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Sense and surprise in competitive trade theory 2010 WEAI presidential address.

I. INTRODUCTION

The competitive theory of international trade is well known for its abundance of "paradoxes." Perhaps the most widely known is the Leontief Paradox, associated with the rather startling results presented by Leontief (1953) that the trade pattern of the United States suggested that its export sectors were more labor-intensive than factor proportions found in its import-competing sectors. This result stimulated decades of research, but is not the focus of the present paper. Other so-called paradoxes include the Metzler (1949) result, wherein a country levying a tariff on an imported item may end up with a lowering of its domestic price. That is, a tariff may not be protective. (1) Lerner (1936), who earlier hinted at the Metzler outcome, emphasized the possibility that a tariff might instead worsen a country's terms of trade, which is at the opposite extreme to the Metzler result. Both of these paradoxes are attributed to possible income effects in demand.

More recently, income effects stemming from asymmetry in demand patterns (among countries) were shown to open the door to paradoxical results if one country makes a transfer to another in a world in which other countries are also engaged in trade in the same commodities. The surprising results: The Giver in the transfer might end up better off (i.e., it may pay to give rather than to receive), and/or the Recipient of the transfer may end up worse off. (2) Finally, a classic result that does not depend on asymmetries in taste patterns, but rather upon the degree of elasticity in demand and the nature of growth is the question of whether a country that unequivocally grows (transformation schedule shifts out) can be made worse off as a consequence of growth (the so-called immiserizing growth paradox). (3) This is an issue familiar to particular sectors of the economy, for example, agriculture--can a good harvest yield lower returns because of the subsequent price fall?

Instead of revisiting these familiar paradoxes here, I wish to concentrate on the production side of competitive models used in international trade and to focus on the question involving ways of judging economic models. Clearly the question of realism often comes up, whether it is in terms of assumptions made or of outcomes expected. Here I suggest a different criterion: Does the model conform in many ways to common sense? (That is, would one be tempted to suggest that the model is not necessary because common sense would lead to the same results?) And, if it does, do the outcomes in certain scenarios seem to be paradoxical or surprising? If so, can the model reveal in simple terms why these somewhat surprising results make sense? (4) I shall restrict myself to a pair of basic models of production used in competitive trade theory--the Specific Factors Model on the one hand, and the Heckscher-Ohlin model on the other. I shall argue that in many ways both conform to common sense, but, in addition, provide the very tools that expose the underlying rationale for surprise.

II. A PRELIMINARY QUESTION

Consider any economy that is characterized by competitive markets and constant returns to scale technology. Suppose, for such an economy, there is an increase in the factor endowment bundle. To fix on an example, suppose there is an increase in the economy's labor force. The very general question I wish to ask is: How does such an economy absorb this increased endowment to maintain full employment of all factors? Note that if this economy is not engaged in international trade there will likely result a change in commodity prices as they adjust in order to equilibrate local supply and demand. Given the points I wish to make later, let me assume that the country is engaged in free trade with the rest of the world. If this economy were particularly small, world prices could be taken as given. Even if world prices are disturbed, it is legitimate to ask how the economy absorbs the extra supplies before any change in commodity prices takes place. (I shall mention an alternative use later that concerns a comparison of two trading communities that face the same world prices in equilibrium.) The general answer to the question is that there are two ways in which a greater labor supply can be absorbed in competitive models: (a) by changing the way in which commodities are produced, that is, increasing the quantity of labor used per unit of capital in all sectors in response to a lowered wage rate and (b) by changing the composition of its output, that is, reallocating resources toward the labor-intensive good(s). To use a more classical language, method (a) refers to changes at the intensive margin, and method (b) refers to adjustments at the extensive margin. The production and trade models examined in the next two sections react quite differently to this question.

III. THE SPECIFIC FACTORS MODEL

The specific factors model is often referred to as the general equilibrium model that best tends to capture processes assumed in most partial equilibrium models. Used verbally by Haberler (1936) and others, it received more formal algebraic treatment in the works of Jones (1971, 1975) and Samuelson (1971), who labeled this the Ricardo-Viner model. The most frequently used and simplest form of the model is for an economy with only two sectors. Both sectors employ an input that is mobile between sectors, usually thought of as homogeneous labor, a factor that works in each sector with a kind of capital that is specific to that sector. A variant, often used in textbooks, considers two industries using mobile labor, with one industry using land as a second input, and the other sector using capital. (5) The multisector version has the advantage that it is almost as easy to analyze, with mobile labor used in all sectors and with each sector employing a factor (say a form of capital) that is only used in that sector. (6)

Consider one such industry, say industry i, and examine the consequences of an increase in the price of the ith commodity, all other commodity prices constant. Such a price rise leads to very common sense output changes: The ith industry attracts labor from all other sectors of the economy, thus causing output in all other sectors to fall. The effect on income distribution also satisfies common sense: the wage rate, w, is driven up by the price increase, but, given that no other commodity prices change, not by as much as the return to the specific factor in the ith sector, [r.sub.i]. The wage increase causes a reduction in the rate of return to specific capitals in all other sectors. In more detail, the unit cost change in the ith sector is, in a competitive equilibrium, brought into equality with that sector's change in commodity price. Furthermore, the relative change in unit costs must equal the weighted average of the changes in the two input prices, with the weights reflecting each factor's importance in total costs, the factor's distributive share, [[theta].sub.Li] for labor and 0Ki for specific capital:

