STOLPER-SAMUELSON REVISITED: TRADE AND DISTRIBUTION WITH OLIGOPOLISTIC PROFITS

Transcription

1 STOLPER-SAMUELSON REVISITED: TRADE AND DISTRIBUTION WITH OLIGOPOLISTIC PROFITS Robert A. Blecker American University, Washington, DC (October 0; revised February 0) ABSTRACT This aer investigates the distributional imact of international trade when goods markets are oligoolistic and firms artially ass-through changes in tariffs into rices and factor costs for differentiated roducts. Trade liberalization raises mark-us and rofit shares in the exort industry and lowers them in the imort-cometing industry, while Stoler-Samuelson effects on real rices of rimary factors are attenuated or ossibly reversed. An extended model shows how offshoring (trade in intermediate goods) can otentially increase mark-us for oligoolistic roducers of final goods. The analysis illuminates why business interests generally suort trade liberalization olicies today, regardless of their countries factor abundance. Professor and Chair, Deartment of Economics, American University, Washington, DC 006 USA, The author would like to thank Bruce Elmslie, Bob Feinberg, Alan Isaac, Mehrene Larudee, Will Milberg, Arlsan Razmi, Gil Skillman, Lance Taylor, and two anonymous referees, along with articiants in the Annual Political Economy Worksho (Queen Mary University of London, 007), the Bernard Schwartz Center for Economic Policy Analysis (The New School, 008), and the Eastern Economics Association meetings (New York, 009), for helful comments and suggestions on earlier drafts. The usual caveats aly. JEL Classifications: F, F, D33, D43, E

2 . INTRODUCTION It is now more than three decades since the old theories of international trade based on the assumtion of erfect cometition began to be sulemented by new theories that analyzed trade under conditions of imerfect cometition (Krugman, 979; Grossman, 990). Yet, with some excetions, the analysis of the distributional imact of trade has continued to be based largely on models that assume erfect cometition in goods markets as well as factor markets. In articular, the theorem of Stoler and Samuelson (94) remains the core modeling framework for analyzing the distributional effects of trade. In the original version of this theorem, free trade raises the real rice of a country s abundant factor of roduction and lowers the real rice of its scarce factor. Many alternative analyses, such as Feenstra and Hanson s (996) model of trade and distribution with intermediate inuts roduced by varying roortions of skilled and unskilled labor, still assume erfect cometition in both goods and factor markets. Nevertheless, the literature on trade in oligoolistic markets has reached some fairly robust conclusions that have strong imlications for how changes in trade olicy (e.g., tariff reductions) affect the rofits of oligoolistic firms. A large literature, surveyed in more detail in the next section, has found that oligoolistic firms may only artially ass-through changes in tariffs or exchange rates into rices of tradable goods; when this occurs, firms also adjust rofit mark-us (or rice-cost margins) as art of a ricing-to-market strategy. Yet, to date there have been remarkably few efforts to re-integrate the lessons from the literature on artial ass-through and flexible mark-us with the core models of international trade and income distribution. One notable excetion is Helman and Krugman (985), who derived the conditions for factor rice equalization to hold in a three-good model where one sector is oligoolistic, and also demonstrated that Stoler-Samuelson redictions about winners and losers from trade can be reversed in the resence of scale economies. However, they did not consider changes in oligoolistic mark-us as an exlanation of the effects of trade on rofits as we do here.

3 In the ast two decades, most of the emirical literature on trade and income distribution has focused on the effects of trade on the relative wages of so-called skilled and unskilled labor. In many of these studies, the overall distributional effects of trade, including the imact on caital, are either not emhasized or ignored altogether. The lack of attention to the imact of trade on the distribution of income between caital and labor is even more striking when one considers the olitical economy of contemorary trade olicy, in which large cororate interests are usually the chief romoters of trade liberalization and economic integration, regardless of the abundance or scarcity of caital in a country. For examle, Pastor (0,. 97) observes that Businesses multinational cororations (MNCs), banks, and small and medium-sized firms have been the main agents for economic integration in all three North American countries, yet only one of them (the US) can be considered caital-abundant while (on a regional basis) Mexico is relatively labor-abundant and Canada is natural resource-abundant. Recently, some attention has been focused on whether globalization or offshoring is leading to a rise in the rofit share of national income (e.g., Onaran, 009; Milberg and Winkler, 00), but so far this work is mainly emirical and the results have not been re-integrated into trade theory. This aer contributes to that theoretical reintegration by drawing uon theories of oligoolistic mark-u ricing to model the rofits of business firms, while continuing to treat the returns to rimary factors of roduction in the traditional Stoler-Samuelson (S-S) manner. In models that assume erfect cometition, the returns to caital are identified with the scarcity rents on fixed (and fully utilized) sulies of caital equiment, while firms are assumed to receive zero economic rofits. However, following the aroach ioneered by Kalecki (954 [968]), in the resence of oligooly with excess caacity, firms receive rofits based on the Excetions include Thomson (997), Leamer (998), and Feenstra and Hanson (996), who included caital in three-factor models (along with skilled and unskilled labor). However, all of these assumed erfectly cometitive goods markets; none incororated artial ass-through of tariff changes or adjustments in mark-us.

