Mundell and Markusen each wrote classic papers on the relationship between trade and factor movement. Mundell showed that substitution holds in the Heckscher-Ohlin model. Markusen challenged the substitution result and showed in five different models that removing barriers to factor movement results in complementarity under free trade, identical factor endowments, and a change in any one of the other assumptions underlying the Heckscher-Ohlin model. The author generalizes Markusen's analysis by considering the liberalization of barriers to factor movement under any non-negative level of protection, and liberalizing trade barriers under factor mobility. He shows that (1) substitution holds at high protection levels, (2) complementarity holds at low protection levels, and (3) either substitution or complementarity hold under large tariff changes.Free Trade,Trade Law,Economic Theory&Research,Trade Policy,International Trade and Trade Rules

Schiff, Maurice

English

Research Papers in Economics

 
Substitution in Markusen’s Classic Trade and 
Factor Movement Complementarity Models*   
 
 
 
Maurice Schiff 
World Bank and IZA 
 
Abstract 
 
Two classic papers on the relationship between trade and factor movement are Mundell 
(1957) and Markusen (1983). Mundell showed that substitution holds in the Heckscher-
Ohlin model. Markusen challenged the substitution result and showed in five different 
models that removing barriers to factor movement results in complementarity under free 
trade, identical factor endowments and a change in any one of the other assumptions 
underlying the Heckscher-Ohlin model. This paper generalizes Markusen’s analysis by 
considering: i) the elimination of barriers to factor movement under any protection level; 
and ii) a change in trade barriers under free factor movement. I show that: a) substitution 
holds under high protection; b) complementarity holds under low protection; and c) either 
substitution or complementarity hold for large increases (reductions) of low (high) 
protection rates. 
    
 
 
World Bank Policy Research Working Paper 3974, August 2006 
 
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the 
exchange of ideas about development issues. An objective of the series is to get the findings out quickly, 
even if the presentations are less than fully polished. The papers carry the names of the authors and should 
be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely 
those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors, 
or the countries they represent. Policy Research Working Papers are available online at 
http://econ.worldbank.org. 
 
 
 
* I would like to thank Mohammad Amin, Arye Hillman, James Markusen, Hillel 
Rapoport and participants at a seminar at Bar-Ilan University for their useful comments. 
WPS3974
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1. Introduction 
  The nature of the relationship between trade and factor movement has long been of 
interest to economists. The two classic papers in this literature are Mundell (1957) and 
Markusen (1983). Mundell used the Heckscher-Ohlin framework to show that international 
trade and factor movement are substitutes.
1 Markusen (1983) provided a strong challenge to 
the conventional wisdom of substitution between trade and factor movement. He presents 
five models in which he assumes free trade and identical endowments, and successively 
changes one of the other assumptions underlying the Heckscher-Ohlin model. He shows that 
eliminating barriers to factor movement results in complementarity.
2 
This paper generalizes Markusen’s (1983) analysis by considering i) the elimination of 
barriers to factor movement under any protection level, and ii) a change in trade barriers 
under free factor movement. I show that substitution holds under high protection levels, 
complementarity holds under low protection levels, and either substitution or 
complementarity hold for large increases (reductions) of low (high) protection rates.3 The 
standard result that an increase and decrease in protection levels have opposite effects 
does not necessarily hold in this case.     
                                                 
1 This result seemed intuitive and was therefore appealing to policymakers and analysts: labor could either 
export labor-intensive goods or migrate and produce them in the destination country. As the then President of 
Mexico Salinas said during the NAFTA negotiations: “We want to export goods, not people.” 
 
2 This result obtains in Markusen and Svensson (1985) as well. Another study is Wong (1986), which 
derives necessary and sufficient conditions for substitutability and complementarity in a general 
equilibrium framework where international differences in factor endowments, tastes or technologies are 
possible. The framework differs from Markusen’s in two ways. First, the paper considers the international 
movement of one factor, with the other factor assumed to be immobile. More importantly, it assumes that 
capital moves without its owners who repatriate the income from capital abroad. This complicates the 
analysis because solutions depend on the assumption about the good used for repatriation.   
 