(1) [[theta].sub.Li] [??] + [[theta].sub.Ki] [[??].sub.Li] = [[??].sub.i]

In sector i, the relative change in the return to capital, [[??].sub.i], must exceed the change in the commodity price, [[??].sub.i], because the relative change in the economy's wage rate, [??], although positive, is prevented from increasing as much as the commodity price because labor is used as well in all other sectors. (7) Now consider the cost situation in one of the sectors in which price has not increased. The increase in the wage rate common to all sectors must, for each such sector without a price increase, put downward pressure on the return to specific capital, because the distributive share weighted average of the relative changes in input prices is zero. The effect of a single price change on the distribution of income well satisfies the criterion of common sense. The equations of change for the competitive profit conditions (i.e., that changes in equilibrium costs are equal to that of price for any commodity produced, as set out in Equation [1]), are of fundamental use in exploring subsequent surprises in trade theory, both for the specific factors model and for the Heckscher-Ohlin model.

The principal characteristic of competitive general equilibrium models is their ability to examine the effect of an economic shock in one sector of the economy on outputs and income distribution in other sectors of the economy as well. Consider, now, the effect of an increase in the economy's endowment of the specific capital used only in sector i on all outputs and the distribution of income assuming that all commodity prices are held constant. Not surprisingly, the return to such capital must fall, attracting labor from all other sectors. With the commodity price in sector i kept constant, such a fall in capital's return puts upward pressure on the wage rate, and this increase in labor costs serves to reduce the returns to all types of specific capital used in other sectors. Although these results make good sense, consider the extent to which the return to sector i's specific factor (whose endowment expands) falls compared to the fall in some other sector's specific factor, say that used in commodity j. In both sectors, the wage rate increases, forcing the returns to specific factors, [r.sub.i] and [r.sub.j], both to fall. Equation (1) would reflect factor-price changes if the change in commodity price for each sector were zero. The possibility that the return to sector j's specific factor, which has not increased in supply, could fall by more than that of the specific factor that has experienced a supply increase depends upon a simple comparison of distributive labor shares in the two sectors. Such a comparison reveals which of the two sectors is more labor-intensive. (8) If [[theta].sub.Lj] were to exceed [[theta].sub.Li], that is, if labor costs loom larger in sector j than in sector i, the increase in the wage rate, common to both sectors, would drive down the return to the specific factor used in the jth sector by more. To many this outcome would seem rather surprising.

Suppose a country wants to raise revenue by imposing an import duty only on one of a pair of import-competing industries. Which industry should it choose? Alternatively stated, what arguments for trade protection could an industry mount? This pair of industries is part of a much larger set of industries not involved in the question of protection, but that would be affected by any subsequent increase in the wage rate (assuming that commodity prices they face are constant throughout). The more labor-intensive of the pair of import-competing industries might argue that it should be the sector to enjoy protection, because labor would likely be more favorably affected. I return to that issue below. But first suppose that the more labor-intensive industry is industry 1, and ask how the specific factors would be affected if protection of a given relative amount is granted the first industry as opposed to the same degree of protection granted the second industry (i.e., the more capital-intensive industry). Make use of relationship (1) in the comparison, with the same relative increase in price offered in each case. Whether it is the first or the second industry that gains protection, the wage rate will increase, but by a small relative amount given all the other industries in which labor is employed, and the specific factor in the favored sector would gain even relative to the degree of protection. But such a gain is bound to be larger for the labor-intensive industry. That industry (industry 1) might try to attract favor because [[theta].sub.L1] exceeds [[theta].sub.L2]; and this is precisely the argument that the gain to [r.sub.1] would be greater than that to [r.sub.2] if the second sector had obtained protection instead. This is what I have referred to (with apologies to Oscar Wilde) as the importance of being unimportant. (9)

Although the wage increase would in either event be quite small in this multisector economy, could the wage rate (as well as the return to capital) really increase more if the labor-intensive sector were the one receiving protection? Details are easy to obtain, but are not provided here. (10) In the specific factors setting, if commodity i is the only sector in which the price increases, the wage increase depends upon two features of technology, as well as upon the importance of commodity i's output relative to the national income, [[theta].sub.i]. Let [s.sub.i] denote the elasticity of demand for labor in sector i compared with the aggregate elasticity of demand for labor in the overall economy, and [i.sub.i] denote the relative labor intensity in the ith sector (this equals the ratio of labor's distributive share in the ith sector to the overall share of labor in the national income, [[theta].sup.L]). Equation (2) shows that the relative wage change is the product of these three elements times the price change, where the product is a positive fraction:

(2) [??] = [[theta].sub.i] [[i.sub.i][s.sub.i]][[??].sub.i].