4 3 rents due to their market ower rather than the scarcity of their caital. In this context, if a change in trade olicy alters the economic rofits of oligoolistic firms, its imact on the returns to the rimary factors of roduction (such as labor or natural resources) will be different from the redictions of standard S-S models that assume zero rofits. The basic S-S insight that trade affects the rices of rimary factors of roduction by changing the rices of goods that utilize these factors in different roortions remains a key foundation for any analysis of the distributional imact of trade, and should not be discarded. Nevertheless, the S-S theorem has to be modified when the assumtion of erfect cometition in roduct markets is relaced by oligoolistic cometition with artial ass-through of tariff changes. We will show that S-S magnification effects on factor rices are attenuated by adjustments of rofit mark-us in industries with artial ass-through of tariff changes, and therefore some of the standard redictions about which factors exerience absolute gains or losses need to be modified. 3 We also obtain new results for the effects of trade on the rofits of firms, which more resemble the redictions of a secific factors model alied to caital that is immobile in each sector (Jones, 97; Neary, 978), rather than a Heckscher-Ohlin (H-O) model with mobile factors. Finally, we will briefly suggest an extension of our modeling framework to address the distributional imact of the offshoring of intermediate inuts. The rest of this aer is organized as follows. Section reviews the relevant literature and discusses the concetual framework. Section 3 resents a modified H-O model of trade with oligoolistic rofits and mark-u ricing. Section 4 alies the model to the distributional effects of changes in foreign rices and tariff rates. Section 5 extends the model to offshoring. Section 6 concludes by discussing the imlications of the model for the olitical economy of trade olicy, 3 This result was artly anticiated by Melvin and Warne (973), who briefly noted that S-S does not hold in the case of ure monooly. However, they did not analyze artial ass-through behavior in oligoolistic industries.

5 4 the limitations of the resent analysis, and directions for future research.. LITERATURE SURVEY AND CONCEPTUAL FRAMEWORK A large literature on theoretical models of international trade with oligoolistic markets arose in the 980s. Some of the most rominent branches of this literature focused on the economic logic of recirocal duming (Brander and Krugman, 983) and the otential for net welfare gains from strategic trade olicies (Brander and Sencer, 984a). Another branch of this literature (Brander and Sencer, 984b; Feenstra, 989) analyzed the artial ass-through of changes in either tariffs or exchange rates into rices of traded goods, a henomenon which occurs when goods rices adjust by less than 00 ercent of the tariff or exchange rate change in the destination country s currency. Tyical results in this literature show that, for examle, if a home country increases its tariff (or if the home currency dereciates), a rofit-maximizing foreign oligoolist will reduce the own-currency rice of its exorts, thereby imlying artial assthrough of the tariff (or exchange rate) change into the rice of home country imorts. Similarly, a tariff reduction (or currency areciation) could induce domestic imorting-cometing firms to reduce mark-us and rices in order to maintain market share in the face of falling imort rices. Brander and Sencer (984b) demonstrated these tyes of results assuming Cournot oligooly, while Feenstra (989) found qualitatively similar results assuming Bertrand oligooly. Thus, contrary to what Eaton and Grossman (986) showed for the gains from strategic trade olicies, the existence of artial ass-through behavior is not sensitive to these alternative assumtions about market structure. Arestis and Milberg (993-94) showed that artial assthrough of exchange rate changes also results in Kalecki s (954 [968]) model of mark-u

6 5 ricing and Eichner s (976) theory of oligoolistic rice leadershi. Heintz (006) models how oligoolistic firms can cature some of the gains from lower rices of imorted manufactured goods, thereby only artially assing through the welfare gains to consumers. Much of the early emirical literature testing these models was motivated by the limited resonses of traded goods rices to the large exchange rate swings of the 980s. Woo (984), Mann (986), and Dornbusch (987) analyzed why US imort rices did not change by the full amounts that would have been exected from the shar areciation and subsequent dereciation of the dollar in the 980s. Ohno (989), Marston (990), and Parsley (993) found emirical evidence for artial ass-through of yen areciation into Jaanese exort rices. Feinberg (986, 989) estimated the ass-through of changes in exchange rates and imort rices into domestic rices, which he found was more likely to be artial (as one would exect) in industries that were more concentrated and roduced more differentiated roducts. Most of these emirical findings have ertained to exchange rate ass-through (see Goldberg and Knetter, 996, for a survey). However, Feenstra (989) demonstrated that changes in tariffs and exchange rates have symmetrical effects on imort rices in a theoretical model of an oligoolistic foreign exort industry, and confirmed this symmetry emirically for US imorts of motor vehicles from Jaan. Later, Castañeda Sabido and Mulato (006) found that tariff reductions squeezed rofit margins in Mexican industries after Mexico liberalized its trade in the late 980s. Mallick and Marques (008) comared exchange rate and tariff ass-through for India, and found that exchange rate changes are more commonly (and more fully) assed through into imort rices than tariff changes, while firms exorting to India more frequently adot strategies to maintain their market share against tariffs than against exchange rate changes (. 765). Nicita (009) incororated emirical estimates of artial tariff ass-through into a broader

