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Economica, 57. 485-93

Pattern of Trade between Underemployed Economies

By RAVEENDRA N . BATRA and HAMID BELADI

Southern Methodist University and University of Dayton

Final version received 6 September 1989. Accepted 13 December 1989.

In this paper, we have analysed the factors determining the pattern of trade between underemployed economics. We find, among other things, that a iow-wage, iand-abundant country exports the iand-using, labour-intensive product to a high-wage, capital-abundant country. We also find conditions under which a high-wage, capital-rich country may export the labour-iniensive product (the Leontief Paradox).

INTRODUCTION

The following facts should be kept in mind while formulating a theory of a country's pattern of trade.

1. The vast majority of trading countries have suffered from chronic unemploy- ment throughout this century. Even many developed economies such as the UK and USA experienced low to high unemployment during the eariy 1920s, throughout the 1930s, at the end of the 1950s, during the eariy 1960s and throughout the 1970s and 1980s.

2. Some countries rich in natural resources export land-using (or land-inten- sive) products, whereas capital-abundant countries mostly export capital- intensive goods, but at times export the labour-intensive products, some- thing that has inspired the literature on the Leontief Paradox.

3. In spite of the presence of trade, the capital-rich countries have higher wages but lower capital rentals than the labour-surplus and/or land-rich countries—a fact conflicting with the factor-price equalization theorems of the popular Heckscher-Ohlin model.

4. Labour-rich countries usually export either labour-intensive or iand-using commodities.

The purpose of this paper is to formulate a theory of trade that explains the 'stylized facts" mentioned above. Neither of the two popular theories, the Ricardian model and the Heckscher-Ohlin model, is compatible with these facts. Both of these models ignore unemployment and are couched in terms of one or two factors, whereas a realistic theory of international trade must assume at least three factors—labour, capital and land (or natural resources)— which have been incorporated into the empirical literature but not into a theory of trade patterns.

In order to explain the pattern of trade, we first construct a two-sector, three-factor mode! of an underemployed economy. We find that the specific- factor model, which has recently regained its lost popularity, is ideal to capturing the facts mentioned above.

L ASSUMPTIONS AND THE MODEL

Let us assume that there are two sectors, X and Y, with X using capital and labour and Y using capital, labour and land. (X could represent all manufactur- ing where land is relatively insignificant, and Y could represent agriculture,

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mining, forestry and fisheries. I Production functions are linearly homogeneous; producers face perfect markets in goods, capital and land, but not in labour, where real wage is rigid, causing general unemployment in the economy. Capital and labour are fully mobile and employed, and all factors are in inelastic supply. In short, we make all the assumptions of the well-known two-sector, specific-sector model, except that the real wage is determined institutionally."

Let Cij be the ratio of the ith factor and thejth product {i = K, U ^ and j = x,y) where K is capital, L is labour and V is land. With full employment of capita] and land, we have

(1) CK.x + C K , y = ^

and

(2) CvvV'= v;

where K and V are inelastic supplies of capital and land. With producers producing in perfect markets, the price of each product equals the unit cost. Let Y be the numeraire, so that its price equals one, F be the relative price of X, w be the real wage rate, r the real rental of capital and p the real rental of land. Then

(3) wC

and

(4) H-C, ,

With linearly homogeneous production functions, each input-output coefficient depends only on factor prices. Therefore

(5)

and

With this equation, the production side of our model is complete. This is a system of nine variables (X, Y, C:,, C , r and p), nine equations and four parameters (w, P, K and V).

II. THE FACTOR-PRICE DEFINITION OF FACTOR ABUNDANCE

Let us assume that there are two countries, a home country (H) and a foreign country (F). Since labour is in excess supply in both countries, we will first define relative factor abundance in terms of fully utilized factors. Suppose the home country is rich in capital but poor in land relative to the foreign country. Then we define H to be capital-abundant and F to be land-abundant if, in the absence of trade,

(7)

In other words, in the absence of trade, the capital-rich country has a higher rental of land relative to that of capital than does the foreign country. What

1990] PATTERN OF TRADE BETWEEN UNDEREMPLOYED ECONOMIES 487

about the wage rate? Since usually the capital-rich countries are high-wage economies, we assume that

(8) Wft s wj.