Suppose industries 1 and 2 are of the same size (i.e., [[theta].sub.1] = [[theta].sub.2]) and relative degree of flexibility in technology (i.e., suppose [s.sub.1] = [s.sub.2]), the wage rate must increase by more if sector 1 were the sector provided protection. That is, in this case both factors of production in the labor-intensive sector would benefit more from protection than would labor and specific capital if the second commodity were the one provided protection. (11) Specific capital in the labor-intensive sector could argue that industry 1 should receive protection because of its greater importance to labor, while labor, in turn, would indeed favor protection in the first sector as well, and be willing to lobby the government for this choice.

Other surprising results can appear in a specific factor setting in which one country (call it Home) is completely specialized in producing commodity X, which uses labor and a specific type of capital, [K.sub.x]. Suppose not all of X-type capital is used at Home. Although owned by Home, some of this capital has been placed in a Foreign Enclave, where [X.sup.E] is also produced with the help of some Foreign labor, [L.sup.*], most of which is used in the Foreign country to produce a different commodity, [Y.sup.*], with the help of their sector-specific capital, [K.sub.y.sup.*]. (12) Now suppose that the world price of commodity X (relative to that of commodity Y) increases. If X-type capital is freely mobile between Home and the Foreign Enclave, what can be said about the effect of the world-wide price increase in X on the location of capital between Home and Enclave? The answer is simple, which may sound surprising: More of Home's X-type capital moves to the Foreign Enclave. To see why, suppose that at first no X-type capital is allowed to move between its two locales. In such a case, in Home, the wage rate increases by the same relative amount as the return to capital, each equal to the relative increase in [p.sub.x]. If the location of Foreign labor is also frozen, in the Enclave both [w.sup.E] and the return to capital also rise by the same relative amount as [p.sub.x]. However, rescinding the ban on factor mobility implies that more Foreign labor would then be attracted to the Enclave, which would serve to raise the return to capital there, thus attracting as well more X-type capital from Home. The new equilibrium will exhibit greater production of [X.sup.E], with more use of capital from Home as a consequence of more Foreign labor coming into the Enclave.

The key to the direction of capital flow induced by the commodity price change is the assumption that Home is completely specialized to commodity X, whereas Foreign has an Enclave into which Foreign labor can flow, released from its production of commodity [Y.sup.*]. That is, the Foreign Enclave has a hinterland ([Y.sup.*] production) from which resources (labor) can be released to help production of [X.sup.E] in the Enclave, whereas Home has no hinterland. Now suppose that such a strong asymmetry is removed by letting Home produce Y as well as X (with a fixed amount of Y-type capital specific to Y-production), but letting X-type capital be the only kind that is internationally mobile. (13) Such a change raises the dimension of the model from a specific factors setting with four inputs and three productive activities to a 5 x 4 model (five productive factors and four activities). Although such a change alters the possible direction of the international flow of X-type capital, somewhat surprisingly it does not change a simple criterion that reveals how the effect on wage rates at Home compares with that in the Foreign enclave. This comparison of wage change in the two locales depends only upon the question of whether X is produced at Home with more or less capital-intensive techniques than those adopted abroad. The result follows directly from the competitive profit equations of change shown in Equation (1): both Home and Enclave face the same relative price rise for X as well as the same equilibrium change in the return to X-type capital. If the production of X at Home is more capital-intensive than in the Enclave (i.e., if [[theta].sub.KX] exceeds [[theta].sub.KX.sup.*]), and given that the wage increase in either country must be smaller than the increase in price, the relative increase in w (if it is an increase) must be less than the relative increase in [w.sup.*]. (14)

IV. THE HECKSCHER-OHLIN MODEL

The most commonly used general equilibrium competitive model of production owes its origins to the pair of Swedish economists, Heckscher (1919) and Ohlin (1933). They both frequently described the model as using three factors (labor, land, and capital), and the more well-known version, the two factor, two commodity model, owes much of its formal development to the work of Samuelson, especially in his joint work with Stolper (Stolper and Samuelson 1941) and his two articles on factor-price equalization (Samuelson 1948, 1949). If used as a model of a country not engaged in international trade, its properties are sensible with few surprises. The bowed-out transformation curve was used even in first-year textbook discussions, and, after the Stolper and Samuelson (1941) paper introduced the concept of a production box, patterned after earlier use of the consumption box, movements along the transformation curve could be seen to be the outcome of shifts of resources from one industry to another along a contract curve in the production box, a collection of points for which ratios of marginal input products are equated between sectors.