7 6 analysis of the imact of trade liberalization on household welfare and income distribution in Mexico. Although the focus in most of this literature has been on the degree of ass-through into rices, the same models also imly that rofit mark-us (or rice-cost margins) are likely to vary in systematic and redictable ways in resonse to either tariff or exchange rate changes in industries that exhibit artial ass-through behavior. For examle, if either foreign countries raise their tariffs or the home currency areciates, we would exect domestic exorting firms who rice to market to reduce their own-currency exort rices relative to their own-currency unit costs, thereby lowering their mark-us. Similarly, if either the home country increases a tariff or the home currency dereciates, domestic imort-cometing firms would be exected to increase their rices relative to their costs (both measured in home currency), thereby raising their markus. Thus, the artial ass-through literature imlies simle and intuitive rules of thumb for how rofit mark-us are likely to adjust in resonse to changes in tariffs or exchange rates. 4 While these resonses of rices and mark-us are well understood, to the best of our knowledge they have not reviously been incororated into a S-S tye of analysis of the imact of trade liberalization on income distribution. In the aroach roosed here, firms will be assumed to receive rofits deriving from their oligoolistic rents, while the rimary factors of roduction (various tyes of labor or natural resources) will be assumed to earn scarcity rents in the conventional fashion for comarability with traditional S-S models. 5 The idea that mark-u ricing by oligoolistic firms can be used as 4 Given that the revious literature is relete with models of how rofit-maximizing firms make these decisions, we refer to summarize the results of those models as rules of thumb rather than to relicate the models here. 5 A series of articles, collected in Steedman (979), showed that the core H-O theorems do not aly to caital when it consists of heterogeneous goods valued at rices that include ositive rofits; see Ethier (979) and Smith (979) for neoclassical rejoinders. However, Steedman and Metcalfe (979) and Steedman (005) have shown that the core H-O theorems (including S-S) continue to hold when alied to rimary, non-roduced factors (such as labor and

8 7 the basis for determining the rofit share of national income was originally develoed by Kalecki (954 [968]). 6 We assume that oligoolistic firms tyically oerate with excess caacity, for a combination of well understood reasons: to maintain barriers to the entry of new firms; to anticiate future increases in demand; and because of indivisibilities in lant and equiment. Assuming excess caacity in a static framework, we can ignore the standard scarcity rents to caital, and treat all rofits as deriving from oligoolistic mark-us. However, from a formal viewoint, nothing in the model develoed below deends on this assumtion; we could alternatively include caital as one of the rimary factors of roductions and assume that it is fully emloyed, in which case its owners would receive scarcity rents for the services of their caital in addition to any economic rents they derive from ownershi of oligoolistic firms. Turning to emirical studies of S-S effects, as noted in the introduction this theorem has often been alied to the effects of trade on wage inequality between more and less skilled workers, rather than the overall distribution of income between caital and labor generally. Emirical evidence for S-S effects in exlaining the skilled-unskilled wage ga in the US economy is, however, mixed (see Lawrence and Slaughter, 993; Thomson, 997; Sachs and Shatz, 998; Leamer, 998; Krugman, 008). Berman, Bound, and Griliches (994) and Bernard and Jensen (997) found that most of the changes in the US skilled wage remium had occurred within industries, rather than between them, contrary to what one would exect from S-S. This finding was initially interreted as imlying that skill-biased technological change, rather than trade, was the main culrit in exlaining the rising skilled wage remium. However, several economists have demonstrated that trade can affect within-industry wage differentials, for land) in the resence of heterogeneous intermediate goods, under certain conditions. 6 Mark-u ricing as a device for determining the rofit share was introduced into models of North-South trade by Taylor (983) and Dutt (988). However, these models assumed fixed mark-us, and did not incororate flexible mark-us into a trade-theoretic analysis of factor-rice determination as we do here.

9 8 examle as a result of the offshoring of inuts (Feenstra and Hanson, 996) or heterogeneity of firms (Egger and Kreickemeier, 009) see Harrison, et al. (0) for a survey. Although these studies have made advances in understanding how trade affects the skilled wage remium, this literature has largely sidesteed the issue of how trade affects the overall distribution of income between caital and labor. A few recent studies have investigated how trade (or globalization more broadly) has affected relative shares of value added. Onaran (009) finds that a measure of oenness (exort intensity) is negatively related to the wage share in the manufacturing sectors of Mexico and Turkey, but not South Korea. Milberg and Winkler (00) find that measures of the offshoring of materials and services inuts have ositive effects on rofit shares using anel data for US industries. These studies are largely emirical and generally rely on existing theoretical models to motivate their econometric analysis. Before roceeding to our own model, one caveat is in order. The literature on labor rents (e.g., Katz and Summers, 989; Blanchflower et al., 996) imlies that a ortion of the oligoolistic rofits in concentrated industries may be catured by workers if they have strong bargaining ower, for examle as a result of union organizing or efficiency wages. In this vein, Bivens (006) finds that labor s bargaining strength declined in the US after the early 980s because globalization imroved what he calls the fallback osition of caital. Rent-sharing by labor is not included in the model in the resent aer, but could be incororated in future extensions of this work. In order to sharen the contrast between our results and the conventional S-S theorem, factor markets will be treated as erfectly cometitive in what follows.

