# 5.2: Heckscher-Ohlin Model Assumptions

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Learning Objectives

1. Learn the main assumptions of a two-country, two-good, two-factor Heckscher-Ohlin (or factor proportions) model.

## Perfect Competition

Perfect competition in all markets means that the following conditions are assumed to hold.

1. Many firms produce output in each industry such that each firm is too small for its output decisions to affect the market price. This implies that when choosing output to maximize profit, each firm takes the price as given or exogenous.
2. Firms choose output to maximize profit. The rule used by perfectly competitive firms is to choose the output level that equalizes the price ($$P$$) with the marginal cost ($$MC$$). That is, set $$P = MC$$.
3. Output is homogeneous across all firms. This means that goods are identical in all their characteristics such that a consumer would find products from different firms indistinguishable. We could also say that goods from different firms are perfect substitutes for all consumers.
4. There is free entry and exit of firms in response to profits. Positive profit sends a signal to the rest of the economy and new firms enter the industry. Negative profit (losses) leads existing firms to exit, one by one, out of the industry. As a result, in the long run economic profit is driven to zero in the industry.
5. Information is perfect. For example, all firms have the necessary information to maximize profit and to identify the positive profit and negative profit industries.

## Two Countries

The case of two countries is used to simplify the model analysis. Let one country be the United States, the other France. Note that anything related exclusively to France in the model will be marked with an asterisk.

## Two Goods

Two goods are produced by both countries. We assume a barter economy. This means that there is no money used to make transactions. Instead, for trade to occur, goods must be traded for other goods. Thus we need at least two goods in the model. Let the two produced goods be clothing and steel.

## Two Factors

Two factors of production, labor and capital, are used to produce clothing and steel. Both labor and capital are homogeneous. Thus there is only one type of labor and one type of capital. The laborers and capital equipment in different industries are exactly the same. We also assume that labor and capital are freely mobile across industries within the country but immobile across countries. Free mobility makes the Heckscher-Ohlin (H-O) model a long-run model.

## Factor Constraints

The total amount of labor and capital used in production is limited to the endowment of the country.

The labor constraint is

$L_C + L_S = L \nonumber ,$

where $$L_C$$ and $$L_S$$ are the quantities of labor used in clothing and steel production, respectively. $$L$$ represents the labor endowment of the country. Full employment of labor implies the expression would hold with equality.

The capital constraint is

$K_C + K_S = K \nonumber ,$

where $$K_C$$ and $$K_S$$ are the quantities of capital used in clothing and steel production, respectively. $$K$$ represents the capital endowment of the country. Full employment of capital implies the expression would hold with equality.

## Endowments

The only difference between countries assumed in the model is a difference in endowments of capital and labor.

### Definition

A country is capital abundant relative to another country if it has more capital endowment per labor endowment than the other country. Thus in this model the United States is capital abundant relative to France if

$\frac{K}{L} > \frac{K^*}{L^*} \nonumber ,$

where $$K$$ is the capital endowment and $$L$$ the labor endowment in the United States and $$K^*$$ is the capital endowment and $$L^*$$ the labor endowment in France.

Note that if the United States is capital abundant, then France is labor abundant since the above inequality can be rewritten to get

$\frac{L^*}{K^*} > \frac{L}{K} \nonumber ,$

This means that France has more labor per unit of capital for use in production than the United States.

## Demand

Factor owners are the consumers of the goods. The factor owners have a well-defined utility function in terms of the two goods. Consumers maximize utility to allocate income between the two goods.

In Chapter 5: The Heckscher-Ohlin (Factor Proportions) Model, Section 5.9: The Heckscher-Ohlin Theorem, we will assume that aggregate preferences can be represented by a homothetic utility function of the form $$U = C_SC_C$$, where $$C_S$$ is the amount of steel consumed and $$C_C$$ is the amount of clothing consumed.

## General Equilibrium

The H-O model is a general equilibrium model. The income earned by the factors is used to purchase the two goods. The industries’ revenue in turn is used to pay for the factor services. The prices of outputs and factors in an equilibrium are those that equalize supply and demand in all markets simultaneously.

### Heckscher-Ohlin Model Assumptions: Production

The production functions in Table $$\PageIndex{1}$$ and Table $$\PageIndex{2}$$ represent industry production, not firm production. The industry consists of many small firms in light of the assumption of perfect competition.

Table $$\PageIndex{1}$$: Production of Clothing
United States France
$$Q_C = f(L_C, K_C)$$ $$Q_C^* = f(L_C^*, K_C^*)$$

where

• $$Q_C$$ = quantity of clothing produced in the United States, measured in racks
• $$L_C$$ = amount of labor applied to clothing production in the United States, measured in labor hours
• $$K_C$$ = amount of capital applied to clothing production in the United States, measured in capital hours
• $$f( )$$ = the clothing production function, which transforms labor and capital inputs into clothing output
• $$^*$$ All starred variables are defined in the same way but refer to the production process in France.
Table $$\PageIndex{2}$$: Production of Steel
United States France
$$Q_S = g(L_S, K_S)$$ $$Q_S^* = g(L_S^*, K_S^*)$$

where

• $$Q_S$$ = quantity of steel produced in the United States, measured in tons
• $$L_S$$ = amount of labor applied to steel production in the United States, measured in labor hours
• $$K_S$$ = amount of capital applied to steel production in the United States, measured in capital hours
• $$g( )$$ = the steel production function, which transforms labor and capital inputs into steel output
• $$^*$$ All starred variables are defined in the same way but refer to the production process in France.

