International Trade - Theory and Policy, 2010a

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 sectorspecific
capital is also assumed; however, in this case the sum of the capital used in all thefirms 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.
Thevalue 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
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