10 9 3. A MODIFIED HECKSCHER-OHLIN MODEL WITH MARK-UP PRICING We use a -good, -factor H-O model alied to a single, small country for simlicity; extensions to models with multile countries or factors are left for future research. The two goods, and, are roduced using two rimary factors of roduction, i.e., non-roduced inuts. One of these factors will be called L for labor, which may be interreted as less-skilled labor or roduction workers. The other factor will be designated as N, which deending on the desired alication of the analysis can be interreted as either land (natural resources), skilled labor (human caital), or ossibly hysical caital. Hereafter, whenever we refer to factor rices we mean only the returns to L and N, while oligoolistic rofits are treated searately. Both factors L and N are freely mobile between industries but comletely immobile between countries. We do not consider intermediate inuts in this section; they will be introduced later. Using the dual cost functions that have become the standard workhorses of international trade models (Feenstra, 004), but assuming oligoolistic firms with ositive economic rofits, the rices of the two goods can be exressed as follows: 7 ( )[ wal qan] ( ) c ( w, q) ( )[ wal qan ] ( ) c( w, q) () () where a ij is the quantity of inut i required er unit of outut j, w and q are the rices of the factors L and N, resectively, 8 c j (w, q) is the unit factor cost function for each good j, and j 0 is the mark-u rate on good j. Since there are no intermediate goods, the share of rofits (in the 7 This secification could be justified by assuming that domestic outut of each good is roduced by a reresentative firm, which would be a ure monoolist in a closed economy, but which has to comete with foreign roducts in an oligoolistic world market as long as tariffs are not rohibitive. Alternatively, one could assume that each domestic industry consists of a small number of firms with identical cost functions, roduct varieties, and ricing behavior. 8 Thus, w is the wage rate for ordinary or less-skilled labor, while q is either the rental rate on land (natural resources), the salary of skilled labor (human caital), or the rental rate on hysical caital (lant and equiment).

11 0 sense of oligoolistic rents) in value added equals the rice-cost margin: j = ( j c j )/ j = j /(+ j ), which is monotonically increasing in the mark-u rate j in each sector j =,. The inut-outut coefficients a ij can either be taken as fixed, or else treated as otimal coefficients derived by cost minimization from neoclassical roduction functions of the form: y f L, N ), j =, (3) j j ( j j where f j () is assumed to have all the usual well-behaved roerties (constant returns to scale [CRS], diminishing marginal roductivity, and satisfaction of all second-order conditions). 9 In the latter case, the unit factor cost functions c j (w, q) are the otimal, minimized unit cost functions that are dual to the roduction functions (3). To enhance comarability with standard trade models, we will assume that the inut-outut coefficients a ij are flexible and are derived (via cost minimization) from roduction functions of the form (3), but all the qualitative results of this aer would still hold if there were fixed coefficients. 0 To formalize the assumtion of excess caacity, we can think of (3) as being embedded in a broader roduction function of the form, K j y j min f j ( Lj, N j ), bj (3) where K j is hysical caital and b j is a fixed coefficient for the ratio of caital to full-caacity outut in each sector j. If we further assume that the binding constraint is always the emloyment of the rimary factors L and N, i.e., f j (L j, N j ) < K j /b j ( j =, ), then the caital constraint is never binding, outut is normally below the caacity level defined by the caital stock, and if also 9 When the a ij are derived by cost-minimization, they are functions of the factor rices, a ij = a ij (w, q), but we suress the factor rices here to avoid notational clutter. 0 Although it is not otherwise imlied by standard definitions of well-behaved roduction functions, we also assume that there are no factor-intensity reversals (FIRs), which requires that the elasticities of factor substitution for the two goods must not be too different. Assuming fixed coefficients is sufficient, but not necessary, to rule out FIRs. Assuming no FIRs is not strictly necessary for our results, but avoids introducing multile equilibria.

12 firms are static cost minimizers then caital would have a zero scarcity rent or shadow rice. However, nothing in the formal analysis below requires us to use (3) under these assumtions; it is sufficient to use (3) and we could ossibly define N as hysical caital (with a ositive scarcity rent of q) if we so choose. Assuming that the domestic industry consists of one or more oligoolistic firms with significant barriers to entry, there is no resumtion that ositive rofits are cometed away by new entrants or that rofit rates are equalized across industries. Also, we do not assume identical technology (roduction functions) or identical homothetic references across countries. In fact, no assumtion about references or technology (other than CRS in roduction) is required for the resent analysis. We assume that, although finished goods markets are oligoolistic, factor markets are erfectly cometitive, and hence factor rices are flexible and there is full emloyment of L and N. [Figure about here] Figure reresents a ossible equilibrium for goods rices and factor rices in the model described by equations () and (), assuming both goods are roduced (i.e., incomlete secialization). How a secific equilibrium configuration of this tye is determined in an oen economy will be discussed in the next section; here we simly wish to illustrate how ositive mark-us j > 0 drive a wedge between goods rices j and unit factor costs c j. The solid curves The author is not aware of any revious literature that exlicitly uses the secification in equation (3). However, this seems to be a mathematically convenient way to exress the imlicit assumtion in many models with excess caacity that the caital constraint is not binding, while still allowing for ossible substitution between other factors. Matters would grow more comlicated in a dynamic setting in which firms also make investment decisions, but that would be beyond the scoe of the resent, static analysis in which the caital stock is taken as given. The original S-S theorem ( strong version ) assumed identical homothetic tastes and identical technologies across countries in roving that the abundant factor necessarily gains from free trade and the scarce factor necessarily loses. However, the more general S-S theorem ( weak version ), which states only that the factor used intensively in the good which goes u (down) in relative rice gains (loses), requires only CRS and incomlete secialization but not identical technology or identical homothetic references. See Chacholiades (978) and Feenstra (004).

