经济学Essay参考案例：Assumptions of the H-O Model

本文是经济学专业的Essay范例，题目是“Assumptions of the H-O Model（H-O模型的假设）”，Eli Heckscher(1919)和Bertil Ohlin(1933)通过强调国家要素禀赋的构成与商品贸易模式之间的关系，为国际贸易的重要和实质性的理论发展奠定了基础。Heckscher-Ohlin (H-O)理论是解释为什么国家与其他国家进行商品和服务贸易的最简单的理论。Heckscher-Ohlin模型是国际贸易理论的一般均衡数学模型，它建立在李嘉图比较优势理论的基础上，基于国家的要素禀赋对贸易格局和商品生产进行预测(Learner 1995)。

Introduction介绍

Eli Heckscher (1919) and Bertil Ohlin (1933) found the basis for crucial and substantial theoretical developments of international trade by emphasizing the relationships between the composition of countries’ factor endowments and commodity trade patterns. The Heckscher-Ohlin (H-O) theory is the simplest explanation for why countries involve in trade of goods and services with other countries. Heckscher-Ohlin model, which is the general equilibrium mathematical model of international trade theory, is built on the Ricardian theory of comparative advantage by making prediction on trade patterns and production of goods based on the factor endowments of nations (Learner 1995).

Assumptions of the Heckscher-Ohlin Model

The following assumptions pertain to the 2*2 model of Heckscher-Ohlin.

It is assumed that there are only two nations (1 and 2) with two goods for trade (X and Y) and two factors of production (capital and labour).

For producing the goods, both nations use the same technology and they use uniform factors of production.

In both countries, good X is labour intensive and Y is capital intensive.

The tastes and preferences of both nations are the same (both countries can be represented in the same indifference curve).

In both nations, the assumption of constant returns to scale is applicable for the production of goods X and Y.

In both nations, specialization in production is not complete.

Goods and factor markets in both nations are perfectly competitive.

There exists perfect mobility of factors of production within each country though international mobility is not possible.

There are no restrictions or limitations to the free flow of international trade. That is, there exist no transportation costs, tariffs, or like other obstructions either to control or to restrict the exports or imports.

It is assumed that there exists full employment of all resources in both nations. That is, there will not be any under employed resource in either nation.

The exports and imports between the nations are balanced. It means that the total value of the exports will be equal to the total value of imports in both nations.

Implications of the Assumptions

The assumptions are made in order to depict the theory in a two-dimensional figure. It is also implied that both countries have access to and use the same general production techniques. The labour-capital ratio (L/K) of commodity X is higher than that of Y in both countries with the same relative prices of factors. As constant returns to scale is assumed, increase in the amount of labour and capital will result in the proportionate increase in the output also. Another implication is that though free international trade exists, both of the countries produce both commodities and it can be presumed that both countries are not small in size.

As the tastes and preferences related to demand are identical in both countries, if the relative prices of the goods are equal, the consumption of goods X and Y will be in the same proportion in both countries. Likewise, in both countries producers, traders and consumers are too small to affect the commodity prices. Mobility of factors of production implies that capital and labour are free to move from areas or industries of lower prices (earnings) to those of higher prices (earnings) until earnings become same equal in all areas or industries. That is, price equalization theory is implied here. International differences in the earnings exist because of the factor immobility in the absence of international trade.

由于两国与需求相关的品味和偏好是相同的，如果商品的相对价格相等，那么两国对商品X和Y的消费比例将相同。同样，在这两个国家，生产者、贸易商和消费者的规模都太小，不足以影响大宗商品价格。生产要素的流动性意味着资本和劳动力可以自由地从价格较低(收入)的地区或行业转移到价格较高(收入)的地区或行业，直到所有地区或行业的收入相等为止。也就是说，这里隐含了价格均衡理论。在没有国际贸易的情况下，由于要素的不流动性，在收入方面存在国际差异。

The assumption of incomplete production specialization implies that the process of specialization in production continues until the commodity prices (either relative or absolute) prices are the same in both countries. Again, if the transportation costs, tariffs or any other restriction are allowed, specialization will continue only until price differences by less than or equal to the costs or tariffs.

The Heckscher-Ohlin ModelHeckscher-Ohlin模型

Heckscher-Ohlin model is generally described as two countries, two goods and two factors model (2x2x2 model). This formulation of HO model was mathematically developed by Paul Samuelson. The goal of the model is to predict the pattern of international trade in commodities between the two countries on the basis of differences in factor endowments in both the countries.