The Stolper/Samuelson paper did at the time seem somewhat surprising. (15) It showed how the imposition of a tariff on imports of a labor-intensive commodity would unambiguously result in a higher real wage rate because the nominal wage rate would increase more than either commodity price. Although this result was set in a context of international trade, the theorem is basically a reflection of the consequence for factor returns of any change in commodity prices whether or not international trade takes place. Such behavior is a direct consequence of an assumption about technology typically made in most models: production in each sector uses two factors to produce a single commodity. That is, joint production is ruled out. (16) To some economists there was indeed a somewhat surprising result posited in the Stolper/Samuelson paper: an economy with fixed overall bundles of capital and labor could, by expanding production of the labor-intensive commodity, raise the capital/labor ratios utilized in both sectors of the economy. Indeed, the "could" should be replaced by "must." The reason: both sectors adopt techniques appropriate to factor prices, and as the wage/rental ratio is driven up by expansion of the labor-intensive commodity, both sectors respond by switching to more capital-intensive techniques. (17)

The great element of surprise in the profession with the 2 x 2 model in a trade context emerged with Samuelson's article in 1948 in the Economic Journal arguing that under appropriate conditions factor prices would be brought into equality between two freely trading economies despite the absence of any world market in capital or labor as reflected in international factor mobility. Of course a major assumption is made, viz. that the two countries have exactly the same technology. (This assumption is often made in Heckscher-Ohlin models in order to isolate conditions at work separate from the technology differences featured in Ricardian-type modeling.) As well, competitive conditions prevail and, very importantly, it is assumed that both countries are actively producing the same pair of commodities. The fact that there was general surprise at this result is evident from what might be termed "revealed journalism": One year later (1949) in the same journal Samuelson was encouraged to write another article, "International Factor-price Equalization Once Again." (18)

The analysis supporting the factor-price equalization theorem rests very much on a setting of free international trade between the two countries (a) that share the same technology; and (b) in which in equilibrium commodity prices are brought together internationally (assuming away all transfer costs or tariffs). The argument: in each country, wage rates and rental rates are related to commodity prices by the equilibrium condition that unit costs of production are equal to commodity prices. Unit costs depend on factor prices. If it is assumed that each country produces both commodities, and if both countries face the same commodity prices they must have the same factor prices because the zero profit condition of competitive equilibrium in a 2 x 2 model provides a pair of equations in two unknowns. (19) The reasoning is fortified by the discussion in Section II on how an economy adjusts to a change in factor endowments if commodity prices are constant. With the same number of factors as commodities in the Heckscher-Ohlin 2 x 2 context, commodity prices uniquely determine factor prices, so that adjustment to any factor endowment changes must be made only at the extensive margin. Thus despite having different factor endowments, with free trade both countries face the same commodity prices and therefore their factor prices (and production techniques used) are also the same.

What happens to the factor-price equalization theorem if countries do not share the same technology? Obviously there is no longer any tendency for free trade to bring about equalization. However, even in this case a strong result obtains, and this might be described as the "Factor-Price Determination" theorem: If a country produces as many commodities that are freely traded on world markets as it has factors of production (two apiece in the simple model), all (both) its factor prices are completely determined by the set of commodity prices ruling in world markets. That is, even though there are presumed to be no direct world markets in factors of production, the country has no power to affect its distribution of income among factors unless it purposely interferes with free trade (e.g., by levying tariffs on imports or taxes or subsidies on exports). It is sometimes argued that free trade is the optimal policy for a small country, that is, one unable to affect world commodity prices. However, the country may put some value on being able to affect its local distribution of income, in which case free trade might be considered too heavy a price to pay. Furthermore, even without equivalence in productivities, consider the possibility that immigration takes place in the more advanced country. As long as traded commodity prices stay constant there will be no pressure for the wage rate to fall. (Try this out on your labor economist colleague.)

[FIGURE 1 OMITTED]

V. MIX AND MATCH

There are numbers of possibilities wherein the setting involves a mixture of the specific factors model and the Heckscher-Ohlin model. The former has been interpreted by Neary (1978) and others in a temporal setting as a short-run version of a model in which capital is specific between sectors, but with the passage of time capital can move and the model becomes a Heckscher-Ohlin model with both factors of production mobile between sectors. (20) In many ways this seems quite realistic, but for some purposes the consequences may appear to be surprising.

Regulations and forms of licensing sometimes have the effect of granting specificity to a form of capital (physical or human) in a setting in which other forms of capital may be exactly similar, but are not allowed to relocate to an industry that makes use of the "licensed" form of capital. Figure 1 makes use of a box diagram showing an initial situation at point A, a point on the contract curve arbitrarily chosen so that the return to capital is the same between industries 1 and 2. Now suppose that there is an increase in the price of the first sector, in which the "licensed" owners of capital work. If these regulations prevent capital from moving from the second industry to the first, labor is the only mobile factor and there is a movement to point B. Capital owners in the first sector are delighted, and their return, [r.sub.1], increases by a greater relative amount than the price increase, with the wage rate rising, but by less than does [r.sub.1]. What would be the fate of the return to capital in the first sector if the "licensing" provision were no longer allowed? If capital in the second sector joined labor in flowing to the first sector in the same proportions used by the first sector until point C on the contract curve is reached, there would be no change in the return to capital in the first sector. However, free mobility of capital as well as labor would prompt an even greater flow of factors until a point such as D is reached. (21) The new equilibrium wage rate, once capital as well as labor becomes mobile, actually falls because I have assumed the second sector is more labor-intensive. Capitalists in the first sector are originally concerned when capital from the second sector invades their turf--but such capital brings with it a higher labor/capital ratio than used in the first sector at B (the equilibrium if only labor were mobile). Higher labor/capital ratios serve to increase capital's return and, although [r.sub.1] has increased more than price if the "licensing" restrictions were in effect (moving the equilibrium to B), [r.sub.1] is increased even more as the labor/capital ratio is raised by the even greater flow of factors from the first industry. (This possibility might prove a hard sell to capitalists in the first industry, and depends, of course, on sector 1 being capital-intensive.)

