), and Irving Kravis, and have been "in the air" for many years. In this paper I present a simple formal analysis which incorporates these elements, and show how it can be used to shed some light on some issues which cannot be handled in more conventional models. These include, in particular, the causes of trade between economies with similar factor endowments, and the role of a large domestic market in encouraging exports. The basic model of this paper is one in which there are economies of scale in pro- duction and firms can costlessly differenti- ate their products. In this model, which is derived from recent work by Avinash Dixit and Joseph Stiglitz, equilibrium takes the form of Chamberlinian monopolistic com- petition: each firm has some monopoly power, but entry drives monopoly profits to zero. When two imperfectly competitive economies of this kind are allowed to trade, increasing returns produce trade and gains from trade even if the economies have iden- tical tastes, technology, and factor endow- ments. This basic model of trade is pre- sented in Section I. It is closely related to a model I have developed elsewhere; in this paper a somewhat more restrictive formula- tion of demand is used to make the analysis in later sections easier. The rest of the paper is concerned with two extensions of the basic model. In Sec- tion II, I examine the effect of transporta- tion costs, and show that countries with larger domestic markets will, other things equal, have higher wage rates. Section III then deals with "home market" effects on trade patterns. It provides a formal justifica- tion for the commonly made argument that countries will tend to export those goods for which they have relatively large domestic markets. This paper makes no pretense of general- ity. The models presented rely on extremely restrictive assumptions about cost and util- ity. Nonetheless, it is to be hoped that the paper provides some useful insights into those aspects of international trade which simply cannot be treated in our usual models. I. The Basic Model A. Assumptions of the Model There are assumed to be a large number of potential goods, all of which enter sym- metrically into demand. Specifically, we as- sume that all individuals in the economy have the same utility function, (1) U= Cis 0<0< I where ci is consumption of the ith good. The number of goods actually produced, n, *Yale University and Massachusetts Institute of Technology. 'A paper which points out the difficulties in explain- ing the actual pattern of world trade in a comparative cost framework is the study of Gary Hufbauer and John Chilas. 950 This content downloaded on Fri, 11 Jan 2013 09:04:30 AM All use subject to JSTOR Terms and Conditions VOL. 70 NO. S KRUGMAN: PA TTERN OF TRADE 951 will be assumed to be large, although smaller than the potential range of products.2 There will be assumed to be only one factor of production, labor. All goods will be produced with the same cost function: (2) li = a +/8xi a,83 > O i= 1 , . .., n where li is labor used in producing the ith good and xi is output of that good. In other words, I assume a fixed cost and constant marginal cost. Average cost declines at all levels of output, although at a diminishing rate. Output of each good must equal the sum of individual consumptions. If we can iden- tify individuals with workers, output must equal consumption of a representative indi- vidual times the labor force: (3) xi = Lci i=1 ,n We also assume full employment, so that the total labor force must just be exhausted by labor used in production: n (4) L= (a+/8xi) i = 1 Finally, we assume that firms maximize profits, but that there is free entry and exit of firms, so that in equilibrium profits will always be zero. B. Equilibrium in a Closed Economy We can now proceed to analyze equi- librium in a closed economy described by the assumptions just laid out. The analysis proceeds in three stages. First I analyze con- sumer behavior to derive demand functions. Then profit-maximizing behavior by firms is derived, treating the number of firms as given. Finally, the assumption of free entry is used to determine the equilibrium number of firms. The reason that a Chamberlinian ap- proach is useful here is that, in spite of imperfect competition, the equilibrium of the model is determinate in all essential respects because the special nature of de- mand rules out strategic interdependence among firms. Because firms can costlessly differentiate their products, and all products enter symmetrically into demand, two firms will never want to produce the same prod- uct; each good will be produced by only one firm. At the same time, if the number of goods produced is large, the effect of the price of any one good on the demand for any other will be negligible. The result is that each firm can ignore the effect of its actions on other firms' behavior, eliminating the indeterminacies of oligopoly. Consider, then, an individual maximizing (1) subject to a budget constraint. The first- order conditions from that maximum prob- lem have the form (5) Ocs9l =Xpii=1.,n where pi is the price of the ith good and X is the shadow price on the budget constraint, that is, the marginal utility of income. Since all individuals are alike, (5) can be re- arranged to show the demand curve for the ith good, which we have already argued is the demand curve facing the single firm producing that good: (6) pi=OX.-1(xi1L)'9 1i=1.,n Provided that there are a large number of goods being produced, the pricing decision of any one firm will have a negligible effect on the marginal utility of income. In that case, (6) implies that each firm faces a de- mand curve with an elasticity of 1 /(1 -9), and the profit-maximizing price is therefore (7) pi=O-lj8w i=l1,.