Heckscher-Ohlin模型一般被描述为两个国家、两个商品和两个因素模型(2x2x2模型)。这种HO模型的表述是由Paul Samuelson在数学上提出的。该模型的目标是在两国要素禀赋差异的基础上预测两国之间的国际商品贸易格局。

Definition: A nation exports the commodities which are produced out of its relatively abundant and cheap factors or resources and imports the commodity which is produced out of relatively scarce factors or resources. In another words, relatively labour abundant country exports relatively labour intensive commodity and imports the relatively capital-intensive commodity. Country 1 exports commodity X because X is the Labor (L) intensive commodity and L is relatively cheap and abundant factor in country 1. Country 2 exports commodity Y because Y is the Capital (K) intensive commodity and K is relatively cheap and abundant factor in country 2.

The theory implicates two things: first, different supply conditions in terms of resource endowments explain comparative advantage and second, countries export goods that use abundant and cheap factors of production and import goods that use scarce and expensive factors.

According to Heckscher-Ohlin theory, international and interregional differences in production costs occur due to the differences in the supply of factors of production. Under free trade, countries export the commodities whose production requires intensive use of abundant factors and import the commodities whose production requires the scarce factors. Hence, international trade compensates for the uneven geographic distribution of factors of production. The theory gives insight to the fact that commodities are the bundles of factors (land, labour and capital). Thus, the exchange of commodities is indirect arbitrage of factors of production and the transfer of services of otherwise immobile factors from regions where factors are abundant to regions where they are scarce.

The H-O theorem identifies the basic reason for comparative advantage and international trade as the different factor abundance or factor endowments among nations. Because of this particular reason, the theory is known as factor proportions or factor endowment theory. The theory postulates that the difference in relative factor endowment and prices is the main reason for the difference in relative commodity prices between two countries.

H-O定理将比较优势和国际贸易产生的根本原因确定为各国要素丰度或要素禀赋的不同。由于这个特殊的原因，该理论被称为要素比例理论或要素禀赋理论。该理论假设相对要素禀赋和价格的差异是造成两国相对商品价格差异的主要原因。

Factor Endowments

Factor endowment can be defined as the ratio of capital to labour (K/L). If the capital – labour ratio in country 1 is greater than in country 2, then country 1 is said to be relatively capital-abundant (and labour-scarce) while country 2 is labour abundant (and capital scarce). Symbolically, this can be represented as:(K/L) 1 > (K/L) 2

Important implication of different factor endowments is for autarky prices of factors of production (the autarky prices are implied in the figure represented below).

For two countries with same demand patterns, relative factor prices leads to relative factor scarcities. Country 2 will have relatively inexpensive labour and country 1 is in a position to provide relatively inexpensive (abundant) capital.

Factor Intensities, Factor Abundance and Production Frontiers under H-O Model

Factor Intensity

Commodity Y is said to be relative capital intensive and commodity X is relatively labour intensive if the capital labour ratio used in the production of Y is higher than that of the production of commodity X.

That is,(K/L) y > (K/L) x

If the for the production of commodity Y, the country use 2K and 2L, then K/L = 1 and if the production of commodity X requires 1K and 4L, K/L=1/4. In this case, it can be said that commodity Y is capital intensity and commodity X is labour intensive. Factor intensity depends on K/L rather than the absolute amount of K and L.

At the equilibrium points, for producing the commodities, both countries choose capital-labour ration that minimize the factor costs at the prevailing relative factor prices.

The relative factor prices are represented as W=w/r where w is the price of labour and r is the price of capital. Though in principle, the factor intensities can be reversed when factor prices change. But it is assumed that this does not exist in H-O model. There is no factor intensity reversal.

Factor Abundance

Factor abundance can be defined in terms of two ways:1) Physical Units and 2) Relative Prices of factors.

In terms of physical units, the overall amount of capital and labour available to each country is taken into consideration (that is, TK and TL). As per this definition, country 2 is capital abundant if the ratio of total amount of capital (TK) to total amount of labour available in country 2 will be greater than that in country 1. The ratio of TK/TL is important rather than total absolute amount of K and L of the countries.

就实物单位而言，考虑到每个国家可用的资本和劳动力总额(即传统文化和传统文化)。根据这一定义，如果国家2的资本总额(TK)与可用劳动力总额的比率大于国家1，则国家2是资本充裕的。重要的是TK/TL的比例，而不是K和L的绝对总量。

Country 2 may have less capital than country 2 and still there may be the capital abundant country if TK/TL in country 2 exceeds TK/TL in country 1.

