# 5.15: The Specific Factor Model- Overview

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Learning Objectives

1. Learn the basic assumptions and results of the specific factor (SF) model.

The specific factor (SF) model was originally discussed by Jacob Viner, and it is a variant of the Ricardian model. Hence the model is sometimes referred to as the Ricardo-Viner model. The model was later developed and formalized mathematically by Ronald Jones (1971)See R. W. Jones, “A Three-Factor Model in Theory, Trade and History,” in Trade, Balance of Payments and Growth, ed. J. N. Bhagwati, R. W. Jones, R. A. Mundell, and J. Vanek (Amsterdam: North-Holland Publishing Co., 1971). and Michael Mussa (1974)Michael Mussa, “Tariffs and the Distribution of Income: The Importance of Factor Specificity, Substitutability, and Intensity in the Short and Long-Run,” Journal of Political Economy, 82, no. 6 (1974): 1191–1203.. Jones referred to it as the two-good, three-factor model. Mussa developed a simple graphical depiction of the equilibrium that can be used to portray some of the model’s results. It is this view that is presented in most textbooks.

The model’s name refers to its distinguishing feature—that one factor of production is assumed to be “specific” to a particular industry. A specific factor is one that is stuck in an industry or is immobile between industries in response to changes in market conditions. A factor may be immobile between industries for a number of reasons. Some factors may be specifically designed (in the case of capital) or specifically trained (in the case of labor) for use in a particular production process. In these cases, it may be impossible, or at least difficult or costly, to move these factors across industries. See Chapter 4: Factor Mobility and Income Redistribution, Section 4.2: Domestic Factor Mobility and Chapter 4: Factor Mobility and Income Redistribution, Section 4.3: Time and Factor Mobility for more detailed reasons for factor immobility.

The SF model is designed to demonstrate the effects of trade in an economy in which one factor of production is specific to an industry. The most interesting results pertain to the changes in the distribution of income that would arise as a country moves to free trade.

## Basic Assumptions

The SF model assumes that an economy produces two goods using two factors of production, capital and labor, in a perfectly competitive market. One of the two factors of production, typically capital, is assumed to be specific to a particular industry—that is, it is completely immobile. The second factor, labor, is assumed to be freely and costlessly mobile between the two industries. Because capital is immobile, one could assume that capital in the two industries is different, or differentiated, and thus is not substitutable in production. Under this interpretation, it makes sense to imagine that there are really three factors of production: labor, specific capital in Industry 1, and specific capital in Industry 2.

These assumptions place the SF model squarely between an immobile factor model and the Heckscher-Ohlin (H-O) model. In an immobile factor model, all the factors of production are specific to an industry and cannot be moved. In an H-O model, both factors are assumed to be freely mobile—that is, neither factor is specific to an industry. Since the mobility of factors in response to any economic change is likely to increase over time, we can interpret the immobile factor model results as short-run effects, the SF model results as medium-run effects, and the H-O model results as long-run effects.

Production of Good 1 requires the input of labor and capital specific to Industry 1. Production of Good 2 requires labor and capital specific to Industry 2. There is a fixed endowment of sector-specific capital in each industry as well as a fixed endowment of labor. Full employment of labor is assumed, which implies that the sum of the labor used in each industry equals the labor endowment. Full employment of sector-specific capital is also assumed; however, in this case the sum of the capital used in all the firms within the industry must equal the endowment of sector-specific capital.

The model assumes that firms choose an output level to maximize profit, taking prices and wages as given. The equilibrium condition will have firms choosing an output level, and hence a labor usage level, such that the market-determined wage is equal to the value of the marginal product of the last unit of labor. The value of the marginal product is the increment of revenue that a firm will obtain by adding another unit of labor to its production process. It is found as the product of the price of the good in the market and the marginal product of labor. Production is assumed to display diminishing returns because the fixed stock of capital means that each additional worker has less capital to work with in production. This means that each additional unit of labor will add a smaller increment to output, and since the output price is fixed, the value of the marginal product declines as labor usage rises. When all firms behave in this way, the allocation of labor between the two industries is uniquely determined.

The production possibility frontier (PPF) will exhibit increasing opportunity costs. This is because expansion of one industry is possible by transferring labor out of the other industry, which must therefore contract. Due to the diminishing returns to labor, each additional unit of labor switched will have a smaller effect on the expanding industry and a larger effect on the contracting industry. This means that the graph of the PPF in the SF model will look similar to the PPF in the variable proportion H-O model. However, in relation to a model in which both factors were freely mobile, the SF model PPF will lie everywhere inside the H-O model PPF. This is because the lack of mobility of one factor inhibits firms from taking full advantage of efficiency improvements that would be possible if both factors can be freely reallocated.

