Choi, E. Kwan

Thompson, Henry

English

Research Papers in Economics

 
 
The Broken Chain of Comparative Advantage 
 
 
 
 
E. Kwan Choi 
 
Iowa State University 
 
 
 
 
Henry Thompson 
 
Auburn University 
 
 
 
 
September 2008 
 
 
 
 
 
The chain proposition of comparative advantage states that when factor prices differ between 
two countries producing many products with two factors, every export of the capital-abundant 
country is more capital intensive than any of its imports.  The present paper shows that the full 
employment condition may break this chain.  It is impossible for a capital-abundant country to 
produce only products with capital intensities greater than its capital-labor endowment ratio.  
 
 
 
 
 
 
Choi, Dept of Economics, Iowa State University, Ames, IA 50011, 515-294-5999, fax 9913, 
kchoi@iastate.edu 
 
Thompson, Economics, Comer Hall, Auburn University, Auburn, AL 36849, 334-844-2910, fax 
5639, thomph1@auburn.edu 
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  1
The Broken Chain of Comparative Advantage 
 
The chain proposition predicts the pattern of trade between two countries producing 
many products with two factors.  In this 2 × n world (n > 2) industry outputs cannot be uniquely 
determined from given factor endowments.  In an attempt to resolve this indeterminacy, Jones 
(1956, p. 6) writes: 
“Ordering the commodities with respect to the capital-labor ratios employed in 
production is to rank them in order of comparative advantage.  Demand conditions 
merely determine the dividing line between exports and imports; it is not possible to 
break the chain of comparative advantage by exporting, say, the third and fifth 
commodities and importing the fourth when they are ranked by factor intensity.” 
Bhagwati (1972) convincingly demonstrates that the chain proposition may not hold 
where factor price equalization occurs.  However, he also suggests (p. 1052) that the 
“proposition, although correct for the case where factor prices are not equalized, is untenable as 
literally stated.  When factor-price equalization is realized, a not unimportant case, a variety of 
crisscrossings are possible.”  
Subsequently, Deardorff (1979) investigates Bhagwati’s conjecture and reasserted that 
the chain proposition holds where factor prices are not equalized.  Specifically, Deardorff (p. 201) 
asserts that “every export of the capital abundant country, by either definition, must be more 
capital intensive than every one of its imports.”  Deardorff’s result has been widely cited in the 
literature.
1  The chain proposition may be deemed to resolve production indeterminacy in the 
model with many products. 
The present note shows that depending on factor endowments, the capital-abundant 
country may export products more labor intensive than some of its imports, and vice versa.  The 
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  2
capital-abundant country certainly cannot produce only the products with capital intensities 
greater than its capital-labor endowment ratio.  Full employment requires that the cone of 
diversification generated by the expansion paths of produced goods spans the factor endowment.  
If the factor endowment point lies outside the diversification cone of the most capital-intensive 
goods, the chain of comparative advantage is broken to satisfy the full employment constraint.  
 
1. A Break in the Chain  
   Consider the production decisions of two countries in the model with two factors and four 
products.  Assume that  
  (i) country A is capital abundant,  ,
AB kk >  where  /
cc c kK L =  is the capital-labor  
endowment ratio of country c, 
 (ii) factor prices are different and  / /
AA BB wr wr > , 
(iii) two industries have capital intensities greater than 
A k  and two other industries have 
capital intensities less than 
B k , i.e., 
2  
  12 34 .
AAAAA kkkkk >>>> (1) 
  Assume there are no factor intensity reversals.  Factor prices between the two countries 
differ and not all conditions for factor price equalization (FPE) are satisfied.  Specifically, FPE is 
not guaranteed with more products than factors. 
In Figure 1, unit value isoquants in country c are labeled  1/ ,
cc
ii y p =  i = 1, 2, 3, 4.  When 
output prices are independently chosen with two factors, each country would produce at most 
two products.  The prices of these two products completely determine factor prices.  The four 
products are ranked by capital intensity as in (i).  Since the wage-rent ratio is higher in country A, 
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  3
the capital intensity for each of its products is higher than in country B, 
AB
ii kk >  for all i.  The 
unit value isoquant  33 1/
AA yp = in country A lies below the unit value isoquant  33 1/
BB yp =  in 
country B.   
Given identical technologies, a higher isoquant implies higher input requirements and a 
higher output level.  That is,  33 1/
BB yp =  at B3 is greater than  33 1/
AA yp =  at A3, implying 
33 ,
BA p p < and country B has a comparative advantage in product 3. 
Deardorff (1979) assumes that factor prices are different between two countries.
 3 
Deardorff’s (1979, p. 201) proof of the chain proposition is stated without regard to the capital-
labor endowment ratio and the full employment constraint.  It implicitly assumes the cone of 
diversification of the “most capital intensive” products spans the factor endowment point.  The 
most capital-intensive products are those with capital intensities higher than  /
oo o kK L = in 
Figure 1, where the unit isocost lines intersect.   
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  4
 
