Download External Economies and International Trade: A Reexamination and more Study notes Literature in PDF only on Docsity!
EXTERNAL ECONOMIES AND INTERNATIONAL TRADE
REDUX∗
GENE M. GROSSMAN AND ESTEBAN ROSSI -HANSBERG
We study a world with national external economies of scale at the industry level. In contrast to the standard treatment with perfect competition and two industries, we assume Bertrand competition in a continuum of industries. With Bertrand competition, each firm can internalize the externalities from production by setting a price below those set by others. This out-of-equilibrium threat elimi- nates many of the “pathologies” of the standard treatment. There typically exists a unique equilibrium with trade guided by “natural” comparative advantage. And, when a country has CES preferences and any finite elasticity of substitution be- tween goods, gains from trade are ensured.
I. I NTRODUCTION
External economies hold a central—albeit somewhat uncomfortable—place in the theory of international trade. Since Marshall (1890, 1930 [1879]) at least, economists have known that increasing returns can be an independent cause of trade and that the advantages that derive from large-scale production need not be confined within the boundaries of a firm. Marshallian exter- nalities arise when knowledge and other public inputs associated with a firm’s output spill over to the benefit of other industry par- ticipants. After Marshall’s initial explication of the idea, a lengthy debate ensued on whether an industry with external economies of scale could logically be modeled as perfectly competitive.^1 Even af- ter the matter was finally resolved in the affirmative by Chipman (1970), trade economists continued to bemoan the “bewildering variety of equilibria [that provide] a taxonomy rather than a clear set of insights” (Krugman, 1995, p. 1251), the apparent tension between the forces of external economies and other, better- accepted determinants of the trade pattern, and the “paradoxical” implication that trade motivated by the gains from concentrating production need not benefit the participating countries.
∗We thank Robert Barro, Arnaud Costinot, Angus Deaton, Elhanan Helpman, Giovanni Maggi, Marc Melitz, Peter Neary, and four anonymous referees for help- ful comments and discussions and the National Science Foundation (under Grant SES 0451712) and the Sloan Foundation for research support. Any opinions, find- ings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation or any other organization.
- For a recount of the debate and its protoganists, see Chipman (1965).
©C (^) 2010 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. The Quarterly Journal of Economics , May 2010
829
830 QUARTERLY JOURNAL OF ECONOMICS
The modeling of external economies began at a time when game-theoretic approaches to imperfect competition were much less developed than they are today. Consequently, the logical con- sistency between external economies and perfect competition was seen as a great advantage in allowing the application of familiar tools of general equilibrium analysis. Economists were comfort- able in assuming that competitors take prices as given in indus- tries with many small firms. By assuming that small producers contribute little to aggregate industry output, they felt similarly justified in assuming that firms treat industry scale as given when assessing productivity and making decisions about their own output. Firms might recognize the link between industry scale and productivity and nonetheless perceive their own costs to be constant. As Chipman (1970, p. 349) noted, “there is no logical contradiction involved in the notion that economic agents do not perceive things as they actually are, and while the idea of treating production functions parametrically may be more subtle and unusual than that of treating market prices in this way, both ideas are of the same logical order.” In application, the competitive models of external economies and trade yielded some discomforting results.^2 A potential for multiple equilibria, noted already by Ohlin (1933, p. 55), was shown more formally by Matthews (1949–1950), Kemp (1964), and Ethier (1982a). Graham (1923) argued that scale economies could reverse the trade pattern predicted by “natural” comparative ad- vantage and Ethier (1982a) proved him correct in a competitive model with external economies. Markusen and Melvin (1981) and Ethier (1982a) observed that country size might play an inde- pendent role in determining the pattern of specialization. Finally, Graham (1923) advanced the possibility of losses from trade, an idea that has been further addressed by Matthews (1949–1950), Melvin (1969), Markusen and Melvin (1981), Ethier (1982a), and others. These “pathologies” are perhaps responsible for the di- minished role that external economies now play in thinking about trade, even as such externalities are still considered to be empiri- cally relevant in many contexts.^3
- There are several good surveys of this literature, beginning with Chipman’s (1965) treatment of the earliest contributions. Subsequent overviews include Help- man (1984), Helpman and Krugman (1985, Ch. 3), Krugman (1995), and Choi and Yu (2002).