3 Lopez and Schiff (1998) show in a three-factor model with migration costs and financing constraints that 
trade and skilled labor are substitutes while trade and unskilled labor are complements.   2
The remainder of the paper is organized as follows. Section 2 presents 
Markusen’s (1983) model and complementarity result. Section 3 shows the conditions 
under which substitution and complementarity obtain under both liberalization of factor 
movement and changes in tariff rates. Section 4 concludes.  
 
2. Complementarity in Markusen’s (1983) Models 
The classic paper on complementarity between factor movement and trade is 
Markusen (1983). Markusen’s objective was to challenge the received wisdom and 
demonstrate that trade and factor movement were as likely to be complements as 
substitutes.  
He assumes identical relative factor endowments in both countries and successively 
changes one of the other basic assumptions underlying the Heckscher-Ohlin model, 
namely i) identical technologies in both countries; ii) identical homothetic preferences; 
iii) constant returns to scale; iv) perfect competition; and v) absence of domestic 
distortions in either country.  
Markusen (1983) presents five models, each corresponding to a change in one of 
these assumptions. He states that the complementarity result in each of his models is 
based on the fact that “… each equilibrium involves a country having the relatively high 
price for the factor used intensively in the production of the export good” (pp. 342-343). 
Thus, factors move to the other country’s sector that uses them intensively, resulting in an 
increase in trade. This implies that trade and factor movement are complements.  
Given that the same finding is obtained in each of Markusen’s models, I 
arbitrarily select the technological difference model to present the complementarity result   3
in this section. The relationship between trade and factor movement under trade barriers 
is derived in Section 3.   
Markusen considers a 2x2 model, with countries 1 and 2 and and sectors X and Y. 
Markusen assumes identical endowments, free trade and prohibitive barriers to the 
movement of factors. Assuming all the other Heckscher-Ohlin conditions hold, including 
identical technology, implies that Country 1 and Country 2 are identical and autarky 
prevails.  
  Assume now that Country 1 has a Hicks-neutral technological advantage in 
sector X, i.e.:    
2 1 ), , ( ), , ( λ λ λ > = = Yj Yj j Xj Xj j j L K g Y L K f X ,                  (1) 
where Xj (Yj) = output of X (Y) in Country j (j = 1, 2), Kij (Lij) = capital (labor) in sector i 
(i = X, Y) in Country j, and  j λ  is the technology level in sector X  in Country j.  
Country 1 has a comparative advantage in the production of X. Thus, it exports X 
under free trade and imports Y. Assume arbitrarily that X is labor-intensive and Y is 
capital-intensive. Then, as Markusen has shown,  2 1 2 1 , r r w w < > .  
Eliminating the barriers to factor movement leads to labor flows from Country 2 
to Country 1 and capital flows from Country 1 to Country 2. This increases the supply of 
labor and reduces the supply of capital in Country 1, and vice versa for Country 2. Thus, 
factors flow to the sector that uses them intensively, resulting in an increase in the 
production of the export sector in both countries and an increase in trade flows. Thus, 
factor movement and trade are complements.   
   4
3. Relationship between Trade and Factor Movement under Trade BarriersMarkusen 
(1983)’s complementarity result was obtained by eliminating barriers to factor movement 
in the absence of protection. This paper generalizes Markusen’s analysis by i) examining 
the relationship between trade and factor movement under any trade barrier, and ii) 
considering the liberalization of both commodity and factor flows.  
I show that substitution obtains for high trade barriers and complementarity for 
low barriers.
4 The latter is presented in Section 3.1 and the former in Section 3.2.  Section 
3.3 examines quantum changes in trade barriers. 
 