Such an example serves to contrast the way in which price changes alter wages and capital returns in the specific factors model and the Heckscher-Ohlin model. Equation (2) for the specific factors model shows that the effect of a price change (say in the first sector only) on the wage rate is dampened, the expression {[[theta].sub.1][i.sub.1][s.sub.1]} being a fraction that multiplies two relative features of technology (the relative labor-intensity ranking, [i.sub.1], and the relative flexibility in sector 1, [s.sub.1]), together with the relative importance of the first sector in the national income, [theta]1. What would the comparable expression for the wage change in the Heckscher-Ohlin model reveal? Refer back to Equation (1), and consider the pair of competitive profit equations of change that would consist of an expression for sector 1 as in Equation (1), and a second for sector 2 that would have a zero value for the price increase. Solve this pair for the relative change in the wage rate to obtain the value shown in Equation (3):

(3) [??] = {[[theta].sub.K2]/[[[theta].sub.K2] - [[theta].sub.K1]]}[[??].sub.1]

In the setting of the preceding paragraph, this shows a drop in the wage rate accompanying an increase in [p.sub.1]. What is noteworthy (in comparing this with the specific factors result shown in Equation [2]) is what is missing: The only feature of technology that is relevant in Equation (3) is the factor-intensity ranking, not the relative degree of factor substitutability and, what may be even more surprising is the absence of any parameter suggesting the importance of the industry that has received an increase in price. In the Heckscher-Ohlin model, it seems to make no difference whether the first sector comprises 50% of the national income or only 2%. (22)

This difference between the two models in the manner in which commodity price changes affect income distribution is also found if technical progress takes place (and, to simplify, commodity prices are kept constant). The two features of any technical progress that takes place in a single industry are the extent of the technical progress and the bias in technical progress. By the extent of technical progress here is meant the Hicksian measure of technical progress, the relative reduction in unit costs of production that would take place if there were no change in factor prices. For infinitesimal changes in technical progress at constant prices in industry i, the effect on income distribution would follow by replacing [[??].sub.i] in Equation (1) by [[pi].sub.i], the Hicksian measure of the extent of technical progress. The bias in technical progress indicates the relative extent to which the ratio of labor to capital that would be utilized after technical progress at initial factor prices would be reduced. (23) For small changes the bias in technical progress does not affect factor prices in the Heckscher-Ohlin setting for the same reason that changes in endowments would not affect factor prices unless commodity prices changed. In the 2 x 2 basic version of the model the real wage rate increases (and the return to capital falls) if technical progress only takes place in the first industry and this industry is relatively labor-intensive, regardless of whether technical progress is of the Hicksian labor-saving or capital-saving kind. (24)

Things are different if technical progress takes place in a specific factors setting: the bias in technical progress indeed affects factor prices for a given extent of the progress even in the infinitesimal case where calculus is used in comparative static exercises (and this, of course, is standard procedure in most trade theory analyses). With more factors than commodities in specific factors models, changes in factor endowments affect factor prices even if commodity prices are constant, so that factor bias in technical progress does have an influence on factor prices independent of the extent of progress. Surprises are to be found nonetheless. The analysis in Jones (1996) for a specific factors setting investigates a case in which all sectors of the economy (for any number of commodities) experience technical progress of the same extent in each, progress that is purely Hicksian labor saving--at initial factor prices a unit of each good would be produced with the same amount of capital but less labor input. Although a natural response in such a case would be that the wage rate (real wage, in the case in which prices are held constant) must fall, note that some factor(s) of production must benefit from technical progress. The surprise that may be in store: labor might be a factor that gains from such progress. What would be required is that elasticities of substitution in production throughout the economy are, on average, sufficiently high. Would Cobb-Douglas suffice? That would be more than sufficient; the condition for labor's real wage to increase in this case of pure labor-saving technical progress is that the average value (over all sectors) for elasticities of substitution in production exceed the ratio of the average relative share of capital to the relative share of labor, a ratio usually taken to be less than 1/2.

[FIGURE 2 OMITTED]