- See, for example, Caballero and Lyons (1989, 1990, 1992), Chan, Chen, and Cheung (1995), Segoura (1998), Henriksen, Steen, and Ulltveit-Moe (2001), and Antweiler and Trefler (2002).
832 QUARTERLY JOURNAL OF ECONOMICS
In the canonical model, country size can be an independent source of comparative advantage. Suppose, for example, that pro- ductivity in the IRS sector is modest when output is small, but not equal to zero. If a small country were to specialize in produc- ing this good, the equilibrium price might be high in light of its meager resource base and a robust level of world demand. Such a high price might invite entry by producers in the large country. In such circumstances, there might be no equilibrium with pro- duction of the IRS concentrated in the small country. The large country would gain a comparative advantage in the IRS industry by dint of having sufficient resources to produce at a large scale. The canonical model readily yields examples with losses from trade (see, e.g., Helpman and Krugman [1985, p. 55]). The autarky equilibrium features underproduction of the IRS good, because firms fail to take into account the spillover benefit from increasing their output on the productivity of others. As is well known, trade can bring harm if it exacerbates a preexisting market distortion (Bhagwati 1971). It stands to reason that trade may reduce wel- fare in a country that shifts substantial resources from the single industry with increasing returns to one with constant returns. In short, the pathologies that emerge from the canonical model rest on two critical assumptions. First, firms contemplate entry only at such small scale that they believe they can have negligible impact on national output and their own productivity. Second, industries are large in relation to countries’ resource en- dowments, so that a small country may lack sufficient resources to meet world demand for the IRS good at a reasonable price. In such circumstances, the demise of activity in the IRS industry due to the opening of trade can spell dire consequences for a country’s productivity and welfare. In this paper, we modify these two familiar assumptions and show how this dramatically narrows the scope for patholog- ical outcomes. We assume in what follows that firms engage in Bertrand competition and that they correctly anticipate their pro- ductivity when they quote a price that would yield nonnegligible sales. And we assume that the world economy comprises a large number of (small) industries, so that any industry can be fully accommodated in any country, no matter what its size. 5
- In our analysis the scope of the external effects is supposed to be the indus- try. So it is essential for us to assume that industries are small relative to country sizes. As advocated by Ethier (1982b), one could also think of externalities that
EXTERNAL ECONOMIES AND INTERNATIONAL TRADE REDUX 833
It is well known that perfect competition and Bertrand com- petition predict similar outcomes in models with homogeneous goods and constant costs. This is true as well—it turns out—in an autarky equilibrium with external economies of scale. However, the predictions of the alternative behavioral assumptions diverge in a world with national external economies and international trade. With Bertrand competition, a firm may be small when its price is the same as that of its (domestic) rivals—as will be the case in the equilibria that we discuss—yet it may recognize that by announcing a price below that offered by other firms in the industry, it can grow to nonnegligible scale. We shall see that the different out-of-equilibrium beliefs under perfect and Bertrand competition yield very different conclusions about the possibility of multiple equilibria and the determinants of the trade pattern. Moreover, the potential role for country size to influence the trade pattern disappears when industries are small in relation to the size of national economies. In a world with many industries, a la Dornbusch, Fischer, and Samuelson (1977; hereafter DFS), a` small country can realize its comparative advantage in whichever sectors it is strongest by serving world demands in a relatively small range of industries. We will find that country size plays no role in determining a chain of comparative advantage, although it does affect the dividing line between imports and exports along that chain. The assumption of a large number of small industries also helps to justify our assumption that firms take factor prices as given. A Bertrand competitor may entertain the prospect of growing large in its industry. But, even if it does so, it will remain small in relation to the aggregate economy so long as each industry uses a small fraction of the economy’s resources. In summary, we study a model with a continuum of industries and national industry-level external economies. We assume that firms in an industry produce a homogeneous product and engage in Bertrand (price) competition in an integrated world market. Countries may exhibit Ricardian technological differences, but they share the same prospects for scale economies, which are as- sumed to be a property of the good being produced. We find in this setting that the trade equilibrium typically is unique and that “natural” comparative advantage determines an ordering of
transcend both industry and country boundaries. However, external economies at the industry level are plausible in the presence of industry-specific knowledge and other nonrival inputs, and the literature cited in footnote 3 points to their empirical significance.