3.1. Complementarity under Positive Tariffs 
Assume that the initial tariff is positive (t > 0). This has no impact on goods or 
factor prices under identical technologies because trade is absent in this case. Since the 
two countries are identical in factor endowments, technology, and preferences, it follows 
that goods and factor prices are identical under these conditions.  
Assume now that, as in Section 2 above, Country 1 benefits from a Hicks-neutral 
technological advantage  1 λ  >  2 λ  in its labor-intensive sector X. This implies that Country 
1 exports X and Country 2 exports Y.  Section 2 showed that the technology shock raises 
the wage rate and reduces capital’s rental rate in Country 1 relative to Country 2, i.e.,  1 w  
>  2 w  and  1 r  <  2 r .  
Given that trade takes place following the technology shock, a tariff in Country 2 
raises the price of its labor-intensive importable Y, resulting in a lower rental rate  2 r  and 
                                                 
4 As in Mundell (1957), trade takes place at the protection levels under consideration.     5
a higher wage rate  2 w . Whether  1 w  >  2 w  and  1 r  <  2 r  or vice versa depends on the tariff 
rate.  
Figure 1 depicts the relationship between the tariff rate and factor flows. The 
figure shows two distinct regions which are separated by the tariff rate t*. At t*,  1 w  =  2 w  
and  1 r  =  2 r , the level of factor movement M = 0, and the impact on M of an infinitesimal 
change in t is  t M ∂ ∂ /  = 0.  
The region where complementarity prevails is defined by the range of tariff rates t 
< t* for which  1 w  > w2 and  1 r  <  2 r . In that range, tariff rates are too low to change the 
relationship between factor prices generated by the technological advantage in good X in 
Country 1.  
We examine the impact of changes in barriers to both trade and factor movement. 
Eliminating barriers to factor movement implies that capital flows to Country 2 and labor 
flows to Country 1. This raises output of the export sector in both countries and reduces 
that of the import sector. Since trade increases as well, it follows that factor movement 
and trade are complements.  
Second, a reduction in the tariff increases trade. It also lowers the price of good Y 
in Country 2, thereby reducing the wage rate w2 and raising the rental rate of capital  2 r . 
Given that  1 w  > w2 and  1 r  <  2 r , it follows that the tariff reduction raises the international 
wedge in factor prices. This results in an increase in the movement of labor from Country 
2 to Country 1 and an increase in the movement of capital from Country 1 to Country 2. 
Since both trade and the movement of labor and capital increase, trade and factor 
movement are complements.    6
This is shown in Figure 1. The derivative  t M ∂ ∂ /  < 0 in the region where t < t* 
and a reduction in the tariff, say from t2 to t3, raises both factor movement (from M2 to 
M3) and trade.  
The same result obtains with a tariff in Country 1. For a low tariff rate, the 
international factor price relationship is  1 w  > w2 and  1 r  <  2 r . A reduction in the tariff rate 
lowers the price of the capital-intensive importable good, resulting in a reduction in  1 r  
and an increase in  1 w , thus raising the international wedge in factor prices. This increases 
factor flows and results in complementarity between trade and factor movement.  
 
3.2. Substitution under Positive Tariffs 
The region where substitution prevails is defined by the range of tariffs t > t* for 
which  1 w  < w2 and  1 r  >  2 r . These tariff rates are sufficiently high to overturn the 
relationship between international factor prices generated by the technological advantage 
in good X in Country 1.   
Liberalization of factor movement results in a movement of labor to Country 2 
and capital to Country 1. The factor movement reduces the output of the export sector in 
both countries and increases that of the import-competing sectors, resulting in a decline in 
trade. This implies that trade and factor movement are substitutes.    
It is important to note that the pattern of trade is the same whether t > t* or t < t*. 
What does change is the pattern of factor movement, with labor moving from Country 2 
to Country 1 in the complementarity case and from Country 1 to Country 2 in the 
substitution case. Similarly, capital moves from Country 1 to Country 2 in the 
complementarity case and from Country 2 to Country 1 in the substitution case.      7
A reduction in the tariff in Country 2 from t to t’ (t >  t’ > t*) raises the level of 
trade and, as before, lowers the wage rate w2 and raises capital’s rental rate  2 r  in Country 
2. This reduces the international wedge in factor prices, thereby reducing factor flows. In 
terms of Figure 1,  t M ∂ ∂ /  > 0 in that region and a reduction in the tariff, say from t0 to t1, 
reduces factor movement (from M0  to  M1) and raises trade. Thus, trade and factor 
movement are substitutes. The same result obtains for a tariff in Country 1.  
Thus, a technology shock in one of the two sectors in one of the two countries 
reduces the international wedge in factor prices under sufficiently high tariff rates and 
results in substitution between trade and factor movement.    
Markusen (1983) showed that complementarity holds under free trade. This paper 
generalizes Markusen’s analysis to the case of protectionist trade policy and shows that 
substitution holds for t > t* and complementarity for t < t*. The latter includes the free 
trade case examined by Markusen.     
Note that the standard result that an increase and decrease in protection levels 
have opposite effects does not necessarily hold here. For instance, at t = t* an increase 
and a decrease in protection both raise factor movement. Similarly, a decrease in 
protection for t > t* and an increase in protection for t < t* both reduce factor movement.  
 