In order to use (7) and (S) in our analysis, we need to analyse the relationship between factor and commodity prices. Totally differentiating (3) and (4), we obtain

(9)

and

( 1 0) d^yW* + dKyr* + Bvyp* = 0

where the asterisk denotes proportional change and $ are the factor shares.^ Thus, r* = (dr/r) and so on. From (9) and (10), we obtain

- - « . ^ W (

and

In obtaining (11)-(13), we have made use of the fact that factor shares add to one. Thus,

Equation (13) shows the effect of P and w on the factor-price ratio {pi r), as ( p * - r * ) / P * < 0 . For any given w, a rise in P unambiguously causes a fall in ip/r), whereas for any P, a rise in w causes a rise in (p/r), provided 6i_^> Oi^y. Since w is constant, a rise in P, the relative price of X, must cause a rise in r, otherwise average cost in X will not rise; but since Py = 1 is constant, p must fall, because with w given, r and p must move opposite to each other. Otherwise average cost in Y will not remain constant. On the other hand, for any P, a rise in w must cause a fall in r in X and hence in Y as well. Since w rises and r falls, the reward of land depends on the labour intensity of Y relative to X. If 0Ky0Lx > ^Lv^Kxy then in the physical sense X is labour-intensive relative to Y, and ( P * / R ' * ) > 0 . When the capital-labour ratio in X and Y is the same, then a rise in w combined with a fall in r equally affects the unit cost in Y which is compatible with the fact that P,, is unchanged at one. However, if Y is capital-intensive relative to X, then the relative unit cost in Y falls, and for its price to remain constant p must rise. Thus, when

then

( P * / H ' * ) > 0 .

On the other hand, when labour share is higher in Y, so that 0LX < ^LV, a rise in w hurts Y more than X. Here (p/r) must fall as w rises (see (13)).

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The two forces that affect (p/r) are thus P and w, but not factor supplies. Figure 1 displays these relationships. The negatively sloped curve AB shows that as P rises ip/r) falls for any w. Then as w rises, the curve AB shifts up to CD (where di^ > 0^.), or down to EF (where Bu < ^/.y).

The relationships obtained in Figure 1 can be used to analyse the effect of factor endowments on the pattern of trade. Let us assume that production functions are the same between the two countries. (This is also an assumption of the Heckscher-Ohlin (H-0) theory.) For the time being, let us also assume that the wage rates are the same as well; that is, ŵ = w,. Under these assump- tions, the same relationship between the factor-price ratio and the commodity- price ratio applies lo both countries. Let FH be such a common curve in Figure 2. Since the home country is relatively capital-abundant, its factor-price ratio (p/r) is placed above the factor-price ratio of the foreign country (see (7)). As a result,

(14) P,<P^,

which shows that under autarky the home price of X is lower relative to that in the foreign country. This means that, in the presence of non-intersecting social indifference curves (which we assume hereafter), the home country will export X and the foreign country will expon Y, the land-using product.' The following theorem is now immediate.

F

FIGURE I

p/r

Ux

FlQURE 2

1990] PATTERN OF TRADE BETWEEN UNDEREMPLOYED ECONOMIES 489

Theorem 1. If the institutionally determined real wages between the two countries are close to each other, then the country relatively well endowed in land or natural resources exports the land-using product, and the relatively capital-rich country exports the other product.

Note that this is a very general theorem, and factor intensities play no role in it. This may explain the trade pattern of most oil-exporting countries, such as Saudi Arabia, Kuwait, United Arab Emirates, Mexico, Venezuela, etc., which are rich in oil and export this product abroad. Other countries, such as Canada, Australia and some Third World countries, export minerals for the same reason. Furthermore, it should be noted that the rigid wage rate may be 'too low' and the country may have to import labour from abroad. Thus, the model may also refer to trade between the Arab countries and the West. Many of the Arab countries in fact import labour from Asian countries.

