The Heckscher-Ohlin Model

1. The Heckscher-OhlinModel J. Peter Neary Oxford University and CEPR

2. Preview: Simple General Equilibrium Models The Heckscher-Ohlin Model: Factor-price equalisation The Stolper-Samuelson Theorem The Rybczynski Theorem The Heckscher-Ohlin Theorem The Specific-Factors Model: Comparative statics Short-run to long-run interpretation

3. The Heckscher-Ohlin Model • [A special case of the general competitive model] • Assumptions: • Perfect competition, constant returns to scale • 2 countries: Home and Foreign (*) • 2 factors: Capital K and LabourL • 2 sectors: y1 and y2 [Sometimes, to fix ideas: Manufacturing M and Food F] • Complete intersectoral factor mobility • Key Concepts: • 1. Factor Abundance (of countries): • Home more labour-abundant: k < k*. • 2. Factor Intensity (of industries/sectors): • Facing the same factor prices, sector 1 [M]is more capital-intensive: • K1/L1 > K2/L2 or k1 > k2 • Assume: No "factor-intensity reversals": One sector always more capital-intensive

4. w r Digression: The Unit Cost Function • Proofs require a new diagram: Unit cost or “isocost” diagram • Profitability of an industry depends on price of its output (p) and prices of its inputs (w and r) • Equilibrium given by the unit cost function: p = c(w,r) • Consider the space of factor prices, w and r: • Given p, we seek the locus of points in this space at which the industry just breaks even (the zero-profit locus)

5. w Variable Coefficients K/L r Digression: The Unit Cost Function (cont.) w Fixed Coefficients • With fixed coefficients, this must be a downward-sloping straight line: p = aLw + aKr • Its slope is: dw/dr = aK/aL = K/L • If coefficients are variable, firms can substitute away from the factor which becomes more expensive K/L r • So, as w/r rises, the curve becomes steeper • Hence curve is convex to origin • At any point, the slope of the tangent to it equals the optimal capital-labour ratio at that wage-rental ratio

6. Digression: The Unit Cost Function (cont.) K • Alternative Ways of Representing a Sector’s Technology • 1. Unit Isoquant Diagram • Q = F(K,L) = 1 • slope = MRS = w/r Q > 1 Q < 1 Q=F(K,L) = 1 w/r L w 2. Unit Cost Curve Diagram p = c(w,r) slope = K/L p < AC [ Exercises: Draw both for cases of: (a) Fixed coefficients (Leontief); (b) Perfect substitutes; (c) Cobb-Douglas.] p = c(w,r) p > AC K/L r

7. “Factor Price Equalisation” (FPE) • Consider any industry: • The zero-profit condition implies that price equals unit costs: • p = c(w,r) • Given p, this defines a locus in (w,r) space • (convex to origin, because c is concave in (w,r)) • Equilibrium must lie on this locus • (since points above imply factor prices too high: losses, leading to exit; and points below imply factor prices too low: super-normal profits, leading to entry) • So, equilibrium for both industries is where the loci meet • p > 0 w w p < 0 c2 [slope=K/L] c1 r r

8. K M . . G' G F . G" L O Qualifications to FPE (i) Non-Existence: (More specifically: non-existence of a fully diversified equilibrium) Taken literally, the theorem suggests that, under free trade, countries with very different factor endowments (e.g., U.S. and India) would have the same factor prices BUT It requires that each country produces both goods. Here is where endowments play a role: They determine whether the two countries will produce both goods. To see this, consider factor space: • If not (e.g., G' or G"), then country cannot produce both goods Wesaw that factor usage in both sectors can be determined given theendowment point G • BUT Key assumption was that G laybetween OM and OF

9. Qualifications to FPE (cont.) • (ii) Non-Uniqueness: • Factor intensity reversals are possible • If: Elasticities of substitution differ enough between sectors • (iii) Same number of goods and factors required: • More goods: each country may produce a different mix of goods, more suited to its own factor endowments. • More factors: Specific-factors model a simple example of a model with m > n, which rules out FPE.

10. The Stolper-Samuelson Theorem • Theorem: An increase in the relative price of the capital-intensive good will increase the rental and reduce the wage, relative to the prices of both goods • Note: It refers to “real” wages and rentals • This implies that wage-earners are unambiguously worse off and capital-owners unambiguously better off

11. w Proof of Stolper-Samuelson E • Initial equilibrium at D. • Exogenous Shock: • Price of M rises • So, values of w and r which Msector can pay and still breakeven are higher • i.e., M unit cost curve moves out • Price of M rises by DE/OD%: % increase in r is greater. D H cF cM2 cM1 O r • BUT: Equilibrium moves sideways to H • M is K-intensive: Return to K (r) rises • F is L-intensive: Return to L (w) falls • So: Unambiguous change in real rental and real wage: • ^pF=0 in diagram but this is only a choice of numeraire • Like Rybczynski, price change has a “magnification effect”

12. Algebra of Stolper-Samuelson • Multi-sectoral extension (Ethier 1974): Suppose: • Hence: • Equation (*) for i=1 implies that at least one wjmust increase relative to all goods prices. • Equation (*) for i¹1 implies that at least one wjmust decrease relative to all goods prices.