-.., n where w is the wage rate, and prices and wages can be defined in terms of any (com- mon!) unit. Note that since 9, ,B, and w are the same for all firms, prices are the same 2To be fully rigorous, we would have to use the concept of a continuum of potential products. This content downloaded on Fri, 11 Jan 2013 09:04:30 AM All use subject to JSTOR Terms and Conditions 952 THE AMERICAN ECONOMIC REVIEW DECEMBER 1980 for all goods and we can adopt the shorthand p =Pi for all i. The price p is independent of output given the special assumptions about cost and util- ity (which is the reason for making these particular assumptions). To determine prof- itability, however, we need to look at out- put. Profits of the firm producing good i are (8) "Ti=pxi-{a+f3xi)}w i=1,...,n If profits are positive, new firms will en- ter, causing the marginal utility of income to rise and profits to fall until profits are driven to zero. In equilibrium, then g=0, implying for the output of a representative firm: (9) xi = aAx/( p/-,8]) = a0/80 1- 0) i= 1,. . ., n Thus output per firm is determined by the zero-profit condition. Again, since a, ,B, and 9 are the same for all firms we can use the shorthand x=xi for all i. Finally, we can determine the number of goods produced by using the condition of full employment. From (4) and (9), we have (10) L _ L(1-9) a +/3x a C. Effects of Trade Now suppose that two countries of the kind just analyzed open trade with one another at zero transportation cost. To make the point most clearly, suppose that the countries have the same tastes and technolo- gies; since we are in a one-factor world there cannot be any differences in factor endowments. What will happen? In this model there are none of the con- ventional reasons for trade; but there will nevertheless be both trade and gains from trade. Trade will occur because, in the pres- ence of increasing returns, each good (i.e., each differentiated product) will be pro- duced in only one country- for the same reasons that each good is produced by only one firm. Gains from trade will occur be- cause the world economy will produce a greater diversity of goods than would either country alone, offering each individual a wider range of choice. We can easily characterize the world economy's equilibrium. The symmetry of the situation ensures that the two countries will have the same wage rate, and that the price of any good produced in either country will be the same. The number of goods pro- duced in each country can be determined from the full-employment condition (11) n=L(1-#)/a; n*=L*(l-0)/a where L* is the labor force of the second country and n* the number of goods pro- duced there. Individuals will still maximize the utility function (1), but they will now distribute their expenditure over both the n goods pro- duced in the home country and the n* goods produced in the foreign country. Because of the extended range of choice, welfare will increase even though the "real wage" w/p (i.e., the wage rate in terms of a representa- tive good) remains unchanged. Also, the symmetry of the problem allows us to de- termine trade flows. It is apparent that indi- viduals in the home country will spend a fraction n*/(n+n*) of their income on foreign goods, while foreigners spend n/ (n+n*) of their income on home country products. Thus the value of home coun- try imports measured in wage units is Ln*/ (n + n*) = LL*/(L + L*). This equals the value of foreign country imports, confirming that with equal wage rates in the two countries we will have balance-of-payments equilibrium. Notice, however, that while the volume of trade is determinate, the direction of trade- which country produces which goods-is not. This indeterminacy seems to be a gen- eral characteristic of models in which trade is a consequence of economies of scale. One of the convenient features of the models considered in this paper is that nothing im- portant hinges on who produces what within a group of differentiated products. There is an indeterminacy, but it doesn't matter. This result might not hold up in less special models. This content downloaded on Fri, 11 Jan 2013 09:04:30 AM All use subject to JSTOR Terms and Conditions VOL. 70 NO. S KRUGMAN: PATTERN OF TRADE 953 Finally, I should note a peculiar feature of the effects of trade in this model. Both before and after trade, equation (9) holds; that is, there is no effect of trade on the scale of production, and the gains from trade come solely through increased product di- versity. This is an unsatisfactory result. In another paper I have developed a slightly different model in which trade leads to an increase in scale of production as well as an increase in diversity.3 That model is, how- ever, more difficult to work with, so that it seems worth sacrificing some realism to gain tractability here. II. Transport Costs In this section I extend the model to allow for some transportation costs. This is not in itself an especially interesting extension al- though the main result-that the larger country will, other things equal, have the higher wage rate-is somewhat surprising. The main purpose of the extension is, how- ever, to lay the groundwork for the analysis of home market effects in the next section. (These effects can obviously occur only if there are transportation costs.) I begin by describing the behavior of individual agents, then analyze the equilibrium. A. Individual Behavior Consider a world consisting of two countries of the type analyzed in Section I, able to trade but only at a cost. Transpor- tation costs will be assumed to be of the "iceberg" type, that is, only a fraction g of any good shipped arrives, with 1 -g lost in transit. This is a major simplifying assump- tion, as will be seen below. An individual in the home country will have a choice over n products produced