1. Alan V. Deardorff University of Michigan
The Heckscher-Ohlin Model: Features, Flaws, and Fixes I: What's the H-O Model Like
Alan V. Deardorff
University of Michigan

2. Themes of the 3 Lectures
The HO Model is largely well behaved in 2 dimensions, even when you include trade costs
In higher dimensions, it is not so well behaved, especially when you include trade costs
Various modifications and extensions of the HO model offer some promise of making it behave better
Nottingham I

3. Outline of Lecture I Overview of the H-O Model The 2×2 Model
Without trade costs
With trade costs
The 2×2×2 Model
Conclusions from the 2×2(×2) Model
Nottingham I

4. H-O Overview The Heckscher-Ohlin (H-O) Model Assumptions
Homogeneous goods and factors
Perfectly competitive market equilibrium throughout (goods and factors)
Production functions
Constant returns to scale
Non-joint
Factors
Perfectly mobile across industries
Perfectly immobile across countries
Countries differ in factor endowments
Industries differ in factor intensities
Nottingham I

5. H-O Overview The Heckscher-Ohlin (H-O) Model Implications
Countries export goods that use intensively their abundant factors (H-O Thm)
Trade draws factor prices closer together across countries, becoming equal in certain circumstances (FPE Thm)
Trade changes real factor prices (S-S Thm)
Benefiting owners of abundant factors
Hurting owners of scarce factors
Rybczynski Thm (output effects of factor accumulation)
Nottingham I

6. The Textbook 2×2 H-O Model
Goods X, Y
Factors K, L
X is K-intensive
Goods are final goods
Trade is
Free and frictionless, or
Subject to simple, constant trade costs per unit (perhaps “iceberg”)
Nottingham I

7. The Textbook 2×2 H-O Model
Analysis: Expanded Lerner Diagram shows
Production
Factor allocations
Factor Prices
Trade
for given
Goods prices
Factor endowments
Thus
Full solution for small open economy
Dependence on prices for large economy
Nottingham I

8. Lerner Diagram K
X=1/PX0
1/wK0
Y=1/PY0
1/wL0 L
Nottingham I

9. Lerner Diagram K E0 X0
X=1/PX0
1/wK0
Y=1/PY0 Y0
1/wL0 L
Nottingham I

10. Lerner Diagram Export K E0 X0 EC = EW X=1/PX0 XC 1/wK0 YC Y=1/PY0 Y0
Import
1/wL0 L
Nottingham I

11. The Textbook 2×2 H-O Model
Behavior
If Endowments inside Diversification Cone
Both goods produced
Factor prices independent of endowments
If Endowments outside Diversification Cone
One good produced
Factor prices depend on endowments
Nottingham I

12. The Textbook 2×2 H-O Model
Sensitivity
All variables (outputs, trade, factor prices) are uniquely determined and depend smoothly on
Endowments
Prices
Adding trade costs vis a vis a single other country
Creates range of world prices for which country does not trade
Outside that range, all variables depend smoothly on trade costs
Nottingham I

13. The Textbook 2×2 H-O Model
Summary
With free and frictionless trade:
Nottingham I

14. The Textbook 2×2 H-O Model
Summary
With iceberg trade costs, t:
Nottingham I

15. Effects of Increasing Capital Endowment, EK
X=1/PX0
1/wK0
cone
Y=1/PY0
1/wL0 L
Nottingham I

16. Effects of Increasing EKSX SX
Rybczynski Thm: SX/EK, rises with EK EK
cone
Nottingham I

17. Effects of Increasing EKSY
Rybczynski Thm: SY Falls with EK SY EK
cone
Nottingham I

18. Effects of Increasing EK
DX, DY DX DY EK
cone
Nottingham I

19. Effects of Increasing EK
TX, TY TX EK TY
cone
Nottingham I

20. Effects of Increasing EKwK
wK0 wK EK wL wL
wL0 EK
cone
Nottingham I

21. Effects of Increasing Labor Endowment, ELK
X=1/PX0
1/wK0
Effects are mirror image of increasing EK EL
Y=1/PY0
1/wL0 L
Nottingham I

22. Effects of Increasing Price of X, PXK
X=1/PX0
1/wK0
Y=1/PY0
1/wL0 L
Nottingham I

23. Effects of Increasing Price of X, PXK
X=1/PX0
1/wK0
Y=1/PY0
1/wL0 L
Nottingham I

24. Effects of Increasing Price of X, PXK
X=1/PX0
1/wK0
Y=1/PY0
1/wL0 L
Nottingham I

25. Effects of Increasing Price of X, PXSX SX PX
(cone)
Nottingham I

26. Effects of Increasing Price of X, PXSY SY PX
(cone)
Nottingham I

27. Effects of Increasing Price of X, PX
DX, DY DY DX PX
(cone)
Nottingham I

28. Effects of Increasing Price of X, PX
TX, TY TX PX TY
(cone)
Nottingham I

29. Effects of Increasing Price of X, PXwK wK
Stolper-Samuelson Thm: wK/PX, wK/PY rise with PX PX
(cone)
Nottingham I

30. Effects of Increasing Price of X, PXwL
Stolper-Samuelson Thm: wL/PX, wL/PY fall with PX wL PX
(cone)
Nottingham I

31. Effects of Increasing Price of Y, PY
Effects are mirror image of increasing PX
Nottingham I

32. Effects of Presence of Trade Costs
Assume iceberg trade cost t−1>0, equals fraction of each good that disappears in transit to world market (must ship t for 1 to arrive)
Implication for domestic prices if world prices are PXw, PYw:
If country exports X: PX=PXw/t; PY=tPYw
If country exports Y: PY=PYw/t; PX=tPXw
If country does not trade:
(PXw/PYw)/t2 ≤ PX/PY ≤ t2(PXw/PYw)
Nottingham I

