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Perfect competition in all markets means that the following conditions are assumed to hold.
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 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 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.
The total amount of labor and capital used in production is limited to the endowment of the country.
The labor constraintA relationship showing that the sum of the labor used in all industries cannot exceed total labor endowment in the economy. isLC + LS = L,
where LC and LS are the quantities of labor used in clothing and steel production, respectively. L represents the labor endowmentThe total amount of labor resources available to work in an economy during some period of time. of the country. Full employment of labor implies the expression would hold with equality.
The capital constraintA relationship showing that the sum of the capital used in all industries cannot exceed total capital endowment in the economy. isKC + KS = K,
where KC and KS are the quantities of capital used in clothing and steel production, respectively. K represents the capital endowmentThe total amount of capital resources available to work in an economy during some period of time. of the country. Full employment of capital implies the expression would hold with equality.
The only difference between countries assumed in the model is a difference in endowments of capital and labor.
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
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
This means that France has more labor per unit of capital for use in production than the United States.
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 = CSCC, where CS is the amount of steel consumed and CC is the amount of clothing consumed.
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.
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.
Table 5.1 Production of Clothing
|QC = f(LC, KC)|
QC = quantity of clothing produced in the United States, measured in racks
LC = amount of labor applied to clothing production in the United States, measured in labor hours
KC = 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 5.2 Production of Steel
|QS = g(LS, KS)|
QS = quantity of steel produced in the United States, measured in tons
LS = amount of labor applied to steel production in the United States, measured in labor hours
KS = 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.
represent the unit labor requirement in clothing production. It is the number of labor hours needed to produce a rack of clothing.
represent the unit capital requirement in clothing production. It is the number of capital hours needed to produce a rack of clothing.
is the unit labor requirement in steel production. It is the number of labor hours needed to produce a ton of steel.
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, is the capital-labor ratio in clothing production. It is the proportion in which capital and labor are used to produce clothing.
Similarly, is the capital-labor ratio in steel production. It is the proportion in which capital and labor are used to produce steel.
We say that steel production is capital intensive relative to clothing production if
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
This means clothing production requires more labor per capital hour than steel production.
Factor intensity is a comparison of production processes across industries but within a country. Factor abundancy is a comparison of endowments across countries.
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.
In fixed factor proportions, aKC, aLC, aKS, and aLS are exogenous to the model and are fixed. Since the capital-output and labor-output ratios are fixed, the capital-labor ratios, and , 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.
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 aKC and aLC 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.
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?”