EXTERNAL ECONOMIES AND INTERNATIONAL TRADE REDUX 835
and a continuum of industries. There, we derive our predictions about the pattern of trade. Section III contains a brief review of the efficiency properties of the model, which sets the stage for the gains-from-trade analysis in the subsequent section. In Section V, we introduce trading costs, first assuming that they are small in relation to the strength of scale economies, and then allowing larger costs. Section VI concludes.
II. A M ODEL OF EXTERNAL ECONOMIES IN A CONTINUUM
OF I NDUSTRIES
We study an economy with a continuum of industries, as in DFS. Goods are indexed by i ∈ [0, 1]. For the time being, we as- sume only that preferences in each country are such that a change in the prices of a measure-zero set of goods has a negligible ef- fect on the demand for all goods other than the ones in this set. Demands need not be identical in the two countries, nor need preferences be homothetic. Goods are produced by a single primary factor, labor. Labor supplies are L and L ∗^ in the home and foreign countries, respectively. Throughout the paper, we take the home wage as nu- meraire. Technology exhibits constant or increasing returns due to external economies at the local industry level. In the home coun- try, ai / Ai ( xi ) units of labor are required for a unit of output, where xi is aggregate home production of good i and Ai (·) is nondecreas- ing, concave, and everywhere has an elasticity smaller than one. 7 In the foreign country, the unit labor requirement is a ∗ i / Ai ( x ∗ i ). There are ni potential producers of good i in the home country and n ∗ i potential producers in the foreign country, where ni ≥ 2 and n ∗ i ≥ 2. The number of potential producers in each country can be very large, but is assumed to be finite. Firms in each in- dustry engage in price (Bertrand) competition in the integrated world market. Each firm recognizes that, if it sets a price above that quoted by any other firm, it will consummate no sales; if it sets a price that is the lowest among all quoted prices, it will capture the entirety of world demand; and if it sets a price that is tied for lowest among a group of competitors, it will share demand with these rivals.
- As in the literature, an elasticity of productivity with respect to output smaller than one is needed to ensure a nonnegative marginal productivity of labor.
836 QUARTERLY JOURNAL OF ECONOMICS
0
p i D C
D
C
E
x i
p i
x i
~
~
F IGURE I Unique Intersection of DD and CC
II.A. Autarky Equilibrium
Figure I shows the inverse demand curve for good i , labeled DD , for a given level of aggregate spending and a given level of any price aggregate that may affect the demand for this good. Firms in the industry take aggregate spending and the relevant price index (if any) as given.^8 The figure also depicts the average cost curve, which is labeled CC. Intersection points are our candidates for industry equilibrium. Suppose firms in industry i announce a price above ˜ pi in Fig- ure I. Then a deviant firm could announce a price a bit lower than that offered by the others. The firm would capture all industry sales, and because its price would exceed its average cost at the resulting scale of production, it would earn a profit. Evidently, the price will be bid down at least to p ˜ i. But a further price cut by any firm would spell losses, because the deviant would capture the market but fail to cover its costs. When the DD curve is ev- erywhere steeper than the CC curve, as in Figure I, the unique intersection point depicts the industry equilibrium. In this equi- librium, price equals industry average cost and an arbitrary (and possibly large) number of firms make sales but earn zero profits. In Figure II, the DD and CC curves have multiple intersec- tions at E ′, E ′′, and E. Neither E ′^ nor E ′′^ represents an equilib- rium, because if all firms charge the price associated with either
- They are justified in doing so, because each industry is small in relation to the aggregate economy. See Neary (2003, 2008), who studies Cournot oligopoly in general equilibrium and similarly uses the existence of many small industries to justify the assumption that when firms compete with rivals in their own sector, they neglect the actions of firms in other industries.