33. Presence of Trade CostsK EC
X=1/PXw
1/wKw
Y=1/PYw
1/wLw L
Nottingham I

34. Presence of Trade Costs
If country exports X K
…which it will if endowment is above this line
ECX EC
X=1/PXw
1/wKw
Y=1/PYw
1/wLw L
Nottingham I

35. Presence of Trade CostsK EC
X=1/PXw
ECY
1/wKw
If country exports Y
…which it will if endowment is below this line
Y=1/PYw
1/wLw L
Nottingham I

36. Presence of Trade Costs
If country exports X K
autarky
ECX EC
X=1/PXw
ECY
1/wKw
If country exports Y
Y=1/PYw
1/wLw L
Nottingham I

37. Effects of Increasing EK in Presence of Trade Costs
If country exports X K
autarky
ECX EC
X=1/PXw
ECY
1/wKw
If country exports Y
Y=1/PYw
1/wLw L
Nottingham I

38. Effects of Increasing EK in Presence of Trade Costs
PX/PY
autarky
t2PXw/PYw
PXw/PYwt2 EK
Y-export cone
X-export cone
Nottingham I

39. Effects of Increasing EK in Presence of Trade CostsSX
autarky EK
Y-export cone
X-export cone
Nottingham I

40. Effects of Increasing EK in Presence of Trade CostsSY
autarky EK
Y-export cone
X-export cone
Nottingham I

41. Effects of Increasing EK in Presence of Trade Costs
TX, TY
autarky TX EK TY
Y-export cone
X-export cone
Nottingham I

42. Effects of Increasing EK in Presence of Trade Costs
autarky wK wK EK wL wL EK
Y-export cone
X-export cone
Nottingham I

43. Effects of Increasing PXw/PYw in Presence of Trade Costs
SX,SY
autarky SX
(ρA =PXA/PYA = autarky price) SY ρA
ρw =PXw/PYw
Y-export cone
X-export cone
Nottingham I

44. Effects of Increasing PXw/PYw in Presence of Trade Costs
DX,DY
autarky DY DX ρA
ρw =PXw/PYw
Y-export cone
X-export cone
Nottingham I

45. Effects of Increasing PXw/PYw in Presence of Trade Costs
TX,TY
autarky TX ρA
ρw =PXw/PYw TY
Y-export cone
X-export cone
Nottingham I

46. Effects of Increasing PXw/PYw in Presence of Trade Costs
wK/PY
autarky
wK/PY ρA
ρw =PXw/PYw
Y-export cone
X-export cone
Nottingham I

47. Effects of Increasing PXw/PYw in Presence of Trade Costs
wL/PY
autarky
wL/PY ρA
ρw =PXw/PYw
Y-export cone
X-export cone
Nottingham I

48. Effects of Increasing Trade Costs
As trade cost, t, rises from zero, Y-export cone and the X-export cone move further apart, and the “autarky” range of factor endowments and world prices gets larger
For any given endowment and world prices, a rise in t reduces the volume of trade and moves other variables in the direction of their autarky values.
Nottingham I

49. Effects of Increasing Trade Costs
Example:
Consider a country whose factor endowments have it completely specialized in good X at world prices
Nottingham I

50. Effects of Increasing Trade Costs: Example
SX,SY
autarky SX SY t
X-export cone
Nottingham I

51. The World Market: The Textbook 2×2×2 H-O Model
To model the world economy, add a second country (country “*”)
Solve for world (relative) price that clears the world market
Nottingham I

52. The World Market: The Textbook 2×2×2 H-O Model
Results
with analogous expressions for the other country
Nottingham I

53. The World Market: The Textbook 2×2×2 H-O Model
Depictions of world equilibrium
Offer curves (Meade)
Integrated-world-economy diagram (Dixit-Norman)
Sufficient (but not elegant) to use supply and demand of just one of the goods
Nottingham I

54. World Equilibrium TX, −TX* TX PX/PY (PX/PY)w −TX* (cone) (cone)*
Nottingham I

55. Conclusions from the 2×2(×2) H-O Model
Equilibria are well defined
Equilibrium quantities are unique
Equilibrium prices are unique up to a numeraire
Nottingham I

56. Conclusions from the 2×2(×2) H-O Model
Includes three types of equilibria
Autarky (when there are trade costs)
Diversified
Specialized
Determinants of equilibrium type are mostly clear
Several relationships between variables depend importantly on type of equilibrium
Nottingham I

57. Conclusions from the 2×2(×2) H-O Model
Classic “Theorems” are clear and precise
Countries specialize, but only if endowment differences are large
Prices and quantities vary continuously with exogenous changes in
Endowments
Trade costs
In particular, trade responds sensibly to
Prices and
Nottingham I

58. What’s Next?
My point in the next lecture will be that some of these attractive properties are lost in higher dimensions – i.e., especially when there are more than 2 of goods and countries
Nottingham I