The Heckscher-Ohlin Trade Model

  1. Introduction 


The Ricardian model explains much of world trade berfore WWII. The world economy was basically agricultural with some manufacturing, which began to appear since the industrial revolution in the 1820s.

The Heckscher-Ohlin (HO hereafter) model is a better description of the world economy after WWII. (Some trade is explained by the factor abundance and others by comparative advantages.) It is based on the assumption that trading countries adopt the same production technologies. It was first conceived by two Swedish economists, Eli Heckscher (1919) and Bertil Ohlin.

Rudimentary concepts were further developed and added later by Paul Samuelson and Ronald Jones among others. There are four major components of the HO model:

  1. Factor Price Equalization Theorem,
  2. Stolper-Samuelson Theorem,
  3. Rybczynski Theorem, and
  4. Heckscher-Ohlin Trade Theorem.

Due to the difficulty of predicting the pattern of trade in a world of many goods, instead of the Heckscher-Ohlin Theorem, the Heckscher-Ohlin-Vanek Theorem that predicts the factor content of trade received attention in recent years.

Eli Heckscher (1879 - 1952)

Heckscher was a Swedish economist. He is probably best known for his book "Mercantilist." Although his major interest was in studying economic history, he also developed the essentials of the factor endowment theory of international trade in a short article in Swedish in 1919. It was translated into English thirty years later.

Bertil Ohlin (1899-1979)

Heckscher's student, Bertil Ohlin developed and elaborated the factor endowment theory. He was not only a professor of economics at Stockholm, but also a major political figure in Sweden.

He served in Riksdag (Swedish Parliament), was the head of liberal party for almost a 1/4 of a century. He was Minister of Trade during World War II.

In 1979 Ohlin was awarded a Nobel prize jointly with James Meade for his work in international trade theory.

Why HO model?

It is based on the assumption that countries have identical production technologies. This model more accurately describes the world economy after WWII.

The Ricardian model is more relevant to the world economy before WWII. There were significant differences in production technologies between industrial countries and developinig countries.

   HO Model = 2 × 2 × 2 model (2 countries, 2 commodities, 2 factors)

          For example, there are two countries (America and Britain); each country is endowed with 2 homogeneous factors (labor and capital) and produces 2 commodities.

          This is the smallest case of "even" model, i.e., the number of commodities is equal to that of factors. Extending the model to a more general case is not easy. In fact, the results obtained from a more general model do not have the clear, common sense interpretations which the simple HO model enjoys.

  2. Factor Price Equalization Theorem
             Among the four main results of the HO theory, FPE is the most fragile theorem. If any of the eight assumptions is violated, it willl not hold. However, perhaps this is the single most important finding in trade theory; it shows how trade affects income distribution of the global economy.

          Of course, the assumptions are somewhat unrealistic in the sense that they are not likely to be observed in the real world. However, even if some of the assumptions are violated, international trade has a tendency to equalize factor prices; it will remove the wage gaps between countries, despite the constraint that trading countries impose on the movement of factors, in particular, on the movement of workers.

 China According to WSJ (June 1, 2010), "Honda Offers Strikers in China 24% Pay Boost "

In June 2010, Honda Motors, China has offered Chinese workers in Beijing a 24% wage hike, raising their average monthly salary from 1500 yuan to 1860 yuan, raising their monthly salary to about $300 per month.

BMW pays $67 per hour in Leipzig and is profitable. US autoworkers used to earn $150,000 (including benefits) a year, which amounts to about $75 per hour. GM pays now (2015) $58 an hour (Ford = $55, Toyota = $50).

Mexican autoworkers get $8 per hour. Hourly wage of Chinese autoworkers is about $2.20, which amounts to $640 per month or $7700 per year for the average workers.
   BMW GM Ford Toyota Mexico China 
 Hourly wages in 2015 $67  $58 $55 $50 $6.00 $3.50 



In autarky, factor prices differ between countries, depending on regional market conditions.

 After free trade

 What will be the impact of free trade on factor prices such as wage and interest rates?

FTA expedites the process of FPE (because of capital movement to Mexico.) The number of auto-making jobs in Mexico rose from 490,000 in 2008 to 675,000 in 2014. (increased 40%)

  3. Assumptions of FPE
 1. No artificial barriers to trade

World trade is assumed to be free from any impediments, such as tariffs, quotas, voluntary export restraints, and exchange control.

In reality, very few countries practice free trade. Most countries protect some industries due to the presence of lobbying.