The capital abundant country cannot produce only the two most capital intensive products 
without violating the full employment constraint.  If country A produces product 1, it also must 
produce another product with capital intensity less than k
A, breaking the chain and producing 
product 3 or 4. 
The full employment condition breaks the chain of comparative advantage under the 
present assumptions.  The capital-abundant country A must produce at least one product whose 
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  5
capital intensity is less than its capital-labor endowment ratio, and may even produce the most 
labor intensive product 4.  The capital-abundant country A cannot produce only the most capital 
intensive goods, those with capital intensities greater than 
o k in Figure 1.  To attain full 
employment, the capital-abundant country A must produce one of the labor intensive products.  
In Figure 1, the capital abundant country A is able to produce combinations (1, 3), (2, 3), 
(1, 4) or (2, 4), but it cannot produce (1, 2) or (3, 4).  Given each of these combinations, the 
labor-abundant country B would produce the other two products and the factor intensity chain is 
broken. 
4  The degree of indeterminacy increases with the number of industries.  
 
2. Concluding Remarks 
The chain of comparative advantage in a world of two factors and many products may 
have broken links when resources are fully employed.  The capital-abundant country might 
produce some labor intensive products even though the labor-abundant country could produce 
them with fewer resources.  The literature on the chain proposition implicitly assumes the capital 
abundant country’s factor endowments lie within the diversification cone of the “most capital 
intensive goods,” a condition that generally is not valid for arbitrary factor endowments and 
factor intensities. 
A recent empirical study by Cavusoglu and Elmslie (2005) on nine U.S. manufacturing 
industries for three periods (1970-1985, 1970-1990, 1970-2000) finds no empirical support for 
the chain proposition that all export industries are more capital intensive than import competing 
industries.
5  Specifically, they (p. 414) report that “the chain version of comparative advantage 
does not hold for any of the periods and any balance weight.”  This empirical result is consistent 
with breaks in the chain of comparative advantage. 
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  6
Full employment and balanced trade are ingredients of a complete model with two factors, 
many goods, and two countries.  As the number of products increases, international equilibrium 
is more likely to be characterized by breaks in the chain of comparative advantage.  
  
References 
Bhagwati, Jagdish (1972), “The Heckscher-Ohlin Theorem in the Multi-Commodity Case,” 
Journal of Political Economy 80, 1052-55. 
 
Bhagwati, Jagdish, Arvind Panagariya and T. N. Srinivasan (1998), Lectures in International 
Trade Second ed., MIT Press, 107-29. 
 
Cavusoglu, Nevin and Bruce Elmslie (2005), “The Chain Version of Comparative Advantage: 
An Empirical Investigation,” Review of World Economics 141, 404-21. 
 
Deardorff, Alan (1979), “Weak Links in the Chain of Comparative Advantage,” Journal of 
International Economics 9, 107-209. 
 
Feenstra, Robert (2004), Advanced International Trade, Princeton University Press, 64-98. 
 
Jones, Ronald (1956), “Factor Proportions and the Heckscher-Ohlin Theorem,” Review of 
Economic Studies 24, 1-10. 
 
Romalis, John (2004), “Factor Proportions and the Structure of Commodity Trade,” American 
Economic Review 94, 67-97. 
 
Vanek, Jarosalev (1968), “The Factor Proportions Theory: The n-factor Case,” Kyklos 21, 749-
56. 
 
                                                 
1 For instance, see Bhagwati, Panagariya and Srinivasan (1998), Feenstra (2004), Romalis (2004), 
and Cavusoglu and Elmslie (2005). 
 
2 This is the minimum assumption for country A to break the chain.  Similarly, 
12 34 /
BB B BBB kkK Lkk >> >> is a sufficient condition for country B to break the chain. 
 
3 Deardorff (p. 199) further assumes that (i) two countries trade with no trade impediments so 
that output prices are equal, (ii) production of each product requires that capital (K) and labor (L) 
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  7
                                                                                                                                                             
are available in fixed supply in each country, (iv) production functions are identical between 
countries, concave and (linearly) homogenous, (v) products are ranked in terms of capital 
intensity,  1 ... n kk >>, where  / ii i kK L ≡ , and hence there are no factor intensity reversals 
between any pair of products, and (vi) perfect competition prevails in both countries. These 
assumptions imply FPE in the 2 × 2 case, and can be extended to the even case where n > 2.  
These assumptions are not sufficient to imply FPE with more products than factors. 
 
4 If output prices adjust to guarantee zero profits, country A in autarky can produce (1, 2, 3), (1, 2 
4), (1, 3, 4), or all four goods and still satisfy the full employment constraint.  The output vector 
is remains indeterminate.  
 
5 Cavusoglu and Elmslie (2005) noted a link between capital intensities and investment-labor 
rankings, a result not predicted by the chain proposition. 
 
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 9 / 9

Advanced International Trade,

Arvind Panagariya

Factor Proportions and the

Factor Proportions and the Heckscher-Ohlin Theorem,”

The Factor Proportions Theory: The n-factor Case,”

The Heckscher-Ohlin Theorem in the Multi-Commodity Case,”

Weak Links in the Chain of Comparative Advantage,”

Breaks in the Chain of Comparative Advantage

http://www.econ.iastate.edu/sites/default/files/publications/papers/p11264-2010-04-05.pdf

Breaks in the Chain of Comparative Advantage

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