3.3. Moving Across Substitution and Complementarity Regions 
This section examines quantum changes in trade policy. Assume that Country 2 
starts with a tariff t > t* and liberalizes its trade to the point where the new tariff t’ < t*. 
Thus, trade liberalization moves the economy from the substitution to the   8
complementarity region, for instance in the case of a reduction in the tariff rate from t = t0   
to t’ = t2.  
Such a move does not necessarily imply that migration increases. For instance, 
with a reduction in the tariff rate from t = t0  to  t’ = t2, migration falls from M0 to M2 and 
substitution obtains over that tariff range. If the tariff declines from t = t0 to any tariff 
level t’ < t3, migration increases, so that migration and trade are complements. Similarly, 
a quantum increase in protection may either increase or reduce the level of factor 
movement.  
Hence, whether trade and factor movement are substitutes or complements 
depends on the initial tariff rate and the extent of its change.
  
 
3.4. Prohibitive Tariff 
  The prohibitive tariff rate at which a country no longer trades might be smaller 
than t*.  In that case, Markusen’s result of complementarity between trade and factor 
movement would generalize to all tariff values t ≥ 0.   
 
4. Concluding Comments 
Mundell (1958) used the Hecscher-Ohlin model to demonstrate that trade and 
factor movement are substitutes. Markusen (1983) challenged the received wisdom and 
showed that complementarity holds under free trade in models with identical 
endowments and a change in any one of the other assumptions of the Heckscher-Ohlin 
model.    9
This paper generalizes Markusen’s (1983) analysis by considering  
i) the elimination of barriers to factor movement under any protection level, and 
ii) a change in trade barriers under free factor movement.   
I show that:  
a) substitution obtains under low trade barriers,  
b) complementarity obtains under high trade barriers, and  
c) a change in trade barriers from the low to the high tariff region or  vice  versa                               
can result in either substitution or complementarity. 
 
These findings have important policy implications. Policymakers are likely to 
select a different trade policy under factor mobility than under factor immobility, 
assuming that they take the impact of trade liberalization on factor movement into 
account. The change in trade policy would likely depend on the direction and extent of 
the associated change in factor movement and whether or not the authorities viewed this 
change as desirable. The latter would depend in part on the impact of the change in factor 
movement on the terms of trade.  
  
 
References 
       Lopez, Ramon and Maurice Schiff. 1998. “Migration and the Skill Composition of the 
Labor Force: The Impact of Trade Liberalization in LDCs.” Canadian Journal of Economics 31 
(2): 318-36. 
          Markusen, James R. 1983. “Factor Movements and Commodity Trade as Complements.” 
Journal of International Economics. 14 (3-4): 341-356. 
          Markusen,  James  R.  and  L.  E.  O. Svensson. 1985. “Trade in goods and factors with 
international differences in technology.” International Economic Review 26: 175-92.  
          Mundell, Robert A. 1957. "International Trade and Factor Mobility." American Economic 
Review 47(3): 321-335. 
          Wong, Kar-yiu. 1986. “Are International Trade and Factor Mobility Substitutes?” Journal 
of International Economics 21: 25 – 43.    10
 
Figure 1.  Relationship between Factor Movement and Trade Policy  
in Markusen’s Models 

Are International Trade and Factor Mobility Substitutes?”

Factor Movements and Commodity Trade as

International Trade and Factor Mobility.&quot;

Migration and the Skill Composition of the Labor Force: The Impact of Trade Liberalization in LDCs.”

Substitution in Markusen's classic trade and factor movement complementarity models

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