 2. No transportation cost

 Transportation costs are assumed to be zero (No natural barriers).

In reality, transportation costs are a significant portion of the marketing costs of most traded goods, especially in agricultural products. Transportation costs declined significantly due to the development of navigational technology and canals.

Remark: This is unrealistic. However, it is not a bad assumption, because transportation costs inhibit and reduce trade volume; it does not reverse the trade pattern between the countries. The purpose is not to ignore reality but to isolate the pure effects of trade.

Galata Museo del Mare, Genoa (Galata Maritime Museum)

Remark: An implication of (1) and (2) is that commodity trade equalizes commodity prices between countries. That is, Americans and Britons pay the same prices for the same commodities.

 3. Perfect Competition (PC) + Full Employment (FE)

PC prevails in both product and factor markets. This assumption rules out monopolistic and oligopolistic market structures. It also rules out price and wage rigidities.

In a perfectly competitive market all buyers and sellers are price takers, i.e., each one is too small to exert market power and influence market prices. All factors are fully employed.

 4. Factors are mobile in each country but are immobile across national borders.

Like Ricardo, HO model draws a sharp distinction between domestic and external factor mobility. The maximum degree of factor mobility is permitted between industries within the same country domestic factor mobility). But neither capital nor labor can cross national borders international factor immobility).

DFM insures that workers move from a low wage region to a high wage region, and capital moves from a low interest country to a high interest region. The net effect is that all factor prices are the same within a country.

IFI implies that Mexican workers are not allowed to work in, or migrate to, the US. 

 5. No specialization

Neither country specializes in one commodity. ⇒ Each country produces both goods.

 6. Production functions exhibit constant returns to scale (CRS) and are differerent between industries  Such a production function is sometimes said to be homogeneous of degree 1 - HD(1) for short here.

          CRS means that a proportionate increase in all inputs increases the output by the same percentage.

Specifically, CRS means:

If y = F(L,K), then y' = F(2L,2K) = 2y.

Along any expansion path (e.g., expansion path 1), output increases at a constant rate as the amounts of inputs increase.

Moreover, MPL and MPK are constant along the expansion paths.

7. Both countries have Identical technologies

Paper was invented by Cai Lun in AD 105. Printing with carved wood blocks appeared during the Tang dynasty. Movable type was invented by Bi Sheng during Song dynasty (c. 1050 AD), but the Gutenberg printing press (1436) made printing popular. Paper technology did not spread to Europe because traveling became risky after the fall of the Roman Empire.

Production functions are the same in America and Britain. The HO model is a long run model. Ohlin argued that "the physical conditions of production are everywhere the same." Some countries may be slow to adopt new technology. With the development of modern telecommunications, information travels fast. This is due to declining transportation and communication costs.

 8. No factor intensity reversal  to be explained later.

An important question is:

Without trade barriers, natural or man-made, free trade will equalize output prices.

Will free trade also equalize factor prices?



  4. Cultural Impacts of FTA

Role Model for other countries


An FTA creates a large free trade area with common factor prices. It increases the economic power of the area and promotes its culture. (e.g., US, China.) FPE also increases factor mobility. One denarius was a good wage for one day's labor anywhere in the Empire.

Especially, low wage countries tend to adopt the culture of the high wage economy.

(i) In 331 BC, Alexander seized the treasury of Persepolis, and minted drachma coins from the silver looted at Susa. On one side these coins showed Alexander as Heracles. Later, Julius Caesar also minted silver denarii with his portraint on the obverse.

The Roman style of government was copied in Western Europe and the Greek became the lingua franca, similar to Butonghua in China.

British Museum.

Julius Caesar's tomb in Palatino Hill, Rome

An Italian inscription which explains that the body of an ancient ruler, Caesar, was deposited here. Julius Caesar laid the cornerstone of the Roman Empire (27 BC - 476 AD). By conquering neighboring countries, Roman government also provided police function and ensured safety of travelers. For example, Praetorian Guard and Roman legions stationed in various outposts provided peace and maintained law and order throughout the Roman Empire. As a result, international trade flourished on an unprecedented scale. Licinius Crassus crushed the Spartacus rebellion (71 BC). Silver denarius was worth about $20-50 (to buy bread as of 2005) during the time of Jesus. pay = 225 denarii (about $5-10,000) during the first century.

(ii) In the West, Caesar and Augustus laid the foundation for a large free trade area (27 BC - 476 AD). Western Europe borrowed the Roman system of government with senate.