Let us now relax our assumption of similar wage rates between the trading partners and assume that the capital-rich country has the higher real wage than the land-rich country. If the labour share of the two sectors is the same, i.e. if L̂x = ^Ly., then w has no effect on (p/r). In this case. Theorem 1 continues to hold regardless of the inter-country wage differential.

In most countries the land-using sectors, especially agriculture and fisheries, also employ larger number of workers per unit of output than the other sector. This is certainly true of developing countries, but may also be valid with some developed economies. It is interesting to note that the autarkic values of (p/r) depends not only on the levels of endowments of different factors but also on the level of the given wage rate. This is clear from equation (13), where {p/r) is seen to depend on w and P. The endowment effect in this case is via the relative price, P. In other words, even if two countries are endowed with the same amounts of the various factors, ip/r) can have different values in the two countries. Let us then assume that Bt^y> fl^v Here a rise in w reduces {p/r) at any P. If w^ > w^, then the home country's curve relating {p/r) and P will lie below FH in Figure 2. Suppose it is given by hh', whereas in the foreign country this relationship is still given by FH. Then the home autarky- price ratio is given by PJ,. Since it is even smaller than before, we conclude that the home country will still import the land-using product and the foreign country will export it. All this leads to the following theorem.

Theorem 2. A relatively low-wage, land-abundant country exports the land- using product if the latter's labour share is no less than the labour share of the other product, which in turn is exported by the relatively high-wage, capital-abundant country.

What is the role of the factor intensities in this theorem? Factor intensities can be defined in the physical sense or in the value sense. In the value sense, the factor intensities can be defined in terms of factor shares. Thus, Y may be said to be labour-intensive relative to X if ff^. > L̂X- But this implies that

or

490 ECONOMICA [NOVEMBER

(p/r)

Therefore, if Bi_v > Bi_^, then ê x > B^y, which means that X is capital-intensive relative to Y in the value sense. In terms of Theorem 2, a high-wage, capital- abundant country exports X when fl^ > L̂X or &K,. <^KJC- Theorem 2 then implies that a high-wage, capjtal-rich country exports the capital-intensive product.

On the other hand, a low-wage country may also be defined as a labour- abundant country. Thus, a land-abundant country with lower real wage may be said to be a labour-abundant country with lower real wage may be said to be a labour-abundant country as well. Theorem 2 then implies also that a labour-rich country exports the labour-intensive product, as Biy> Bj^^. AM this leads to another theorem.

Theorem 3. A high-wage, capital-abundant country exports the capital-inten- sive product, and a low-wage, land- and labour-abundant country exports the land-using, labour-intensive product.

This theorem is somewhat reminiscent of the Heckscher-Ohlin theorem which highlights the role of factor intensities and inter-country factor endowments.

What happens if the land-using product is not labour-intensive in the value sense, so that 0^ < ^L. ? Here Theorem 3 may not hold, in which case the well-known Leontief Paradox can occur*

If ^L.<^tA, then from (13). {p/r) rises with a rise in w. This case is illustrated in Figure 3, where, unlike in Figure 2, hh' lies above FH., and the home-autarky price ratio may or may not be below the foreign-autarky price ratio. Figure 3 illustrates the case where Ph<P,, so that the high-wage, capital-abundant home country will stilt export X but X is now the labour- intensive product. Similarly, the low-wage, land-abundant country exports Y, which is capital-intensive relative to X. This is the Leontief Paradox. Thus, our model, which yields a Heckscher-Ohlin type of theorem, is also capable of explaining the Leontief Paradox.