So far the remarks about the Heckscher-Ohlin model have been focused on the case of two produced commodities. If a country is engaged in free international trade the case of many commodities is simple to handle because trade allows a great concentration in the number of commodities produced without restricting the number of commodities a country might consume. (The Ricardian model, of course, shows this in the extreme case in which the movement to free trade allows a country to concentrate on producing the single commodity in which it has the greatest comparative advantage.) The reason: No more commodities need be produced than the number of factors of production--one in the Ricardian case, and two in the 2 x 2 Heckscher-Ohlin model. Suppose in a trading world with many commodities only a pair of factors, capital and labor, is required to produce each. Figure 2 illustrates how a country that is growing and developing, such that its overall capital to labor endowment ratio increases, changes the pattern of its production with growth. The input requirements for each of four different commodities are shown in Figure 2, with required capital/labor input ratios rising monotonically as wage/rental rates increase. (25) Furthermore, assume that as the country (call it Home) develops, world commodity prices remain unchanged. Such given prices lead to the heavily lined locus whereby production patterns systematically change with growth: if Home's endowment capital/labor ratio is quite small, Home concentrates on producing the most labor-intensive commodity, 1. When Home becomes more capital abundant, its wage/rental ratio improves until it is able to start producing the second commodity as well as the first. (26) At this stage further small increases in the endowment capital/labor ratio leave factor prices unchanged because Home is producing both commodities at given prices. Asymmetrical changes are taking place along this first "flat" in Figure 2: as K/L increases, Home shifts resources out of the first commodity into the second, until it is completely specialized to the second commodity. Further increases in K/L from that point do result in increases in the wage/rental ratio, until Home can begin producing commodity 3, even more capital/intensive than commodities 1 and 2. Such a process with endowment growth continues for any number of commodities traded on world markets (only four commodities in Figure 2).

My own experience teaching this material to undergraduates is that the kind of situation shown in Figure 2 is more interesting to them than is the basic 2 x 2 Heckscher-Ohlin model. Here the basic question becomes, "Which commodities does a country produce?" Because a country can specialize to a great extent when it enters into international trade, as its circumstances change (becoming more developed--increasing its capital/labor endowment proportions) the answer to this question systematically changes. As well there is the question: "As capital is accumulated, or as immigration occurs, are wages and returns to capital changing?" The answer is maybe, sometimes yes and sometimes no. And if more than a single commodity is produced, note that at the microlevel growth is not apt to be balanced. That is, in a context of trade, there typically will be some (one in this simple case) sector expanding while another contracts. Uneven growth patterns at the microlevel are to be expected even if at the macro level (i.e., in the aggregate) the country were to grow at a fairly regular rate. (27)

Although Figure 2 does exhibit Home concentrating its production when engaged in trade either to a single or a pair of commodities, suppose that there are many more commodities consumed and produced on world markets. Without increasing the number of productive factors used in an industry beyond two (and thus maintaining the simplicity of not having to deal with the possibility of factor complementarity or different degrees of substitutability) it is possible to alter this setting by creating a hybrid model making use of both of the two production models being discussed in this paper, the specific factors model and the Heckscher-Ohlin model. (28) Let some labor (or capital as well as labor) be used each period to produce new capital equipment (i.e., to engage in investment). To simplify (leaving some of the alternative important features to macro-economists), assume that it is a constant flow of inputs each period that is used for investment purposes. The crucial feature is that newly created capital is of the form that is specific to the particular sector, or pair of sectors, that in that period yield the highest rate of return to capital. This selection (to the best single or pair of commodities) may not be the same as was made in the previous period or the period previous to that. In other words, there may be several or more sectors actively producing this period because in the past these sectors have been the winners attracting new investment even though they are no longer winners in the current period. Eventually the return to specific capital in some sectors may no longer remain positive, leading Home to stop producing that commodity. (As well, technical progress may result in better types of specific capital so that older types no longer stay in use.) Thus labor not used for current investment is absorbed in two other kinds of activity: (a) it is used with the new capital to produce (or increase production of) this period's sector(s) yielding the highest return to capital, and (b) it is used in cooperation with the specific capital found in other sectors that have been favored in the past and are still actively producing. The consequence: History matters, and although any producing sector uses only a pair of inputs, the panoply of current production of commodities and array of specific factors is much less compressed than in the 2 x n version of the Heckscher-Ohlin model. Furthermore, it might even be the case that new investment is not made in any export sector, but instead is received by a sector that competes with imports. (29)

VI. CONCLUDING REMARKS

As mentioned in Section I, competitive trade theory has on display a number of surprising results (or paradoxes) whose source resides primarily in the nature of income effects in demand. (30) These are results which can be developed in the so-called Exchange Model which, I would argue, can be thought of as one of a set of four prominent competitive models of production that are used in trade theory. The Exchange Model is one in which outputs of each commodity available in supply are considered fixed (or, as in the case of immiserizing growth, change by an arbitrary amount, independent of any change in commodity prices). To introduce production in such a setting let the economy have a pair of different kinds of labor, each suited only to a particular occupation so that if the factor endowment bundle is fixed, so is the commodity endowment vector. The opposite extreme is the Ricardian model, in which the transformation schedule exhibits a constant rate at which production of one commodity can be reduced to produce more of the other. The final two sets are those discussed in this paper, the specific factors model and the Heckscher-Ohlin model.