838 QUARTERLY JOURNAL OF ECONOMICS
output xi is equivalent to
σ θ i ( xi ) < 1,
where θ i ≡ A ′ i ( xi ) xi / A ( xi ) is the elasticity of the productivity func- tion with respect to output. A sufficient condition for existence of an industry equilibrium with finite xi is σ θ i ( x ) < 1 for all x. 10 We will assume that an equilibrium with finite output exists in every industry, either because these sufficient conditions are satisfied, or for any other reason. In the autarky equilibrium (denoted again by tildes), aggre- gate spending E ˜ equals aggregate income L. Then product-market equilibrium requires
(2) x ˜ i =
b σ i p ˜− i σ L P^ ˜^1 −σ^
for all i ,
whereas price equal to average cost implies
(3) p ˜ i =
ai Ai ( ˜ xi )
for all i.
This gives a system of equations that jointly determine outputs and prices in all industries. We note in passing that the autarky equilibrium with Bertrand competition is the same as would arise under perfect competition, were firms to take their own productivity as given. Price in every industry is equal to average cost. Firms earn zero profits. Demand equals supply for all goods. And the labor market clears.
II.B. Trade Equilibrium
We now open the economy to international trade. Again, com- petition between the potential producers in a country drives price for every good i down to average cost. But now it also must be the case that a potential producer in the “other” country does not wish to shave price further. If home producers in industry i quote the price w ai / A ( xi ), a foreign firm could announce a price a bit lower than that, capture sales of xi , and achieve labor productivity of
- Ethier (1982a, p. 1247) invokes essentially the same assumption as a con- dition for stability of equilibrium in his two-industry model. Here, the assumption ensures uniqueness of equilibrium, without need to invoke an ad hoc stability analysis.
EXTERNAL ECONOMIES AND INTERNATIONAL TRADE REDUX 839
0
w * B
B I
A
A
1 F IGURE III Free Trade Equilibrium
a ∗ i / Ai ( xi ). Such a strategy would be profitable if its per-unit cost, w∗ a i ∗ / Ai ( xi ), were less than the quoted price. Therefore, concen- tration of industry i in the home country requires
ai Ai ( xi )
w∗ a ∗ i Ai ( xi )
(Note that w = 1, because the home wage is the numeraire.) Simi- larly, if production of good i is concentrated in the foreign country, it must be that
ai Ai ( x ∗ i )
w∗ a ∗ i Ai ( x ∗ i )
Assuming that each good is produced in only one location (which will be true in equilibrium), the equilibrium price of a good equals the lesser of the two average costs evaluated at the equilibrium scale of world production; that is,
(4) pi = min
[
ai Ai ( ¯ xi )
w∗ a i ∗ Ai ( ¯ xi )
]
for all i ,
where ¯ xi is world output of good i in the trade equilibrium. Now order the goods so that α i ≡ ai / a ∗ i is increasing in i and define I by α I = w∗. Then (4) implies that goods with i ≤ I are produced in the home country and goods with i > I are produced in the foreign country. 11 Figure III—familiar from DFS—depicts
- For notational convenience, we adopt the convention that the marginal good is produced in the home country, although this is neither determined by the model nor consequential.
EXTERNAL ECONOMIES AND INTERNATIONAL TRADE REDUX 841
enough of any good to meet the pressures of world demand. The relative size of the two countries affects the margin I between the sets of each country’s import and export goods, but it cannot affect the ordering of goods in those sets. In short, by incorporating many industries and amending firms’ perceptions about their own productivity, we have over- turned several conclusions from the canonical analysis. Multiple equilibria are not pervasive and “natural” comparative advantage rules. A pedagogically interesting special case arises when the coun- tries share identical technologies and differ only in labor supplies. This setting has been used by some authors to argue that trade induced by external economies will not equalize factor prices in a pair of countries that differ only in size.^12 However, this conclusion also rests on the assumption that individual industries are large in relation to the sizes of the national economies. In our model, when ai = a ∗ i for all i , if w∗^ = 1, all industries will locate in the low- wage country. This is not consistent, of course, with labor-market clearing in the other country, so factor prices must be equalized. With equal factor prices and identical technologies, the pattern of specialization is not determined. What is determined is only the aggregate employment levels in the two countries which, in equi- librium, match the exogenous labor supplies. A small country can employ its labor force in equilibrium by producing and exporting a moderate number of goods produced in relatively small quanti- ties or a smaller number of goods that require greater numbers of workers to meet world demand. In any case, differences in country size are accommodated by the number of goods produced in each country and not by the identities of which goods are produced where.