In terms of relative factor prices, country 2 is capital abundant if PK/PL is lower in country 2 than in country 1. As the price of capital is taken to be the interest rate, r and the price of labour is wage, w, then PK/PL= r/w. The ratio of r/w is important, not the absolute level of r or w, in determining whether a country is capital abundant or labour abundant. The first definition takes only the supply of factors into consideration, while the second considers both supply and demand factors.

Factor Endowments and Production Frontiers

When country 2 is capital abundant and the commodity Y is capital intensive, country 2 can produce relatively more of commodity Y than in country 1. Similarly, if country 1 is labour abundant and commodity X is labour intensive, country 1 can produce relatively more of commodity X than country 2. This situation gives a relatively flatter and wider production frontier curve for country 1 than country 2.

Diagrammatic Representation of H-O Model

The following figure represents the Heckscher-Ohlin model diagrammatically. As it is assumed, two countries have same tastes and preferences for demand, both the countries are represented in the same indifference map.

I is the highest indifference curve that country 1 and country 2 can achieve separately in the absence of international trade. The points A and A/ represent equality of production and consumption of both countries in the absence of trade. The tangency points of A and A/ determine the no-trade equilibrium prices of PA and PA/ in country 1 and country 2 respectively.

I是国家1和国家2在没有国际贸易的情况下分别能达到的最高的无差异曲线。A和A/代表两国在没有贸易的情况下生产和消费的平等。A和A/的切点分别决定了PA和PA/在国家1和国家2的非贸易均衡价格。

When PA < PA/, country 1 has comparative advantage in the production of commodity X and country 2 has comparative advantage in commodity Y.

The right side of the figure shows that country 1 specializes in commodity X and Country 2 in commodity Y when both countries involve in international trade.

Specialization proceeds at point where country 1 achieves the point B and country 2 reaches at point B/. At these points transformation curves are tangent to the common relative price line of PB. 

Country 1 exports commodity X in exchange for commodity Y and consumes at point E on the second indifference curve (IC II). Likewise, country 2 exports commodity Y in exchange for commodity X and the relative equilibrium point of country 2 is point E/ which coincides with point E.

In this context, it is important to note that country 1’s exports of commodity X equal country 2’s imports of commodity X (that is, BC=C/B/). Similarly, country 2’s exports of commodity Y equal country 1’s imports of commodity Y (that is, B/C/= CE).

When PX/PY>PB, country 1 wants to export more of commodity X than country 2 is able to import at this high relative price, and PX/PY tends to diminish to PB, which is equilibrium and normal price. Likewise, when PX/PY< PB, country 1 is in a position to export less of commodity X than country 2 desires to import at this low relative price and gradually, PX/PY tends to rise towards PB.

当PX/PY>PB时，国家1想要出口比国家2能进口更多的商品X，而PX/PY趋于PB，这是均衡正常价格。同样，当PX/PY< PB时，国家1出口的X商品比国家2在这个较低的相对价格下进口的要少，PX/PY逐渐向PB上升。

At point E, more of commodity Y and less of commodity X than at the point A are involved. However, country 1 will gain from international trade because E lies on higher indifference curve (IC II). Similarly, though at E/ more commodity of X and less commodity of Y are involved compared to the point of A/, country 2 gains from the trade because E/ lies on higher indifference curve, IC II.

Prepositions of H-O theorem and other empirical Studies

As a connotation of H-O theorem, three other prepositions or theorems are associated:

Factor price equalization theorem 2) Stopler-Samuelson theorem and 3) the Rybcsynski Theorem (Jone 2002).

The Factor Price Equalization Theorem要素价格均衡定理

Even though the national frontiers rule out the international mobility of factors, free trade in commodities leads to reduce the disparities in demand relative to supply of factor and thus to decrease the disparities in factor returns among different countries. International free trade leads to sharing of same technology by different countries and bringing of equality of factor returns if the factor endowments are similar and sufficient quantity of commodities are produced commonly (Samuelson 1992).

虽然国家边界排除了要素的国际流动，但商品的自由贸易导致减少要素的需求相对于供应的差距，从而减少不同国家间要素回报的差距。如果要素禀赋相似，共同生产足够数量的商品，国际自由贸易就会导致不同国家共享相同的技术，带来同等的要素收益(Samuelson 1992)。

The Stolper- Samuelson Theorem

Changes in relative commodity prices as brought by free international trade have strong effects on the factor prices or rewards. If there is no joint production, some factors may raise their rewards uncontrollably and other rewards may be lowered unambiguously. If the number of factors equals the number of commodities and production is non-joint, the relative changes in commodity prices will raise the price of any particular factor (Uekawa, 1971).