There is a recent example in competitive trade theory that serves to illustrate the theme that a good criterion for a model is that it corresponds to common sense as well as being capable of yielding (and explaining) surprising results. The multicommodity version of the Ricardian model was used by Samuelson (2004) to admonish those economists who seemed to be excessive in their praise for the benefits flowing from the world's movement toward greater degrees of globalization. It was not that Samuelson disagreed with the general favorable outcome of such globalization, but he was anxious to emphasize that not every country would gain all the time, because more trade might result (and generally would) with terms of trade turning against some countries. At the time of his article, pointing to oil-importing countries would provide a good example. In terms of results found with this Ricardian model, I mention in passing the possibility which Jones and Roy Ruffin (2008) analyzed concerning gains or losses to a country (call it Home) which has an absolute advantage in many goods (say all) compared with another (call it Foreign). Suppose Foreign acquires through stealth or gift the superior technology whereby Home's best export commodity is produced. Could Home gain by such a loss? The answer we found seemed to us surprising: Consider the relative size of the two trading countries, [L.sup.*]/L. There is a sequence of such relative sizes such that, with some restriction on demand (say Cobb-Douglas with equal spending shares among commodities for both countries), Home would actually gain even though it has lost its best export commodity. Involved is a balancing of the gain to Home consumers from being able to take advantage of a lower price for its former best export commodity and the potential loss from an increase in price of other goods produced in Foreign and imported by Home when Foreign's wage rate increases from the technological acquisition. The word "when" should be changed to an "if" because for some pairs of country size the foreign wage rate either does not increase, or at least not by very much. This result would indeed seem surprising. (31)

A common characteristic is found in all these cases discussed here and mentioned earlier: They all reflect possibilities that are found in competitive general equilibrium models of production, in which there is always more than one market--some are commodity markets and some are factor markets. Surprising results can be found when these markets interact, even though the structural form for production may seem to be very simple and to reflect common sense. This is what gives these models value in trying to understand, say, the possibilities involved when countries trade with each other.

doi: 10.1111/j.1465-7295.2010.00335.x

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(1.) This result also served to query the argument put forward by Stolper and Samuelson (1941) that a tariff imposed by a country importing a labor-intensive product (a country presumably like the United States) would unambiguously raise the real wage. As a consequence, the Stolper/Samuelson wording was frequently changed to asking about the effect of a change in the domestic relative price of a commodity upon the real wage.

(2.) The literature on what came to be called the Three-Agent Transfer Problem is quite extensive (and, at times, a bit contentious), and includes Johnson (1960), Komiya and Shizuki (1967), Gale (1974), Chichilnisky (1980), Brecher and Bhagwati (1981), Yano (1983), Bhagwati, Brecher, and Hatta (1983), and Jones (1984, 1985).

(3.) The literature goes back to Edgeworth (1894) and, in the 1950s. to Johnson (1953, 1955), and Bhagwati (1958).

(4.) When I was an undergraduate student at Swarthmore College, I recall mentioning to a History Professor (Prof. George Cuttino) that I was thinking of majoring in Economics. In an effort to dissuade me, Prof. Cuttino remarked, "Economics is just horse sense couched in verbiage." That sounded great to me, so I did decide on Economics.

(5.) See, for example, Chapter 5 of Caves, Frankel, and Jones (2007).

(6.) The recent focus (in so-called "new, new" trade theory) is on the heterogeneity of firms within an industry. The specific factors model can usefully be used in such an analysis by letting the returns to a factor specifically tied to a firm differ among the industry's various firms. This allows for a competitive model to be used in firms having different productivities, as captured by Ricardian "differential rents" to specific factors within an industry.

(7.) The "hat" notation for the relative change in the wage rate, say, equals dw/w. Note that for the left-hand side of Equation (1) to represent the relative change in unit costs for small changes, it is not necessary to assume that technology is rigid (i.e., fixed input/output coefficients), because for small changes the alterations in techniques of production called for by factor price changes lead to second-order changes in unit costs.

(8.) It may seem surprising to speak about factor-intensity rankings in specific factors models where commodities employ different kinds of capital. However, commodities do use labor as a common factor, and thus a labor distributive share comparison can be made. It turns out that in the 2 x 2 Heckscher-Ohlin model in which both commodities use a common type of capital (as well as labor), so that physical factor proportions used in the two industries can be compared, such an intensity ranking corresponds exactly to a comparison of labor distributive shares.

(9.) See Jones (2007b).

(10.) See Caves, Frankel, and Jones (2007), Supplement to Chapter 5.

(11.) This result, wherein both wage rate and return to capital in one sector might increase more than in another even for the same degree of industry protection may seem less surprising by considering Equation (1). With [[??].sub.i] > [??] > [??] for either industry (if each get protection), both [??] and [[??].sub.i] could be larger in the first sector than comparable values for the second sector as long as labor's share is larger in the first sector than in the second, which I am assuming.

(12.) See Jones and Dei (1983) as well as Jones (2000), Chapter 3.

(13.) For details, see Jones (1989).

(14.) This is an example of how, even in a fairly large dimensional general equilibrium framework (17 equations in this 5 x 4 setting with given commodity price for commodity Y [and [Y.sup.*]] and a given price increase for commodity X), some results do not need the full set of equations of change--here only the use of Equation (1) for Home and the comparable equation for X-production in the Enclave is required. Of course more information would be necessary to determine in which direction X-capital moves.

(15.) It was rejected by the American Economic Review, and published later by the Review of Economic Studies in the United Kingdom.