III. EFFICIENCY AND THE FIRST-BEST
Both in autarky and in a trade equilibrium, efficiency re- quires equality between the marginal rate of substitution and the marginal rate of transformation for every pair of goods. In our setting, utility-maximizing consumers equate as usual the marginal rate of substitution between goods to the relative price. But, in general, the marginal rate of transformation is not equal to the relative price due to the presence of production externalities.
- See, for example, Markusen and Melvin (1981) and Ethier (1982a).
842 QUARTERLY JOURNAL OF ECONOMICS
Therefore, neither the autarky equilibrium nor the free-trade equilibrium achieves an efficient allocation of labor. To see this, note that the marginal product of labor in industry i in the autarky equilibrium is Ai ( ˜ xi )/
[
ai (1 − θ i )
]
. 13 It follows that the autarky marginal rate of transformation between good i and good j is
MRT^ ˜ i j =
[
1 − θ i ( ˜ xi ) 1 − θ (^) j ( ˜ x (^) j )
]
ai / Ai ( ˜ xi ) a (^) j / A (^) j ( ˜ x (^) j )
[
1 − θ i ( ˜ xi ) 1 − θ (^) j ( ˜ x (^) j )
]
p ˜ i p ˜ (^) j
where the second equality follows from (3), that is, from price equal to average cost. Therefore, the autarky relative outputs of goods i and j can be efficient only if it happens that θ i ( ˜ xi ) = θ (^) j ( ˜ x (^) j ). Similarly, the free-trade relative outputs can be efficient only if θ i ( xi ) = θ (^) j ( x (^) j ). With relative prices equal to relative average costs, they will not generally be equal to relative marginal costs. A set of Pigouvian subsidies could be used to achieve the autarky first- best. A similar set of subsidies, together with a set of optimum tariffs, could do likewise for a country that trades. It should be clear from the discussion that the autarky equi- librium achieves the first-best in the special case in which all in- dustries bear a constant and common degree of scale economies.^14 If θ i ( x ) ≡ θ for all x and i , the equality between price and average cost in every industry ensures equality between relative prices and marginal rates of transformation. With trade, the first-best still requires a set of optimal tariffs to improve the terms of trade. But gains from (free) trade can be established for this special case in the usual way. 15
- Let Li be employment in industry i. Then xi = Ai ( xi ) Li / ai , so dxi = ( Ai / ai ) dLi +^
( A ′ i / ai ) dxi or
dxi dLi^ =^
Ai ai
( 1 1 − θ i
) .
- See Chipman (1970) for an early formal demonstration of this point.
- For the case of constant and common elasticities θ, the free-trade out- put vector maximizes the value of domestic output given prices. We can prove gains from trade using the standard revealed-preference argument: The value of the free-trade consumption vector at the prices of the trade equilibrium equals the value of the free-trade output vector at those prices, which exceeds the value of autarky output vector at those prices, which in turn equals the value of the autarky consumption vector at those prices. So consumers could buy the autarky consumption bundle in the trade equilibrium with the income available to them. If they chose not to do so, it must be that they prefer the trade consumption bundle. This argument assumes, of course, that aggregate demand can be represented as the outcome of maximizing a well-behaved utility function, which will be true, for example, with homothetic preferences.