III. FACTOR PRICES UNDER FREE TRADE

Under free trade, the Heckscher-Ohlin theorem gives rise to a single outcome, namely that absolute and relative factor rewards are completely equalized

1990] PATTERN OF TRADE BETWEEN UNDEREMPLOYED ECONOMIES 491

between countries. This is one of the most serious flaws of this theorem, because we live in a trading world where factor prices are far from equal.

In our model, however, a variety of outcomes is possible in the free trade equilibrium. Let us first consider the least likely outcome. Suppose, in the absence of trade, that real wages are the same internationally. In this case one common FH curve applies to both countries in Figure 4. Assume that transport costs are zero or negligible; then the same product-price ratio prevails in both countries in the free trade equilibrium. Let Pg be such a price ratio. When FH applies to both countries, then {p/r) is the same in both countries in the free trade equilibrium. This is the case where the absolute factor prices will also be equalized. Even if wages differ between H and F, the FH curve applies to both countries if 0,^ = 6i^,.. In this case (p/r) will be similar internationally but absolute factor prices will differ. Since iv̂ > w,, r,, < rj. This is because r and w are negatively related. And since {p/r)h = {p/r)f, then Ph<pf- Thus, here is a case where relative factor prices of land and capital are globally equal but absolute factor prices are not. All this leads to the following theorem.

Theorem 4. If wages are the same across the countries, then free trade leads to an equalization of all factor prices. If the capital-abundant country is the high-wage country but labour shares are the same between the two sectors, then the relative factor prices of land and capital are equalized but the capital rental and the land rent are lower in the capital-abundant country than in the land-abundant country.

When SL^ < 6i_y and w>, > w,, much of Theorem 4 continues to be valid, although relative factor prices of land and capital in H and F are no longer the same. In this case, the home curve representing the relationship between ip/r) and P lies below FH, which now represents F. In Figure 4, the home curve is now given by hh and in free trade equilibrium, {p/ r)h is given by OA which lies below (p/r)^, the factor-price ratio in F. Still, when w^ > Wf, r,, < Tf. This is because, from (11), it is clear that

(15) r = r{P,w)

with Tp = {dr/dP) > 0 and r^. = (dr/dw) < 0, for all values of 0^. and Ot,.. Thus, with H';, > Wf, rf<r,. Since (p/r),, <ip/r)j in free trade, clearly Pf<pi, in the free trade equilibrium.

p/r

B

p/f).

A

F s

V

\ ^ ^ ^

\ .

* \

FIGURE 4

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When ^L, > di_y, the home curve (h'h') now lies above FH in Figure 4. In the free trade equilibrium,

(16) {plr),>{pfr)f,

but since ŵ > ny, ^s'^^s-'" view of (16), however, p/may no longer be lower than ph under free trade. The following theorem is now immediate.

Theorem 5. Under free trade, the high-wage, capital-rich country has a lower rental of capital than the low-wage country, but the international relationship of the land rental depends on factor intensities.

IV. TRADE AND FACTOR PRICES

In the Heckseher-Ohlin model, trade benefits the country's abundant factor but hurts its relatively scarce factor. In our model, assuming that the land- abundant country exports the land-using product and the capital-abundant country exports the other product (which is ensured when 0(.,. ^^(_J, trade will lower the reward of land and raise the reward of capital in the home country, and do the opposite in the foreign country. This is because in this case, under autarky, P^ < P,. Therefore, in the presence of profitable trade, the relative price of X rises in the home country and falls in the foreign country. Consequently r will rise in H but fall in F, and p will fall in H and rise in F. TTie following theorem is now immediate.

Theorem 6. When the labour share in the land-using sector is no lower than that in the other sector, trade benefits a country's abundant factor and hurts the scarce factor.''

It should be noted that Theorem 6 may not be valid if 6^^ > Bi_y.