(16.) For a discussion (and disagreement) about the importance of ruling out joint production see Samuelson (1992) and Jones (1992). In this two-factor setting, the lack of joint production means that each of the two production activities uses both factors to produce a single commodity.

(17.) In the Stolper/Samuetson paper, techniques are assumed to be sensitive to factor prices, so that a tariff on labor-intensive importables causes both labor and capital to move along the contract curve in the production box towards production of importables, raising capital/labor ratios in both sectors. This kind of argument is correct, but a question can be raised about this result if technology is rigid in both sectors, in which case there is no change in either output and capital/labor ratios used in each sector remain constant. The result still holds. Indeed, a more simple argument suffices (whether or not technology is flexible): Use Equation (1) with a positive price change for the labor-intensive industry and a similar equation with a zero price change for the capital-intensive sector, and solve the pair for the factor-price response. This leads to a wage rate response to a change in a commodity price as shown below in Equation (3). See Jones (1965).

(18.) Some years later Hicks (1960), in referring to the simple Heckscher-Ohlin 2 x 2 model with fixed input/output coefficients, thought it strange that with given commodity prices the returns to labor and capital would be independent of factor supplies and that full-employment levels of outputs seemed to be determined independent of demand for given factor supplies.

(19.) This of course assumes that relative factor intensities differ between commodities. As well, as Samuelson emphasized in his 1949 article, it assumes that the relatively labor-intensive commodity in one country is the same as that in the other. The opposite case leads to the factor-intensity reversal problem, much discussed after the appearance of the Leontief (1953) Paradox. As discussed later, in the multicommodity case equalization of factor prices with trade requires that both countries produce the same pair of commodities.

(20.) An alternative method in which specific capital can be converted to mobile capital was suggested by Sanyal and Jones (1982) in which capital of one specificity can be converted to capital of another through international trade.

(21.) The movement from B to C first, and then to D is quite arbitrary; the important movement is from B to D, revealing that when capital also becomes mobile both factors move towards the capital-intensive first sector in a way that increases the labor/capital ratio used in both sectors (in response to a lower wage rate).

(22.) Recall that expressions such as (2)and (3)refer to infinitesimal changes. For finite price changes these solutions are roughly correct, but if the first sector is very small, not much of a price reduction in the first sector would be necessary for the economy to become completely specialized in the second sector, thus making further price reductions for the first having no effect on the economy's nominal wage rate, although it does on real wages.

(23.) Let [[??].sub.Li] and [[??].sub.xi] denote the relative decreases in unit labor and capital requirements per unit output in the ith sector that would take place with technical progress if factor prices were kept constant. The labor-saving bias in technical progress in sector i would be measured by {[[??].sub.Li] - [[??].sub.Ki]}.

(24.) Bias does matter if technical progress is of finite size. However, there is still a surprise left: In the work of Findlay and Jones (2000), an illustration is provided that contrasts two possibilities of technical progress in the capital-intensive sector (in the 2 x 2 setting), with each possibility yielding the same (Hicksian) extent of technical progress. One possibility illustrates a slight capital-saving bias in technical progress that also saves on labor. The other exhibits labor-using technical progress in the capital-intensive sector. In both cases wages fall (since progress is only in the capital-intensive sector). However, the fall in the wage rate is more severe in the case in which progress has a labor-using bias. The rationale for this surprising result is found in the fact that if there is a labor-using bias in the capital-intensive commodity the gap separating factor intensities between sectors is narrowed. (For example, note the denominator in the solution for the wage change in Equation [3], which, if it is narrowed in absolute terms, causes the wage rate to fall even more if the first sector is capital intensive.)

(25.) These curves are drawn (arbitrarily) so that no factor-intensity reversals take place.

(26.) Figure 2 is based upon what is called the "Hicksian Composite Unit Value Isoquant," as found in the work of Jones (1974) and Caves, Frankel, and Jones (2007, pp. 106-108).

(27.) Further details are found in the work of Jones (2004). This explanation assumes that all commodities are traded on world markets, a situation that does not take account of nontraded commodities.

(28.) This hybrid model is described briefly by Jones (2007a).

(29.) That is, this period's highest rate of return to capital might be found in a sector in which output is quite a bit less than current consumption.

(30.) Once again I ignore the Leontief Paradox in this catalogue.

(31.) Another example in which trade theory suggests a surprising possibility for wage rates has emerged from the literature on fragmentation of production activities whereby various parts or "fragments" may separately be produced in different locales, sometimes in different countries. In this literature, there emerges the possibility that a quite labor-intensive fragment of production might be outsourced from a highly developed country to a country with much lower wage rates. The commonly accepted view that such outsourcing must result either in greater unemployment or lower wage rates in the developing country does not necessarily follow--Home wages might increase. The Heckscher-Ohlin framework is exploited by Jones and Kierzkowski (2001) to describe how this can happen. More recently this kind of phenomenon has been discussed by Grossman and Rossi-Hansberg (2008) and Baldwin and Robert-Nicoud (2010).

Jones: Xerox Professor of Economics, University of Rochester, Rochester, NY 14627-0156. Phone 585-275-2688, Fax 585-256-2309, E-mail ronald.jones@ rochester.edu
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