844 QUARTERLY JOURNAL OF ECONOMICS
In a world with trade, producers of good i face the world demand
b σ i p − i σ L P^1 −σ^
p , w∗^ L ∗
where c ∗ i ( p , w∗^ L ∗) > 0 is the foreign demand for good i in the trade equilibrium (an arbitrary function of the vector of prices p and foreign income, w∗^ L ∗). The hypothesis that P > P ˜ implies that P^1 −σ^ < P ˜^1 −σ^ under the assumption that demand is elastic (σ ≥ 1). The intuition is that the substitution effect of the higher price level outweighs the income effect on the demand for good i , so the inverse demand curve with trade— DD in the figure—lies to the right of D ˜ D ˜ under the maintained hypothesis. The average cost curve with trade is depicted by CC and is given by
min
[
ai A ( ¯ xi )
w∗ a i ∗ A ( ¯ xi )
]
where x ¯ i again is the total world output of good i. This curve coincides with C ˜ C ˜ for i ≤ I ; that is, for goods that are produced by the home country in the trade equilibrium. It lies below C ˜ C ˜ (as depicted in Figure IV) for goods that are produced abroad ( i > I ); these goods are imported by the home country only because their average cost is less than it would be with domestic production. In either case, the intersection of DD and CC lies below and to the right of E ˜. As the figure makes clear, our hypothesis that P > P ˜ implies pi < p ˜ i for an arbitrary good i , be it one that is exported in equi- librium or one that is imported. Therefore, all prices are lower in the trade equilibrium than in the autarky equilibrium (relative to the domestic wage). But this is a contradiction, because the price index cannot rise if each element in the index falls. We conclude that P < P ˜ and thus U > U ˜ ; that is, the home country gains from trade! Because P < P ˜ and σ ≥ 1, the inverse demand curve DD may, in fact, be to the left or to the right of D ˜ D ˜. Apparently, aggregate output in some industries might fall as the result of the open- ing of trade. Nonetheless, the impact of these cases cannot be so great as to negate the overall gains that come from interna- tional specialization according to comparative advantage and the realization of greater scale economies due to the expansion of the market.
EXTERNAL ECONOMIES AND INTERNATIONAL TRADE REDUX 845
IV.B. Inelastic Demands
Next consider the case of σ < 1, that is, inelastic demands. Because there are gains from trade as σ approaches one from above,^16 and the model is continuous in the parameter σ , trade losses for some σ would imply the existence of a σˆ such that P ( ˆσ ) = P ˜( ˆσ ), in the obvious notation. Let us suppose this to be true, and consider further the autarky and trade equilibria that would arise when σ = σˆ. The demand function with trade and the price–equals– average cost relationship (4) imply
x ¯ i Ai ( ¯ xi )
b σ i ˆ p^1 i −^ σˆ L P^1 −^ σˆ^ min[ ai , a ∗ i w∗]
c ∗ i ( p , w∗^ L ∗) Ai ( ¯ xi )
b σ i ˆ p i^1 −^ σˆ L P^1 −^ σˆ^ ai
where the inequality in the second line follows from the fact that ai ≥ min[ ai , a ∗ i w∗] and c ∗ i ( p , w∗^ L ∗) > 0. Now suppose that pi > p ˜ i. Then, with ˆσ < 1 and P = P ˜,
b σ i ˆ p^1 i −^ σˆ L P^1 −^ σˆ^ ai
b σ i ˆ p ˜^1 i −^ σˆ L P^ ˜^1 −^ σˆ^ ai^ =^
x ˜ i Ai ( ˜ xi )
Therefore x ¯ i / Ai ( ¯ xi ) > x ˜ i / Ai ( ˜ xi ). But the function xi / Ai ( xi ) is in- creasing in xi by the assumption that θ i ( xi ) < 1. So the string of inequalities implies ¯ xi > x ˜ i , which in turn implies that pi < p ˜ i. This contradicts our supposition that pi > p ˜ i. We conclude that pi < p ˜ i for all i , which in turn implies that P < P ˜. It follows that there can exist no ˆσ for which the price index under autarky is the same as the price index with trade. Again, the home country gains from trade! Figure V illustrates the autarky and free-trade equilibrium in a typical industry i when σ < 1. With P < P ˜ and σ < 1, the DD curve necessarily lies to the right of the D ˜ D ˜ curve. The CC curve is identical to C ˜ C ˜ for i ≤ I and strictly below it for i > I. It follows that ¯ xi > x ˜ i for all i. In this case, trade expands the world
- The limiting case of the CES as σ → 1 is equivalent to Cobb–Douglas preferences. Gains from trade for these preferences can be established directly. With a constant spending share bi on good i in the home country
x ¯ i A ( ¯ xi ) = bi^ L min[ ai , w∗ a i ∗ ]
c ∗ i ( p , w∗^ L ∗) A ( ¯ xi )
bi^ L ai = ˜ xi A ( ˜ xi ) .