13. Policy Application: Trade and Wages • The debate: • Increase in relative demand for skilled labour in OECD • Higher wage dispersion in U.S. and U.K., higher and more dispersed unemployment rates in Continental Europe • Is Trade the Explanation? • Increased competition from low-wage countries • => Lower price of unskilled-intensive good (“S” instead of “K”) • => Lower relative wage, by the Stolper-Samuelson Theorem: w [slope=S/L] r

14. Policy Application: Trade and Wages (cont.) • Problems with the Trade Explanation: • Predicts a fall in S/L in both sectors • Predicts a rise in w/r in exporting countries (LDC’s) • Observed changes in price and import volume are not sufficient to explain the changes • More plausible explanations: • Labour-saving technical progress • Outsourcing • BUT: Existing explanations assume perfect competition: • Cannot explain changes in profits or mark-ups • Lower import prices the only form of “increased competition” • Empirical evidence that market structure affects trade impact on unskilled wages • [Oliveira-Martins (1994), Borjas and Ramey (1995), Neary (RIE 2002)]

15. The Rybczynski Theorem • At constant prices, an increase in one factor endowment will increase the output of the good intensive in that factor by a greater proportion and reduce the output of the other good

16. K Expansion Path • Isoquant diagram Fig. 4-1 illustrates technology in one sector • If factor prices are fixed, then least-cost point on any particular isoquant is determined: • slope = MRS = w/r Q2=F(K,L) Q1=F(K,L) w/r L • Assume that factor prices remain fixed; from FPE, we know that this must be true if goods prices are fixed • With CRS, locus of least-cost points on different isoquants is a straight line from origin [“Expansion Path”] • Now, combine the expansion paths for the two sectors in one country to give the “Edgeworth-Bowley Box”: Fig. 4-8. • Assumptions of fixed endowments (dimensions of box) and full employment pick out production points in both sectors

17. M KF KM F O LF G LM The Edgeworth-Bowley Box I Start with expansion path for sector F (Leave out the isoquants) Add expansion path for sector M Recall: M is more K-intensive Now: Rotate the second through 180° (not just 90°); and set axes equal to home endowments of both factors

18. LM G KM K = KF+ KM KF F M O LF L = LF+ LM The Edgeworth-Bowley Box II E Point E illustrates equilibrium factor inputs and outputs in both sectors

19. The Rybczynski Theorem G G’ K F E’ E O L • Now: consider a change in factor endowments; e.g., an increase in L • Goods prices do not change, hence neither to factor prices and factor proportions • Output and usage of both factors in K-intensive sector (M) must fall; while they must rise in L-intensive sector (F)

20. Summary of Rybczynski Theorem N.B. Use a “hat” to denote a rate of change (a.k.a. growth rate): • (^K=0 in diagram, but because of CRS this is not crucial: only relative factor endowments matters for relative outputs) • Economic mechanism? • Increase in L puts downward pressure on wagew • [though in equilibrium the wage does not actually fall] • This encourages expansion of L-intensive sector, F • L-intensive sector draws capitaland labour from other sector • [Note from diagram: F-sector ends up absorbing more labour than the economy’s extra endowment] • Since factor prices settle at their original level, both sectors end up with the same factor proportions as initially • Expanding sector grows by more than the economy average

21. Rybczynski Theorem (cont.) • Note: Theorem is very surprising - Economic growth occurs, yet output of one industry falls • Basic idea: Source of growth is asymmetric; effect on pattern of outputs is even more asymmetric: asymmetry is magnified. • Real-world examples? • Black Death in 13th century Europe • Great Famine in Ireland, 1846-49 • Russian emigration to Israel in 1990’s

22. Heckscher-Ohlin Theorem • Theorem: A country has a comparative advantage in the good that uses relatively intensively the country’s relatively abundant factor • Basically, extends the Rybczynski theorem from a time-series to a cross-section context, and neutralises the effects of demand differences between countries • Steps in Proof: • Illustrate Rybczynski theorem in PPF diagram and reinterpret it in terms of a cross-section comparison between countries, which differ only in endowments of K (not L) • This shows that at the same prices, the more K-abundant country produces relatively more of the more K-intensive good. • Hence its relative supply curve (XM/XF) lies to right of the other country’s

23. The Rybczynski Theorem in Output Space y2 • Rise in labour endowment => PPF shifts out, but in a biased way • “Rybczynski line” links points on old and new PPF with same slope: The theorem implies that it must be downward-sloping A B p p y1

24. Home PPF Heckscher-Ohlin Theorem (cont.) y2 • Now: Interpret Rybsczynski Theorem in a Cross-Section Q Q* Foreign PPF y1 • Home is more capital-abundant; so at the same prices, it has: • Higher output of the capital intensive good y1; and • Lower output of the labour-intensive good y2

25. Heckscher-Ohlin Theorem (cont.) • Final step: Homothetic tastes • Imply that relative demands are the same at home and abroad • So: Production bias translates into a trade bias

26. O* A D • The FPE Set and Inter-Industry Trade E K C G O L B