Production functions are assumed to be identical across countries within an industry. Thus both the United States and France share the same production function $$f( )$$ for clothing and $$g( )$$ for steel. This means that the countries share the same technologies. Neither country has a technological advantage over the other. This is different from the Ricardian model, which assumed that technologies were different across countries.

A simple formulation of the production process is possible by defining the unit factor requirements.

Let

$a_{LC} \: \left[ \frac{labor \cdot hrs}{rack} \right] \nonumber$

represent the unit labor requirement in clothing production. It is the number of labor hours needed to produce a rack of clothing.

Let

$a_{KC} \: \left[ \frac{capital \cdot hrs}{rack} \right] \nonumber$

represent the unit capital requirement in clothing production. It is the number of capital hours needed to produce a rack of clothing.

Similarly,

$a_{LS} \: \left[ \frac{labor \cdot hrs}{ton} \right] \nonumber$

is the unit labor requirement in steel production. It is the number of labor hours needed to produce a ton of steel.

And

$a_{KS} \: \left[ \frac{capital \cdot hrs}{ton} \right] \nonumber$

is the unit capital requirement in steel production. It is the number of capital hours needed to produce a ton of steel.

By taking the ratios of the unit factor requirements in each industry, we can define a capital-labor (or labor-capital) ratio. These ratios, one for each industry, represent the proportions in which factors are used in the production process. They are also the basis for the model’s name.

First, $$\frac{a_{KC}}{a_{LC}}$$ is the capital-labor ratio in clothing production. It is the proportion in which capital and labor are used to produce clothing.

Similarly, $$\frac{a_{KS}}{a_{LS}}$$ is the capital-labor ratio in steel production. It is the proportion in which capital and labor are used to produce steel.

### Definition

We say that steel production is capital intensive relative to clothing production if

$\frac{a_{KS}}{a_{LS}} > \frac{a_{KC}}{a_{LC}} \nonumber .$

This means steel production requires more capital per labor hour than is required in clothing production. Notice that if steel is capital intensive, clothing must be labor intensive.

Clothing production is labor intensive relative to steel production if

$\frac{a_{LC}}{a_{KC}} > \frac{a_{LS}}{a_{KS}} \nonumber .$

This means clothing production requires more labor per capital hour than steel production.

### Remember

Factor intensity is a comparison of production processes across industries but within a country. Factor abundancy is a comparison of endowments across countries.

### Heckscher-Ohlin Model Assumptions: Fixed versus Variable Proportions

Two different assumptions can be applied in an H-O model: fixed and variable proportions. A fixed proportions assumption means that the capital-labor ratio in each production process is fixed. A variable proportions assumption means that the capital-labor ratio can adjust to changes in the wage rate for labor and the rental rate for capital.

Fixed proportions are more simplistic and also less realistic assumptions. However, many of the primary results of the H-O model can be demonstrated within the context of fixed proportions. Thus the fixed proportions assumption is useful in deriving the fundamental theorems of the H-O model. The variable proportions assumption is more realistic but makes solving the model significantly more difficult analytically. To derive the theorems of the H-O model under variable proportions often requires the use of calculus.

### Fixed Factor Proportions

In fixed factor proportions, $$a_{KC}$$, $$a_{LC}$$, $$a_{KS}$$, and $$a_{LS}$$ are exogenous to the model and are fixed. Since the capital-output and labor-output ratios are fixed, the capital-labor ratios, $$\frac{a_{KC}}{a_{LC}}$$ and $$\frac{a_{KS}}{a_{LS}}$$, are also fixed. Thus clothing production must use capital to labor in a particular proportion regardless of the quantity of clothing produced. The ratio of capital to labor used in steel production is also fixed but is assumed to be different from the proportion used in clothing production.

### Variable Factor Proportions

Under variable proportions, the capital-labor ratio used in the production process is endogenous. The ratio will vary with changes in the factor prices. Thus if there were a large increase in wage rates paid to labor, producers would reduce their demand for labor and substitute relatively cheaper capital in the production process. This means $$a_{KC}$$ and $$a_{LC}$$ are variable rather than fixed. So as the wage and rental rates change, the capital output ratio and the labor output ratio are also going to change.

## Key Takeaways

• The production process can be simply described by defining unit factor requirements in each industry.
• The capital-labor ratio in an industry is found by taking the ratio of the unit capital and unit labor requirements.
• Factor intensities are defined by comparing capital-labor ratios between industries.
• Factor abundancies are defined by comparing the capital-labor endowment ratios between countries.
• The simple variant of the H-O model assumes the factor proportions are fixed in each industry; a more complex, and realistic, variant assumes factor proportions can vary.

Exercise $$\PageIndex{1}$$

1. Jeopardy Questions. As in the popular television game show, you are given an answer to a question and you must respond with the question. For example, if the answer is “a tax on imports,” then the correct question is “What is a tariff?”
1. The term used to describe Argentina if Argentina has more land per unit of capital than Brazil.
2. The term used to describe aluminum production when aluminum production requires more energy per unit of capital than steel production.
3. The two key terms used in the Heckscher-Ohlin model; one to compare industries, the other to compare countries.
4. The term describing the ratio of the unit capital requirement and the unit labor requirement in production of a good.
5. The term used to describe when the capital-labor ratio in an industry varies with changes in market wages and rents.
6. The assumption in the Heckscher-Ohlin model about unemployment of capital and labor.

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