13 labeled c and c reresent the unit factor cost functions, c j (w, q) ( j =, ). These curves are drawn as convex to the origin on the assumtion of ositive and finite elasticities of substitution in the roduction functions (3); with fixed coefficients, these curves would be linear. The c curve is drawn as steeer than c assuming, without loss of generality, that good is L-intensive, i.e., (a L /a N ) > (a L /a N ). 3 The equilibrium factor rices are (w 0, q 0 ). Under the standard assumtion of erfect cometition, goods rices (, ) would equal unit factor costs (c, c ), and the curves reresenting the latter could be called zero rofit conditions. However, with ositive mark-us ( j > 0) which for exository uroses we take as exogenously given here (adjustments in mark-us are modeled in the next section) rices are reresented by the higher dashed curves and. In the latter situation, factor market equilibrium occurs where c and c intersect, while the intersection of and has no articular significance. With ositive mark-us j > 0, factor ayments (total costs) are lower than the firms total revenues, and the difference (i.e., the ga between the rice and cost curves in Figure ) is accounted for by firms oligoolistic rofits. 4. EFFECTS OF TRADE ON INCOME DISTRIBUTION Next, we roceed to model how the distribution of income both between the two rimary factors L and N and between those factors and the rofits of the firms that emloy them is affected by international trade. We assume that the domestic firms in each industry, and, roduce a final good that is an imerfect substitute for its foreign counterart. The rices of the foreign varieties are and, which are taken as exogenously given on the small country 3 The sloes of the c and c curves are equal to (a L /a N ) and (a L /a N ), resectively.

14 3 assumtion. Thus, and are the rices of domestically roduced varieties of the same goods, exressed in a common currency for convenience. Since home and foreign roducts are imerfect substitutes, we assume that there is two-way trade in both goods, and home and foreign varieties of each good do not generally sell for the same rices. Suose, without loss of generality, that the home country is a net exorter of good and net imorter of good. We assume also that the home country imoses a tariff on imorts of good but not on imorts of good, i.e., there is no rotection in the sector in which the country is a net exorter, and similarly the foreign country imoses a tariff on good but not good. Then, also assuming no transortation costs for simlicity, the rice of home exorts of good in the foreign market is ( t ), where t 0 is the foreign ad valorem tariff rate, and the rice of imorts of good in the home market is ), where t 0 is the home tariff rate. ( t For mathematical convenience, we ostulate the following reduced-form or rule-ofthumb relationshis between home and foreign rices for each good: B (4) T T B (5) where B j > 0, 0 j < (j =, ), and, for notational convenience, we use tariff factors equal to one lus the tariff rates, T = + t for home exorts and T = + t for home imorts. In (4) and (5), the B j terms are constants that reresent the qualitative characteristics that affect whether the home or foreign variety of each good, j =,, commands a higher rice, while the exonents j reresent the degree of ass-through of the tariffs (or foreign rices) into home rices, which deends on the degree of substitutability of the home and foreign varieties of each good in consumtion and the oligoolistic firms strategic behavior (which are not modeled

15 4 here exlicitly, but rather incororated into the j arameters). Thus, j is the elasticity of the rice of the home variety with resect to a change in the tariff-adjusted rice of the foreign variety. 4 Perfect substitutes would imly B j = and j = 0, in which case there would be full ass-through; as the goods become less substitutable, j rises above 0, j falls below, and the ass-through into rices of domestic varieties becomes more and more artial. Equations (4) and (5) in down the domestic rices in relation to the (given) rices of foreign varieties; we need two additional equations to determine the mark-u rates and thereby in down the unit factor costs in () and (). 5 For the mark-u on the exort good, we assume T c ( ),, 0 < (6) where is a constant reflecting other (exogenous) determinants of the home firms mark-u rate, and is the elasticity of the mark-u factor (+ ) with resect to the ratio T c, which reflects home cost cometitiveness (including the effect of the foreign tariff). 6 Thus, when home exortables become more cometitive with foreign roducts (because of a rise in the foreign rice or a reduction in the foreign tariff), home firms in the exort sector raise their mark-us. 4 Thus, equation (4) imlies that a lower foreign tariff allows home exorting firms to increase their rices, while equation (5) imlies that a lower tariff in the home country induces home imort-cometing firms to reduce their rices in order to reserve market share. Note that this secification imlicitly assumes the absence of rice discrimination domestic and foreign firms each sell their roducts at the same re-tariff rices whether they are sold at home or exorted. This is not necessarily realistic, but simlifies the analysis by restricting the number of different goods rices that have to be considered in evaluating real factor rices. 5 It might be thought that equations (6) and (7) in combination with (4) and (5) overdetermine the mark-us, but this is not the case because (4) and (5) ertain only to the ass-through of foreign rices into domestic rices but, in the resence of oligooly and ositive rofits, are not sufficient to determine unit factor costs or (equivalently) markus. See the discussion of the two tyes of ass-through in the model, below. 6 Analogous measures of home cometitiveness have been used by (or are imlicit in) Blecker (989), Feenstra (989), and Arestis and Milberg (993-94). In rincile, it might be argued that mark-us should be determined in relation to relative unit costs (foreign-home), rather than the ratio of foreign rices to home unit costs, but this would require modeling the simultaneous determination of foreign mark-us and ass-through, which we elide here based on the small country assumtion. Also, home firms might lack information on foreign costs, but can observe foreign rices. Note that erfect cometition (zero rofits) is the secial case in which j = and j = 0, while a ositive but rigid mark-u is the case in which j > and j = 0 ( j =, ). Also note that both j and j ( j =, ) may reflect, among other factors, the ease or difficulty of domestic entry.

