The Heckscher-Ohlin Trade Model

Introduction

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.

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.

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.

Factor Price Equalization Theorem

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

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

Assumptions

1. No barriers to trade
             World trade is assumed to be free from any impediments, such as tariffs, quotas, voluntary export restraints, and exchange control.

2. No transportation cost

   	After the industrial revolution in the mid 1800s, major cities were connected by railrods, reducing the transportation costs further. Lawrence of Arabia helped the Arabs to recapture Aqaba from the Turks. Arabs eventually ousted Turks from the region now known as Saudi Arabia. As a result, Israel gained its independence in 1948.
   Procession of Horsemen and Chariots, Eastern Han, 25-220 AD.	Romans built good roads such as Via Appia and Via Ignatia, connecting various parts of the Empire, reducing the transportation costs. Good roads made it possible for the Romans and the Chinese to utilize horse drawn chariots for fast communication and transportation.There were bandits in various regions and pirates in the ocean, but the Romans made it sufficiently safe for ordinary people to travel.
   Oxcart, Han dynasty
   Luke 15:13 "Not long after that, the younger son got together all he had, set off for a distant country and there squandered his wealth in wild living. 14 After he had spent everything, there was a severe famine in that whole country, and he began to be in need. 15 So he went and hired himself out to a citizen of that country, who sent him to his fields to feed pigs.	This parable (of "lost" son or prodigal son) suggests that people were able to travel easily to foreign countries during the time of Jesus. Travel was relatively safe and affordable for the emerging middle class.

   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.

   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.

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 or migrate to the US.

5. No specialization

             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.

6. Production functions exhibit constant returns to scale (CRS) and differ among 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 the expansion path k, output increases at a constant rate as the amounts of inputs increase.

7. Identical technology between trading countries

             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.
   

   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? (Characters in regular font are the commentaries like those of Bible interpreters.) This book written by Confucius (551 - 473 BC) before Plato and Socrates includes Zhu Xi's commentaries. This edition was printed in Japan before Meiji Restoration. Trade spreads technologies. 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), and metal movable type in Korea around 1230, long before the Gutenberg printing press (1436).

8. No factor intensity reversal

   
   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.

   Will commodity price equalization result in factor price equalization?

Julius Caesar's tomb in Palatino Hill, Rome (May 2003)	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).

Unit Value Isoquants

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

(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

(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.

          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

An ironing woman, Edgar Degas. How will her wage be affected by free trade?

Proof

1. PC in factor markets + No specialization imply

   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.

2. The same is true in the foreign country. w* = p*₁MP*_L1 = p*₂MP*_L2

   r* = p*₁MP*_K1 = p*₂MP*_K2

3. 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?

4. 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.
     

   • 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 = MP_Li, MP*_Ki = MP_Ki.

5. 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% during this period. 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).

   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?

FPE is not observed in the real world. What does this mean?

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. 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. 

Convergence of Long run Income

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 20%, but it is expected to decline. Due to its high savings rate, China was able to maintain the growth rate of 9% over the last 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.

Business Week, September 1, 2003, page 44.

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.

IBM shut the plant last November, moving the work to China, where wages are 75% cheaper. Dutch electronics maker Royal Philips Electronics and Singapore contract manufacturer Flextronics International Ltd. hae moved an addional 1,500 Hungarian jobs to China in the past 18 months. Flextronics also has closed a 1,000-worker plant in the Czech Republic. The closings are sending shudders across eight formerly communist countries just as they are gearing up to celebrate their entry into the European Union on May 1.
...
The labor markets of Asia, especially China, are beginning to pull away industrial investments that helped this region rebuild after communism's collapse. "Their whole goal has been to join the EU," says Humphrey W. Porter, president of Flextronics Europe. "The risk is that they don't realize this is a rat race. And it's just the beginning, not the end."
...
But Eastern Europe's cost advantage is shrinking by the day. In the past two years, real wages have risen by 20% in Hungary and 11.5% in the Czech Republic, according to Vienna-based Erste Bank. Despite the runup, wages in Eastern Europe's most dynamic economies are still 25% lower than those in Western Europe. But the gap is widening with China, where wages have stayed at about $100 per month for unskilled factory workers. Even Eastern European companies, such as Hungary's Karsai Plastics Holding, are opening plants in China.