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

$$\frac{K}{L}>\frac{K^{\ast }}{L^{\ast }}\text{,}$$

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

$$\frac{L^{\ast }}{K^{\ast }}>\frac{L}{K}\text{.}$$

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

Heckscher-Ohlin Model Assumptions: Production

The production functions in Table 5.1 "Production of Clothing" and Table 5.2 "Production of Steel" represent industry production, not firm production. The industry consists of many small firms in light of the assumption of perfect competition.

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

$$a_{LC}\left[\frac{\text{labor}-\text{hrs}}{\text{rack}}\right]$$

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

Let

$$a_{KC}\left[\frac{\text{capital}-\text{hrs}}{\text{rack}}\right]$$

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

Similarly,

$$a_{LS}\left[\frac{\text{labor}-\text{hrs}}{\text{ton}}\right]$$

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

And

$$a_{KS}\left[\frac{\text{capital}-\text{hrs}}{\text{ton}}\right]$$

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.

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.