16 5 Similarly, in the imort-cometing sector, the home country mark-u is determined by T c,, 0 < (7) where is a constant reflecting other (exogenous) determinants of the sector s mark-u, and is the elasticity of the mark-u factor with resect to the home cost cometitiveness ratio for good, T c. Thus, when imort-cometing goods become more cost cometitive (for examle, because foreign rices rise or home tariffs are raised), domestic roducers of these goods increase their mark-us. We assume that the elasticities of the mark-u factors with resect to the cost cometitiveness of home goods j (j =, ) are constant for simlicity. For mathematical convenience, we convert these equations into growth rate form and solve the model using an extended version of the famous Jones (965) algebra. 7 Changes in the rices of home goods (varieties) are obtained directly from logarithmic differentiation of (4) and (5), assuming that the B j (j =, ) are constants: ( )( T ( )( T ) ) (8) (9) where a ^ indicates an instantaneous growth rate or roortional rate of change. Thus, home rices rise if foreign rices are increasing, or if the foreign tariff on exorts is lowered, or the home tariff on imorts is raised, but in each case there is artial ass-through into domestic rices as long as 0 < j <. Using equations (), (), and (4) through (7), on the assumtion that the B j and j (j =, ) are constants, the roortional changes in unit factor costs are: c ( A T ) (0) 7 The model solutions in levels are given in the Aendix.

17 6 c ( A T ) () where A j j j j (assuming the further restriction that j + j < ). Changes in marku rates of firms are then obtained from equations (8) through (), and can be written as: c ( T ( c T ) ) () (3) The mark-u rate rises (i.e., the rice increases roortionally more than unit factor costs) in each sector if the tariff-adjusted foreign rice increases, and falls if the tariff-adjusted foreign rice decreases, rovided that there is artial ass-through of the foreign rice change or tariff change into domestic rices (i.e., 0 < j < ) and the mark-u is flexible (0 < j < ). In effect, there are really two different kinds of ass-through in this model: ass-through into domestic rices, which deends only on the j arameters, and ass-through into domestic factor costs and mark-us, which deends on both the j and j arameters. In terms of causality, exogenous changes in tariff rates or foreign rices lead to less-than-roortional changes in rices of home goods via (8) and (9), and then to changes (also less-than-roortional) in unit factor costs via (0) and () and mark-u rates and rofit shares via () and (3) lus the definition of j. To solve for the changes in factor rices ŵ and q, we must use a simultaneous equations aroach. Logarithmic differentiation of the cost functions c j (w, q) yields c w L N q c w L N q (4) (5)

18 7 where ij is the share of factor i in the unit cost of good j (thus, Lj = wl j /c j and Nj = qn j /c j ). Combining equations (0) and () with (4) and (5), the resulting air of equations can be exressed in matrix form as q w T A T A N L N L ) ( ) ( (6) and the solution for factor rice changes is ) ( ) ( T A T A q w L L N N θ (7) where is the matrix on the RHS of (6). 8 The determinant of this matrix is = L N L N, which is ositive if good is L-intensive ( N L N L ) and negative if good is N-intensive ( N L N L ). Given that L + N = and L + N =, it can easily be shown that = L L = N N. For the sake of illustration, and without loss of generality, we assume that good is L-intensive, which imlies = L L = N N > 0. From (7), the solutions for the factor-rice changes ŵ and q are: ) ( ) ( N N N N T A T A w (8) ) ( ) ( L L L L T A T A q (9) which can be written as )] ( ) ( [ ) ( N N N T A T A T A w (0) 8 Equation (7) reduces to the conventional S-S solution if A = A =, which would hold if home and foreign goods were erfect substitutes ( j = 0), regardless of whether the mark-u was flexible (i.e., even if j > 0), because then there would be full ass-through into both rices and factor costs (since, with domestic rices always equal to tariff-adjusted foreign rices, mark-us would not actually change).

19 8 q [ A ( T ) A ( T )] L A ( T ). () L L Because of the comlexity of (0) and (), we will consider a series of secial cases in order to illuminate their imlications. First, we consider an exogenous increase in the rice of the foreign variety of good ; then, we will consider equal-roortional tariff reductions in both sectors. 4. An increase in the foreign rice Consider first an increase in the rice of the foreign variety of good ( > 0), holding the rice of the foreign variety of good and both tariff rates constant ( T T = 0). We know from (8) and (9) that ( ) > 0 =. By equation (), the mark-u rate in sector rises (this can also be seen by comaring equations 8 and 0, and noting that j > A j ), while by (3) the mark-u in sector is unaffected. We can also infer from () that q < 0, and therefore q < 0 =, so the owners of N lose absolutely in terms of either good, or. Equation (0) imlies that ŵ > 0, which also imlies ŵ >, so L-workers definitely gain in terms of the imorted good. However, in this model unlike the traditional S-S model it is ambiguous whether L-workers (owners of the factor used intensively in the good that increased in rice) gain or lose in terms of that good, i.e., whether there is a magnification effect in the sense that the wage rises more than roortionally to the rice of good. Recalling that there is two-way trade in nationally differentiated goods, so home workers consume both domestic and foreign varieties of good, note that (0) combined with (8) imlies (after much maniulation) that the real wage in terms of the home variety of good rises (i.e., w ) if and only if /[( )( )] < N / N, while (0) imlies that the real wage in