## Specific Factor Model Results

The SF model is used to demonstrate the effects of economic changes on labor allocation, output levels, and factor returns. Many types of economic changes can be considered, including a movement to free trade, the implementation of a tariff or quota, growth of the labor or capital endowment, or technological changes. This section will focus on effects that result from a change in prices. In an international trade context, prices might change when a country liberalizes trade or when it puts into place additional barriers to trade.

When the model is placed into an international trade context, differences of some sort between countries are needed to induce trade. The standard approach is to assume that countries differ in the amounts of the specific factors used in each industry relative to the total amount of labor. This would be sufficient to cause the PPFs in the two countries to differ and could potentially generate trade. Under this assumption, the SF model is a simple variant of the H-O model. However, the results of the model are not sensitive to this assumption. Trade may arise due to differences in endowments, differences in technology, differences in demands, or some combination. The results derive as long as there is a price change, for whatever reason.

So suppose, in a two-good SF model, that the price of one good rises. If the price change is the result of trade liberalization, then the industry whose price rises is in the export sector. The price increase would set off the following series of adjustments. First, higher export prices would initially raise profits in the export sector since wages and rents may take time to adjust. The value of the marginal product in exports would rise above the current wage, and that would induce the firms to hire more workers and expand output. However, to induce the movement of labor, the export firms would have to raise the wage that they pay. Since all labor is alike (the model assumes labor is homogeneous), the import-competing sector would have to raise its wages in step so as not to lose all of its workers. The higher wages would induce the expansion of output in the export sector (the sector whose price rises) and a reduction in output in the import-competing sector. The adjustment would continue until the wage rises to a level that equalizes the value of the marginal product in both industries.

The return to capital in response to the price change would vary across industries. In the import-competing industry, lower revenues and higher wages would combine to reduce the return to capital in that sector. However, in the export sector, greater output and higher prices would combine to raise the return to capital in that sector.

The real effects of the price change on wages and rents are somewhat more difficult to explain but are decidedly more important. Remember that absolute increases in the wage, or the rental rate on capital, does not guarantee that the recipient of that income is better off, since the price of one of the goods is also rising. Thus the more relevant variables to consider are the real returns to capital (real rents) in each industry and the real return to labor (real wages).

Ronald Jones (1971) derived a magnification effect for prices in the SF model that demonstrated the effects on the real returns to capital and labor in response to changes in output prices. In the case of an increase in the price of an export good and a decrease in the price of an import good, as when a country moves to free trade, the magnification effect predicts the following impacts:

1. The real return to capital in the export industry will rise with respect to purchases of both exports and imports.
2. The real return to capital in the import-competing industry will fall with respect to purchases of both exports and imports.
3. The real wage to workers in both industries will rise with respect to purchases of the import good and will fall with respect to purchases of the export good.

This result means that when a factor of production, like capital, is immobile between industries, a movement to free trade will cause a redistribution of income. Some individuals—owners of capital in the export industry—will benefit from free trade. Other individuals—owners of capital in the import-competing industries—will lose from free trade. Workers, who are freely mobile between industries, may gain or may lose since the real wage in terms of exports rises while the real wage in terms of imports falls. If workers’ preferences vary, then those individuals who have a relatively high demand for the export good will suffer a welfare loss, while those individuals who have a relatively strong demand for imports will experience a welfare gain.

Notice that the clear winners and losers in this model are distinguishable by industry. As in the immobile factor model, the factor specific to the export industry benefits, while the factor specific to the import-competing industry loses.

## Key Takeaways

• The specific factor (SF) model is designed to evaluate the real-world phenomenon that some factors of production are more mobile between industries than others. It does that by assuming that one factor (capital) cannot move between industries, while the other factor (labor) can freely move.
• In all other respects, the SF model is like the H-O model.
• The SF model shows that upon opening to free trade, the real rents in the exports industry rise, real rents in the import-competing industry fall, and real wages in both industries may rise or fall.

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 in economic models to describe a factor of production that is so specialized that it can only be used in a single industry.
2. Of increase, decrease, stay the same, or ambiguous, this is the effect of trade on the real return to specific capital in the export industry.
3. Of increase, decrease, stay the same, or ambiguous, this is the effect of trade on the real return to specific capital in the import industry.
4. Of increase, decrease, stay the same, or ambiguous, this is the effect of trade on the real wages when labor is the mobile factor in a specific factor model.
5. Of increase, decrease, stay the same, or ambiguous, this is the effect of trade on the real wage with respect to the imported good when labor is the mobile factor in a specific factor model.
6. Of increase, decrease, stay the same, or ambiguous, this is the effect of trade on the real wage with respect to the exported good when labor is the mobile factor in a specific factor model.

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