V. CONCLUSIONS

Using a two-sector, three-factor model in which land is a specific factor and wages are institutionally determined, we have analysed the factors determining the pattern of trade between underemployed economies. Our results are com- patible with many observed facts. Under the assumptions usually used in the H-0 model, we find that a low-wage, land-abundant country exports the land-using, labour-intensive product to a high-wage, capital-abundant country. On the other hand, if the low-wage country is said to be labour-abundant, then a labour-abundant country exports the land-using, labour-intensive good and the capital-rich country exports the capital-intensive good. This is nothing but a version of the Heckscher-Ohlin theorem derived in a model of unemployment.

The paper also derives plausible conditions under which a high-wage, capital-rich country may export the labour-intensive product. This tends to explain the Leontief Paradox.

Under free trade, if wages are the same across countries, all factor prices are equalized. However, if the capital-abundant country is a high-wage country, then the reward of capital is higher in the low-wage country even under free trade. Thus, unlike the Heckscher-Ohlin model, a variety of outcomes regard- ing factor prices in free trade is possible in our model.

1 9 9 0 ] PATTERN OF TRADE BETWEEN UNDEREMPLOYED ECONOMIES 4 9 3

Finally, we conclude that under realistic conditions trade benefits the country's relatively abundant factor and hurts its relatively scarce factor.*

ACKNOWLEDGMENT

We wish to thank two anonymous referees for helpful comments to a previous draft of this paper.

NOTES

1. The earlier trade models of rigid wages have mainly involved the two-sector, two-factor Heckscher-Ohlin type of model; see e.g. Das (1981). Yu {1982) and BhandaH (1986). The main weakness of this type of model is that it leads to a linear transformation curve or constant average costs in the industries. The production side thus yields limited and unrealistic results. In an earlier paper (1988), Batra and Beladi have shown that, even with rigid real wages, the specilic*factor model used here generates increasing average cost functions for the two indus- tries. The input-output coefficient lechnique utilized here greatly simplifies the analysis. For another application of this technique, see Lahfri (1983).

2. In obtaining these equations, it must be noted that the competitive producer, facing given factor prices, equates the derivative of this unit cost to zero, thereby minimizing his average cost. Thus,

^y + n/Q,, + pdCvy = dAC, = 0

where 4 C , is the average cost of Y. Similarly for X. 3. In order to see the importance of this assumption in the context of the factor-price definition

of factor abundance and the Heckscher-Ohlin theorem, see Batra {1973, Chapter 3). 4. For the latest analysis of the Leontief Paradox, see Casas and Choi (1985). 5. See Pattanaik (1974) for an application of this type of analysis to the effects on savings in a

developing economy. 6. In this paper we have ignored [he well-known physical definition of international factor

abundance, and have focused only on the factor-price definition. This is because labour is not fully employed and does not act as a constraint on the two outputs. However, a physical type of definition does suggest itself. We could define country H to be capital-abundant and country F to be labour-abundant, if

with

By using a fully fledged production model constructed by the authors elsewhere (1988), it is possible to show thai ail our results are valid in terms of the physical definition as well. In the interest of brevity, however, we leave this task to the reader.

REFERENCES

B A T R A , R. (1973). Studies in the Pure Theory of International Trade. New York: St Martin's Press.

——and B E L A I J I , H . (1988). Specific factors, unemployment and trade theory. WeUwirtschaftliches Archiv, 124,435-43.

B H A N D A R I , J . S. (1986). Commercial Liberalization in Less-Developed Countries. New York: Praeger.

CASA.S, F. R. and C H O I , K, E . (1985). The Leontief Paradox: continued or resolved. Journal of Political Economy, 93, 610-15.

D A S , S. P, (1981). Effect of foreign investment in the presence of unemployment. Journal of International Economics. I I , 2 4 9 - 5 7 .

LAHtRi, S A J A L (1983). Capacity constraints, alternative technologies and input-output analysis. European Economic Review, 27, 147-53.

P A T T A N A I K , P. K. (1974). Trade, distribution and saving. Journal of International Economics, 4, 77-81.

Yu, E D E N (1982). Unemployment and the theory of customs union. Economic Journal, 92,399-404.