20 9 terms of the foreign variety rises (i.e., w ) if and only if /( ) < N / N. Recalling that reflects the degree of mark-u adjustment and reflects the degree of roduct differentiation, the higher are these two arameters, the more artial is the ass-through of the foreign rice increase into domestic factor costs, and the less likely it is that the magnification effect holds in regard to the real wage in terms of good, whether of the domestic or imorted variety. Also note that N / N < since good is L-intensive, so this ratio is lower if the ga in factor intensities between the industries is greater. If the magnification effect does not hold, then L- workers gain only if they consume relatively large quantities of good and may lose if they consume relatively large quantities of good the more so if they consume a lot of the foreign variety, whose rice increases by more than the domestic variety. Putting these results together, we can see that any of the following sets of inequalities may hold in this situation: w 0 q (a) w 0 q (b) w 0 q. (c) Thus, contrary to the standard S-S theorem (in which only a could hold, with ), it is ossible for both rimary factor owners to lose from an increase in the rice of the exorted good, if ass-through is very artial and if the owners of the factor used intensively in roducing the good that increased in rice consume relatively large quantities of that good (esecially the foreign variety). 9 These results may be summarized in the Stoler-Samuelson-Kalecki (SSK) theorem: 9 Analogous results obtain when the rice of the foreign variety of the imorted good increases, holding the rice of the foreign variety of good and both tariff rates constant.

21 0 Assuming that oligoolistic firms in a small rice-taking country roduce two goods that are imerfect substitutes for the same foreign goods using CRS technology, an increase in the rice of a foreign good causes a smaller rise in the domestic rice of the same good, and increases the mark-u rate (rice-cost margin) and rofit share in the industry which roduces that good. The real rice of the rimary factor of roduction used intensively in the roduction of the other good definitely falls, while the real rice of the factor used intensively in the good that increased in rice may either rise or fall deending on the extent of artial ass-through of the foreign rice change into rices and factor costs and the roortions in which this factor s owners consume the two goods. This theorem is contrasted with the standard S-S theorem in Figure. If, as in the conventional S-S analysis, the goods were erfect substitutes and the goods markets were erfectly cometitive, then the foreign rice curves and would also reresent unit factor costs in the home country. If rises to while remains constant, factor rices would shift from the levels marked by a suerscrit 0 to the levels marked by a suerscrit 3. In this case, the roortional rise in w (from w 0 to w 3 ) would be greater than the roortional rise in, signifying a magnification effect for the factor used intensively in the good whose rice increased (L in this examle). [Figure about here] However, with ositive rofit mark-us and differentiated roducts, the home country rices and differ from the foreign rices and (home rices are not shown in Figure to avoid cluttering the diagram), and the unit cost curves are at the levels c and c (which must be below the home rice curves, although they could be either above or below the foreign rice curves). 0 Assuming artial ass-through into factor costs, the unit cost curve for industry shifts u (from c to c ) by a smaller roortion than the rise in either or (comare equations 8 and 0, and recall that A < ). Then, when w rises from w to w, even though this change in 0 In drawing Figure we have assumed that the domestic unit factor cost curves are below the foreign rice curves, although this is not strictly necessary if home varieties are suerior in quality. What is critical to the analysis here is that that the shifts in the unit cost curves are roortionally smaller than the shifts in the corresonding rice curves.

22 w is roortionally greater than the change in c, we cannot be sure whether the change in w is roortionally greater or less than the changes in and. The result is what we call an attenuated Stoler-Samuelson effect (the smaller shift from w to w ) instead of the traditional Stoler-Samuelson magnification effect (the larger shift from w 0 to w 3 ). The more artial is the ass-through into factor costs, the smaller will be the shift in c, and hence the greater is the likelihood that L-workers could lose in terms of good (either foreign or domestic varieties). 4. Recirocal trade liberalization Suose that there are equal-roortional tariff reductions in the home and foreign countries, i.e., T T T 0, holding the rices of the foreign varieties constant ( = 0). Clearly, from (8) and (9), the changes in home rices are = ) T > 0 > ( ) T so there ( will be artial ass-through of the tariff reductions into domestic rices as long as home and foreign goods are imerfect substitutes ( j > 0, j =, ). If, in addition, mark-us are sensitive to international cometitiveness ( j > 0, j =, ), then equations () and (3) show that the marku rate will rise for firms in industry (the exort sector) and fall in industry (the imortcometing sector) and rofit shares will adjust in the same directions by the definition of j. Assuming T T T 0 in (0) and (), the changes in factor rices can be reduced to w ( A N N > 0 (3) N A N ) T If the foreign roducers also have artial ass-through of the tariff changes, they will adjust the rices of their varieties to the tariff reductions. In that case, what would matter to the home country would be the net changes in the tariff-adjusted foreign rices, T and T. However, incororating foreign rice resonses into this modeling framework is left for future research.

