The Heckscher-Ohlin Trade Model

The Heckscher-Ohlin (HO hereafter) model 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 goods trade pattern 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)

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.

          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.

          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.

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 $280 per month.

In July 2012, the average monthly wage in Shenzen was 3,900 yuan ($616). The minimum wage in Shenzhen is the highest, 1,500 yuan ($240).

BMW pays $67 per houw in Leipzig.

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

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.

 Transportation costs are assumed to be zero.

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.

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 illuminate the pure effects of trade.

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

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.

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. 

Neither country specializes in one commodity. After the introduction of free trade, neither country specializes in one commodity, as in Ricardian model.

Each country produces both goods.

          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.

Paper was invented by Cai Lun in AD 105. Printing with carved wood blocks appeared during the Tang dynasty. Movable type made of ceramic was invented by Bi Sheng during Song dynasty (c. 1050 AD), long before the Gutenberg printing press (1436). 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. The is a result of declining transportation and communication costs.

An important question is:

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

Will free trade also equalize factor prices?

Cultural impacts of

FPE

The creation of a large free trade area unifies and promotes its culture and power. Especially, low wage countries tend to adopt the culture of high wage economy.

(i) 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 EU. Now most invoices are written in English even between countries not involving the US.

(ii) In the West, Caesar and Augustus laid the foundation for a large free trade area (27 BC - 476 AD). Romans built roads to Lutetia (now Paris) and aquiduct there during the first century AD, and founded Londinium (now London) around 43 AD.

(iii) In China, Qin Shihuang united the warring states, and created a large free trade area in 221 BC. China's culture spreads to Korea and Japan through trade.

The first page of Analects of Confucius contains two verses in bold: The Master said, "Is it not a pleasure to learn something and practice it often? "Is it not a joy to have friends visiting you from far away quarters?

This book written by Confucius (551 - 473 BC) before Plato and Socrates includes Zhu Xi's commentaries. This edition was printed in Japan more than 200 years ago. Evidence that trade spreads technologies.

Museum of Fine Arts, Boston

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

Figure 1, Unit value isoquant

(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.

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

Specialization:

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.

Figure 5, Common Isocost Curve

w = w*, r = r*.

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

How will her wage be affected by free trade?

w = p₁MP_L1 = P₂MP_L2

r = p₁MP_K1 = P₂MP_K2

w/r = MP_L1/MP_K1 = MRTS₁ = the slope of UVI: y₁ = 1/p₁.

= MP_L2/MP_K2 = MRTS₂ = the slope of UVI: y₂ = 1/p₂.

Thus, in the Home country, a common isocost curve is tangent to both UVIs.

 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?

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, MP_L and MP_K are constant along the expansion path of each industry. The following diagram illustrates MP_L 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 (MP_L and MP_K) are constant along any expansion path.

w* = p*_iMP*_Li = p_iMP_Li = w, (wage equalization)

r* = p*_i MP*_Ki = p_iMP_Ki = r. (interest rate equalization)

 Retail prices during 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 ied.

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?

2. 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.

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

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).

A Chill Wind Blows from the East

At first glance, IBM's computer disk drive factory in Szekesfehervar, Hungary, doesn't look the picture of industrial decline. Built just eight years ago, its bright facade still glows from a hillside overlooking a bustling shopping plaza. But a closer look reveals an unnatural stillness. Loading docks that once were piled high with components lie empty. Turnstiles that admitted 3,700 workers a day are chained.