International Trade - Theory and Policy, 2010a

textile production consists of equipment such as looms, while the capital used in steel production requires
equipment such as blast furnaces. Since each type of capital is designed for use in a specific production
process, we call it “specific capital.” We can imagine that if the capital from one industry were shifted to
another, its productivity in the new industry would be zero. Simply imagine the usefulness of a blast
furnace in textile production and you should see the point! Thus for capital to remain fully employed, it
must remain in the same industry—it is immobile, or stuck in its respective industry.
We assume labor, on the other hand, is homogenous and perfectly freely mobile between the two
industries. This will imply that a firm’s choice problem is reduced to the decision of how much labor to
hire and how much to produce to maximize its profits, given that it has a fixed amount of capital available
to use. We’ll assume for simplicity that the capital stock in each industry is exogenously fixed and there is
no investment in new capital.
Single-Firm Equilibrium in the Specific Factor Model
In this context, a firm will maximize it profits when it produces a level of output such that the wage it
must pay to workers is equal to the value of the marginal product at the chosen level of output. This is
written in equation form for a textile firm as follows:
w = PT MPT.
The left-hand side of the equation represents the hourly wage the firm pays its workers. The right-hand
side is the value of the marginal product, which consists of the product of the market price of output (PT)
and the marginal product of production (MPT). The marginal product, in turn, represents the additional
output that can be obtained by increasing the labor input by one unit. For example, if MPT = 10, this
means that by adding one more hour of labor, ten additional meters of cloth could be produced. The units
of the expression MPT are meters of cloth per hour of labor (m/hr.). When multiplied by the price,
measured as dollars per meter, the product, PT MPT, yields the number of dollars that could be earned per
hour of additional labor applied in production. This then is the definition of the value of the marginal product
in this context. It is measured in dollars per hour, the same as the wage is measured—a good thing since
they must be equal to each other!
To see why this condition will hold when the firm maximizes profit, we will graph these expressions
in Figure 5.12 "Specific Factor Model—Single-Firm Equilibrium", which depicts the value of a marginal
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