International Trade - Theory and Policy, 2010a

The total amount of revenue earned by the firm on the market is given by the total shaded area (green +
purple). This corresponds to the area under the VMPT line between 0 and LE units of labor. Without the
use of calculus, it is difficult to describe why this is so. Nonetheless, since the VMP gives the additional
revenue earned for each additional unit of labor, one can imagine beginning back at L = 0 and increasing
labor in small increments. The vertical distance to the VMP line would be added to the total revenue for
every increment in labor. Adding each of these vertical lines together between L= 0 and L = LE yields total
revenue earned by the firm and is given by the total shaded area.
Finally, since there are only two factors of production—labor and specific capital—it must follow that the
total revenue equals the sum of the wage bill and the capital bill, where the capital bill represents the total
amount of money paid to the capital owners. In equation form we could write
total revenue = wage bill + capital bill.
Since the total revenue is given by the total shaded area and the wage bill is given by the lower shaded
area, the capital bill must be given by the upper purple shaded area. Again, this area represents the total
amount of money the firm must pay to the owners of capital used in production. It is not the rental rate,
however. The rental rate is given by the rental bill divided by the total quantity of capital units used in
production. In other words, the rental rate in textiles, rT, is given by
rT = rental bill/KT,
where KT is the fixed amount of specific capital available for use in the industry.
Similarly, the wage rate in textiles, wT, is given by
wT = wage bill/LE.
Two-Firm Equilibrium in the Specific Factor Model
The economy consists of two industries, textiles and steel, each of which is choosing labor input so as to
maximize profit. Thus when both industries operate and both maximize profit,
wT = VMPT
for textiles and
wS = VMPS
for steel, where wT and wS are the wage rates paid to workers in textiles and steel, respectively. With
homogeneous and perfectly mobile labor, another condition must also hold, namely, the labor constraint:
LT + LS = L.
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