The Rybczynski Theorem

If there is unbalanced growth in factor supplies, it may lead to stronger asymmetric changes in outputs also. If the quantity of factors of production and commodities are evenly matched and production is non-joint, this pattern of asymmetry may pertain to growth in some factors of production (if there is given commodity prices) and may lead to the reduction of outputs.

Empirical Legitimacy and Leontief’s Investigation实证合法性与里昂蒂夫的调查

Leontief (1953) was the first to confront the Heckscher-Ohlin model with empirical investigation. He had developed a set of data in the frame of input-output accounts for the U.S economy and he computed the amounts of labour and capital used in each industry for 1947. Likewise, he made use of U S trade data for the same year to compute the factors of production (labour and capital) used in the production of $1 million of US exports and imports.

Leontief(1953)是第一个用实证研究对抗Heckscher-Ohlin模型的人。他在美国经济的投入产出核算框架内开发了一套数据，并计算了1947年各个行业的劳动力和资本使用量。同样，他利用同年的美国贸易数据来计算生产要素(劳动力和资本)用于生产100万美元的美国出口和进口。

Each column of the table shows the amount of labour and capital required to occur $1 million worth of international trade (exports or imports) to United States in the year 1947.

Firstly Leontief measured the capital and labour required for the exports from US. This estimation required the labour and capital used in each and every exporting industry and from the first row of the table, it is seen that $2.5 worth of capital was used to export worth of $1million. For labour, 182 person-years were used to produce the same exports.

Taking the ratio of labour and capital, it can be said as in the third row of the table, each labourer is working with $13,700 worth of capital. Turning to the import side of the calculation, there emerged a problem non-availability of data on foreign technology. Still Leontif managed to estimate the model assuming that same technology of US used in imports. The estimation on imports (i.e., $3.1 million of capital, 170 person- years and capital-labour ratio as $18,000) indicates that capital labour ratio of imports is higher than that of US exports. But US economy is found in 1956 as capital-abundant and this appears to contradict the H-O theorem. Thus the findings of Leontief came to be called as “Leontief Paradox” (Learner 1995).

以劳动力和资本的比率为例，我们可以在表格的第三排看到，每个劳动者都有价值13700美元的资本。在计算的进口方面，出现了一个问题，即无法获得有关外国技术的数据。尽管如此，莱昂提夫还是成功地估算出了这个模型，前提是美国在进口中使用了同样的技术。对进口的估计(即310万美元的资本，170人-年，资本劳动比为18,000美元)表明，进口的资本劳动比高于美国出口的资本劳动比。但1956年的美国经济是资本充裕的，这似乎与H-O定理相矛盾。因此Leontief的发现被称为“Leontief悖论”(Learner 1995)。

Under the framework of H-O theorem, many explanations have been proposed for the existence of this paradox.

U S and foreign technologies are not same unlike the assumption of H-O theorem.

The year 1947 was not usual year as World War II has just ended

As H-O model assumes, the U S was not engaged in free trade.

Other Empirical Estimations of H-O model

By examining the limitations of Leontief ‘s estimation, Bowen, Leamer and Sveikauskas (1987) estimated the H-O model by using data on a large number of countries. It was estimated to check whether countries are net exporters of the factors of production (which are relatively abundant) as factors of production are indirectly embodied in the trade. Cline (1997) suggested a more generalized H-O model by taking into account more and disaggregated factors of production. It was recognized that factor endowments change over a period of time as the investment and technological advances occur.

Concluding Remarks

H-O theorem has been vehemently criticized on many grounds including in terms of its basic assumptions. Some empirical studies even questioned the validity of the theory. Despite of the many criticisms and drawbacks, H-O theory has its own merits and contributions in the theoretical history of international trade.

H-O定理在许多方面受到了激烈的批评，包括其基本假设。一些实证研究甚至质疑该理论的有效性。尽管存在许多批评和缺陷，但H-O理论在国际贸易理论史上有其自身的优点和贡献。

By taking both commodity and factor prices into consideration, H-O theory provides a more and satisfactory explanation of international trade.

通过同时考虑商品价格和要素价格，H-O理论为国际贸易提供了更令人满意的解释。