(iii) Standardization: one government, one language(Greek), and Roman standardization. All roads lead to Rome. Romans built roads to Lutetia (now Paris) and aquiducts during the first century AD, and founded Londinium (now London) around 43 AD. The Roman empire also became a common market (mobile factors). People in the Mediterranean world spoke one language (Greek), had one government (Roman) and traded freely throuout the Empire. It provided the basis for developing the Western civilization.

(iv) In China, Qin Shi Huang united the 7 warring states, and created a large free trade area in 221 BC, built roads and standardized Chinese characters.

Analects of Confucius, printed by the Imperial printing press, Edo (Tokyo) 1700s.This book written by Confucius (551 - 473 BC) before Plato and Socrates includes Zhu Xi's commentaries. This edition was printed in Japan in the 1700s.

(v) Since the US created a large free trade area by eliminating interstate trade tax, it became a dominant power in the 20th century. European countries are imitating the US by creating the EU. Now most invoices are written in English even between countries not involving trade with the US.


Museum of Fine Arts, Boston

During the period of the Empire, portorium (tariff) was quadragesima (1/40 = 2.5%) of the value of imported goods. Gradually, the silver content of denarius was reduced to cover the budget deficit. The Roman army grew from 250,000 troops to over 600,000.

w = 225 denarii (legionaire, about $10,000 today),
w = 2250 denarii (centurion was paid ten times the basic wage. Some centurions were paid more.)

  Since the 1960s, the massive tide of globalization is changing the lives and economies of large trading blocs.

  5. Unit Value Isoquants
 Definition A unit value isoquant is a locus of input combinations that yield $1 worth of output.

(1) Among many isoquants choose the one for which p*2y2 = 1, or y2 = 1/p*2.

Figure 1, Unit value isoquant


 Different production functions (2) Different production functions yield different isoquants:

Two different UVIs intersect each other.

Figure 2

In Figure 2, industry 2 is more capital intensive than industry 1.

 Efficient productoin If factors are not chosen optimally, production costs will be higher unnecessarily.

(3) Choose y2, L2, and K2 to

maximize Π = p*2y2 - wL2 - rK2

subject to y2 = F2(L2,K2).

Once the desired output is chosen, the cost must be minimized. The equilibrium condition is:

MRTS = w/r

Figure 3, Implication of cost minimization


Survival of 1 industry only.

(4) "No specialization" implies that a common isocost curve must be tangent to both unit value isoquants. Suppose not.

Figure 4
Arbitrary factor prices (w,r) results in specialization in one commodity.

An arbitrary pair of factor prices (w,r) cannot prevail, because it causes the economy to specialize in one good. For instance, given the factor prices represented by the slopes of the two isocost curves, industry 2 survives at point A (p2y2 = c2) The tangency points (both A and B) yield exactly $1 revenue. But the production costs at points 1 and 2 will differ. For example, C1 > C2 = 1. Thus, firms will produce only commodity 2, which costs less but yields the same revenue. That is, the country specializes in good 2 in the above example.

 No specialization  Thus, for a given pair of output prices (p1,p2), there exists a unique pair of factor prices (w,r). This implies that a pair of output prices completely determines a pair of factor prices. Within a country, (p*1,p*2) ⇔ (w,r).

Figure 5, Common Isocost Curve



  6. Factor Price Equalization Theorem
 FPE  Given assumptions 1 - 8, factor prices will be equalized between countries. That is,

w = w*, r = r*.

An ironing woman, Edgar Degas, National Gallery, Washington, DC

How will her wage be affected by free trade?

Wages of skilled labor or professionals (MDs and lawyers) are protected because medical and legal services are not traded.


 Proof PC in factor markets + No specialization imply

w = p1MPL1 = P2MPL2

r = p1MPK1 = P2MPK2


 The same is true in the foreign country.

w* = p*1MP*L1 = p*2MP*L2

r* = p*1MP*K1 = p*2MP*K2


No Barriers to Trade + No Transportation Costs imply

p*1 = p1 and p*2 = p2. (Free trade implies output price equalization)

Thus, w* = p*1MP*L1 = p1MP*L1.

But will marginal products of labor in any industry be the same in the two countries, when they depend on K and L used? (yes, if they are on the same expansion path!)


Identical Technologies

IT: both countries have the same isoquant maps. This and (3) imply that HC and FC have the same set of unit value isoquants.

No FIR implies that expansion paths are unique in each country, and the two countries have the same expansion paths, as shown in Figure 6.