at home and n* products produced abroad. The price of a domestic product will be the same as that received by the producer p. Foreign products, however, will cost more than the producer's price; if foreign firms charge p*, home country consumers will have to pay the c.i.f. price 13* =p*/g. Simi- larly, foreign buyers of domestic products will pay p^=p/g. Since the prices to consumers of goods of different countries will in general not be the same, consumption of each imported good will differ from consumption of each domestic good. Home country residents, for example, in maximizing utility will consume (p/j3*)l/(l-") units of a representative im- ported good for each unit of a representa- tive domestic good they consume. To determine world equilibrium, however, it is not enough to look at consumption; we must also take into account the quantities of goods used up in transit. If a domestic resi- dent consumes one unit of a foreign good, his combined direct and indirect demand is for 1 /g units. For determining total de- mand, then, we need to know the ratio of total demand by domestic residents for each foreign product to demand for each domestic product. Letting a denote this ratio, and G* the corresponding ratio for the other country, we can show that (12) (p/p*)A/() -)go/(l -) * =(P/ P*)- 1/(1 - ))gO(-) The overall demand pattern of each indi- vidual can then be derived from the require- ment that his spending just equal his wage; that is, in the home country we must have (np+an*p*)d=w, where d is the consump- tion of a representative domestic good; and similarly in the foreign country. This behavior of individuals can now be used to analyze the behavior of firms. The important point to notice is that the elastic- ity of export demand facing any given firm is 1 /(1 - 0), which is the same as the elastic- ity of domestic demand. Thus transportation 3To get an increase in scale, we must assume that the demand facing each individual firm becomes more elastic as the number of firms increases, whereas in this model the elasticity of demand remains unchanged. Increasing elasticity of demand when the variety of products grows seems plausible, since the more finely differentiated are the products, the better substitutes they are likely to be for one another. Thus an increase in scale as well as diversity is probably the "normal" case. The constant elasticity case, however, is much easier to work with, which is my reason for using it in this paper. This content downloaded on Fri, 11 Jan 2013 09:04:30 AM All use subject to JSTOR Terms and Conditions 954 THE AMERICAN ECONOMIC REVIEW DECEMBER 1980 costs have no effect on firms' pricing policy; and the analysis of Section I can be carried out as before, showing that transportation costs also have no effect on the number of firms or output per firm in either country. Writing out these conditions again, we have (13) p=w,f/0;p*=w*f3/0 n=L(l-#)/a; n* = L*(l-0)/a The only way in which introducing transportation costs modifies the results of Section I is in allowing the possibility that wages may not be equal in the two countries; the number and size of firms are not af- fected. This strong result depends on the assumed form of the transport costs, which shows at the same time how useful and how special the assumed form is. B. Determination of Equilibrium The model we have been working with has a very strong structure- so strong that transport costs have no effect on either the numbers of goods produced in the countries, n and n*, or on the prices relative to wages, p/w and p*/w*. The only variable which can be affected is the relative wage rate w/w* = &, which no longer need be equal to one. We can determine o by looking at any one of three equivalent market-clearing con- ditions: (i) equality of demand and supply for home country labor; (ii) equality of de- mand and supply for foreign country labor; (iii) balance-of-payments equilibrium. It will be easiest to work in terms of the balance of payments. If we combine (12) with the other equations of the model, it can be shown that the home country's balance of payments, measured in wage units of the other country, is a*nw an * (14) B= L*- + L L*n + n* n+an* UcL* *L+L*- L+aL*] B(w) FIGURE I Since a and a* are both functions of p/p* =o, the condition B=O can be used to determine the relative wage. The function B(o) is illustrated in Figure 1. The relative wage c is that relative wage at which the expression in brackets in (4) is zero, and at which trade is therefore balanced. Since a is an increasing function of w and a* a de- creasing function of c, B(w) will be nega- tive (positive) if and only if w is greater (less) than co, which shows that X3 is the unique equilibrium relative wage. We can use this result to establish a sim- ple proposition: that the larger country, other things equal, will have the higher wage. To see this, suppose that we were to compute B(w) for co= 1. In that case we have a=a* < 1. The expression for the balance of pay- ments reduces to (14') B=LL*[ UL+L- L+GL*] But (14') will be positive if L > L*, negative if L L*, less than one if L < L*. This is an interesting result. In a world characterized by economies of scale, one This content downloaded on Fri, 11 Jan 2013 09:04:30 AM All use subject to JSTOR Terms and Conditions VOL. 70 NO. 5 KRUGMAN: PA TTERN OF TRADE 955 would expect workers to be better off in larger economies, because of the larger size of the local market. In this model, however, there is a secondary benefit in the form of better terms of trade with workers in the rest of the world. This does, on reflection, make intuitive sense. If production costs were the same in both countries, it would always be more profitable to produce near the larger market, thus minimizing transportation costs. To keep labor