But this implies ¯ xi > x ˜ i for all i and therefore pi < p ˜ i for all i. The home worker’s real income increases in terms of every good.
EXTERNAL ECONOMIES AND INTERNATIONAL TRADE REDUX 847
produced everywhere and not traded at all. For every good, trade can flow in only one direction. Before proceeding, we need to specify the market structure that we will consider. Models with oligopolistic competition and trade are distinguished by whether markets are deemed to be seg- mented , so that firms can announce arbitrarily different prices in different geographic locations, or integrated , so that price differ- ences cannot exceed the cost of shipping between the two mar- kets. 17 In our setting, the two market structures yield identical outcomes in the absence of transport costs, so we did not need to address this issue before now. However, equilibria for segmented and integrated markets differ in the presence of trading costs. We will pursue here the slightly simpler case of segmented markets, although the interested reader can readily apply our methods to verify that outcomes with integrated markets are qualitatively similar. We assume from now on that ti > 1 units of good i must be shipped from any location in order to deliver one unit of the good to the other country. We also assume that scale economies are strictly positive (i.e., A i ′ (·) > 0 for all i ). We consider first the case in which ti is small for all i , in a sense that will become clear. We then turn to larger trading costs.
V.A. Low Transport Costs
The addition of transport costs introduces the possibility that it will be attractive for a firm or firms to produce only for the local market. Such firms would enjoy an advantage relative to foreign producers inasmuch as they could serve the market without incur- ring the shipping costs. However, they would face a disadvantage relative to firms that serve both markets from their smaller scale of production. The case of “low” transport costs arises when, for every good, the former potential advantage from local production is outweighed by the latter cost. Let us ignore for a moment the possibility that a firm may tar- get a single market. If all firms contemplate selling both locally and abroad, competition among producers in a given location will bid the pair of prices down to the firms’ cost of serving the respec- tive markets. If home firms succeed in capturing both markets, these costs are w ai / Ai ( xi + x ∗ i ) and w ai ti / Ai ( xi + x ∗ i ) for the home
- See, for example, Venables (1994), who compares outcomes for a Bertrand duopoly with constant production costs and ad valorem trading costs under the alternatives of segmented and integrated markets.
848 QUARTERLY JOURNAL OF ECONOMICS
and foreign markets, respectively. 18 Thus, no deviant firm in the foreign country can profit by shaving these prices and capturing both markets if [ w ai Ai
xi + x ∗ i
w∗ a i ∗ ti Ai
xi + x i ∗
]
xi
[
w ai ti Ai
xi + x i ∗
w∗ a i ∗ Ai
xi + x i ∗
]
x i ∗ ≤ 0
or if
(5)
ai a i ∗
w∗ w
ti xi + x i ∗ xi + ti x i ∗
If, on the other hand, the inequality in (5) runs in the opposite direction, then foreign firms can sell at their costs of serving the home and foreign markets, w∗ a i ∗ ti / Ai
xi + x i ∗
and w∗ a ∗ i Ai
xi + x i ∗
respectively, and no deviant home firm can profit by undercutting this pair of prices. Suppose now that (5) is satisfied and consider a foreign de- viant that seeks to undermine production in the home country by capturing only its local market. It could do so by announcing a pair of prices such that its local price were a bit below w ai ti / Ai
xi + x i ∗
and its price for exporting to home consumers were prohibitively high. This deviation is unprofitable if and only if [ w ai ti Ai
xi + x ∗ i
w∗ a ∗ i Ai
x ∗ i
]
x i ∗ ≤ 0
or
ai a ∗ i
w∗ w
Ai
xi + x ∗ i
Ai
x i ∗
ti
Analogously, if (5) is violated, then a deviate home firm will not be able to profit by undercutting foreign producers in (only) the home market if and only if [ w∗ a ∗ i ti Ai
xi + x i ∗
w ai Ai ( xi )
]
xi ≤ 0
- Although we continue to take the home wage as numeraire, we will re- tain w in the expressions in this section, because it improves the clarity of the arguments.