(k1 = k*1, k2 = k*2).

Marginal product of each input depends on the amounts of K and L. However, for CRS industries, MPL and MPK are constant along the expansion path of each industry. The following diagram illustrates MPL maintains constant height along the expansion curve Ok2.

Figure 6. Effects of CRS on marginal products.

Recall that along any expansion path, output increases at a constant rate. Hence, marginal products (MPL and MPK) are constant along any expansion path.

   HD(1) or CRS: Expansion paths are rays from the origin, along which MPs remain constant. Each country chooses an input allocation along each expansion path, depending on its resource endowment. However, regardless of their locations, A = (L1,K1) and B = (L*1,K*1), marginal product of each input does not depend on the output level; it depends only on the capital-labor ratios. In Figure 5a, CRS implies that marginal products remain constant along each expansion path, regardless of the output levels. Thus,  MP*Li = MPLi, MP*Ki = MPKi

w* = p*iMP*Li = piMPLi = w, (wage equalization)

r* = p*i MP*Ki = piMPKi = r. (interest rate equalization)


Retail prices during the Edo period (1603-1868).

Tax on harvests (rent) was about 40 - 50% during this period. Similarly, rent was 70% of harvest in Korea during the 18th century. No good statistics were available in America until after WWII.

R. P. Dore (Far Eastern Survey, 1958) noted that "in pre-war Japan nearly half of the cultivated area was farmed by tenants. Only a third of the nation's farmers owned all the land they farmed. About a quarter rented nearly all their land. ...average rents represented nearly half of the gross value of annual yield.

Land rent was in fixed amounts of harvest, which was about half the harvest in 1930 (Toshihiko Kawagoe, 1999).

The Great Famine in Ireland in 1845. About half a million were evicted and 1 million died.

Potato Famine in Ireland. The Ordnance Survey 1834 in the Parish of Killygarvan noted : "The old method of paying the rents by the produce on a farm of six acres was thus : the potatoes and oats fed the family, the oat straw the cow, the Barley paid the November rent, its straw thatched the cabin. The flax turned into cloth kept the family engaged in winter and paid the May rent". (rent was bout 7 £)


Rents were often over half the annual farm revenue during Meiji period.

Pressured by General MacArthur, Japanese government in 1946 instituted a land reform, which helped tenant farmers to purchase the land they cultivate at low prices.

What will be the impact of trade on land rent?


  7. If FPE is not observed in the real world
FPE in auto industry

Volkswagen workers reject UAW

Workers are not interested in a wage hike (which will benefit workers that remain hired) but long run survival of the industry and LR employment.

 If not FPE, then what? 1. It could mean that the Heckscher-Ohlin model does not apply to all trade patterns. It applies to industries in which factor proportions are important, e.g., agriculture and manufacture.

2. Tariffs and transportation costs may be high.

Watermelon price is high in Japan ⇒ a high tariff in Japan.

square watermelon (from Japan) is $800 in Moscow ⇒ a high tariff in Russia.

In practice, transportation costs are not negligible. Free trade does not equalize output prices or wipe out factor price differentials completely, but will reduce the gap in factor prices between countries.


 3. Capital is more mobile than labor. If FPE does not hold, both factors have incentives to move across national boundaries. If stringent restrictions are imposed on migration, it is the capital that will move in search of lower labor costs. This means outsourcing and a huge job loss in high wage countries, unless there is a restriction on capital mobility.

Capital mobility further reinforces the effect of free trade to equalize factor prices.




8. A Glimpse into the Future of the World Economy

 Will income be equalized?  In the long run, the division between LDCs and developed economies may become blurred.
   National income is written as wL+ rK.

wL + rK = (w + rK/L)L = (w + rS/L)L.

Since w and r are equalized in the world market, there are two elements that determine long run national income.

Population or labor force (L) and the savings rate (S/L).

Per capita income is (w+rS/L).

   Beyond a certain threshold level of income, per capita savings rate is a decreasing function of per capita income or wage. For example, China's household savings rate is over 40%, but it is expected to decline. Due to its high savings rate, China was able to maintain the growth rate of 9% over the past 25 years. As the savings rate declines with the rise in per capita income, per capita income approaches a limit that is attained by high income. Eventually, in a stationary state, a nation's economic power is measured by its population. In the short run, its wage also matters. However, population growth also stops once the wage reaches a threshold level.
GDP per capita   Lichtenstein ($138,000) -> Zimbabwe ($340) in 2014