23 q ( A A L L < 0. (4) L L ) T Thus, L definitely gains relative to N, but with domestic rices of both goods changing, it is not obvious whether real factor rices rise or fall in terms of both goods or not. Evidently, the real rice of the factor used intensively in exorted goods rises in terms of the imorted good, i.e., w/ and w/t both increase. Also, the real rice of the factor used intensively in imortcometing roduction definitely falls in terms of the exorted good, i.e., q/ and q/ both rise. However, it is not clear whether the changes in real factor rices are absolute or magnified, in the sense that the rice of each factor rises or falls in terms of the good in which it is used intensively, i.e., does w/ increase and does q/ or q/t decrease? Whether w/ increases deends on whether w ( A A ) T, N N > ( ) T N N or A N N A N N >, which can be exressed as ( A )( ) <. N N Since the denominator of the ratio on the LHS must be ositive, the higher are (the sensitivity of sector mark-us to international cometitiveness) and (the degree of roduct differentiation for good ), the more artial is the ass-through into factor costs in the sector in which L is used intensively, and also the lower is the ratio (i.e., the greater the ga in N N factor intensities between the two sectors, since N < N ), the greater is the likelihood that these inequalities will be reversed and w/ will decrease. In the latter situation, whether L-workers gain or lose will deend on their consumtion bundle, contrary to the S-S theorem in which it does not matter which goods the factor owners consume. Similar considerations ertain to whether q/ falls, which analogously deends on The results for w/ are unambiguous, since w rises while is unchanged and there is no tariff by assumtion.

24 3 whether ( A )( ) < L L. The higher are and (i.e., the more artial the ass-through into factor costs in sector ), and the lower is L L (i.e., the greater the ga in factor intensities, since L < L ), the more likely that this inequality could be reversed and q/ would rise. Also, q/t falls if and only if ( A )( ) < L L. Sufficiently high values of or, or a low enough ratio L L, could reverse this inequality and allow N-owners to gain in terms of imorts of good. If either of these inequalities is reversed, then the overall real gains or losses to N-owners would deend on their consumtion bundle, contrary to S-S. All these results may be summarized in the recirocal trade liberalization corollary to the SSK theorem: Under the same assumtions as for the SSK theorem, if both the home and foreign countries reduce their imort tariffs by the same ercentage, the mark-u rate (rice-cost margin) and rofit share rise in the home exort industry and fall in the home imort-cometing industry. The real rice of the factor used intensively in the exort industry definitely rises in terms of the imorted good, but may either rise or fall in terms of the exorted good, while the real rice of the factor used intensively in the imort-cometing industry definitely falls in terms of the exorted good but may either rise or fall in terms of the imorted good. If the ass-through of the tariff reductions into factors costs is sufficiently artial, the effects on real factor rices will deend on the roortions in which the factor owners consume the two goods. [Figure 3 about here] The effects of recirocal trade liberalization on rices of domestic factors and domestically roduced goods are illustrated in Figure 3. The domestic rice of good rises while the domestic rice of good falls, and the unit factor costs shift in the same direction as the rice for each good but (assuming artial ass-through of the tariff cuts into factor costs) by a smaller roortion. The changes in factor rices with ositive mark-us and artial ass-through (from w to w and q to q ) are smaller than they would be, if mark-us were zero and there was full ass-through (from w 0 to w 3 and q 0 to q 3 ). Although it may not be visually obvious, it is ossible

25 4 for the increase from w to w to be roortionally smaller than the increase in the rice of good (from to ) and for the decrease from q to q to be roortionally smaller than the decrease in the rice of good (from to ). This would require a relatively large difference in factor intensities between the two sectors (so that c would be much steeer than c ) and relatively little (more artial) ass-through (so that the shifts in c and c would be relatively small). 5. TRADE IN INTERMEDIATE GOODS AND OFFSHORING As emhasized in several studies cited earlier, some of the imact of international trade on factor rices may come through outsourcing or offshoring, i.e., vertical trade in intermediate inuts, within a given industry, rather than trade in finished roducts. 3 This section briefly addresses how the analysis of trade with imorted intermediate goods can be modified to incororate oligoolistic rofits and differentiated roducts, similar to the analysis in the revious section. For this urose, we use a very simle model from Feenstra (004,. 06-) in which there is one final good, z, that is roduced using inuts of two intermediate goods, and (for simlicity, no other inuts are used in final goods roduction). The intermediate goods in turn are roduced using only inuts of the rimary factors L and N. 4 Home and foreign intermediate goods are assumed to be erfect substitutes in roduction and to be sold in erfectly cometitive markets, while and here we differ from Feenstra the final good is assumed to be differentiated and roduced by oligoolistic firms with ositive mark-us. Both final goods and intermediate goods are traded and, for simlicity, we assume 3 The term offshoring is often referred by economists to the more oular outsourcing, because the latter can also refer to a situation in which a firm contracts out for inuts or services domestically rather than imorting them. 4 Feenstra includes caital (K) as an inut into intermediate goods, but it is irrelevant to his results since he assumes that its cost share is the same in both goods ( K = K ). We simlify by omitting caital here.