ECONOMY

onald rogowski 817
Under the general principle of declining marginal productivity of each factor, MPL in
each country decreases as the country’s population increases. Again before migration,
the total product in country A is just the sum of all the marginal products, or the
total area under the MPL curve; labor in country A receives its wage times its total
labor, or the area of the darkly shaded left-side rectangle; owners of capital receive
the remainder, or the area of the lightly shaded left-side triangle. Similarly labor in
country B receives the area of the darkly shaded right-side rectangle, capital the area
of the medium-shaded right-hand triangle.
If labor can migrate freely between the two countries (and assuming that no capital
moves with it), labor will flow from B to A (shifting the vertical line of division
between the two countries to the right) until the wage is equalized in the two countries
at w ′ . The wage in country A will fall, that in country B will rise; country A capitalists
will benefit, country B capitalists will be harmed. But world production will increase,
since after migration world product will include the diagonally striped center triangle
that, before migration, was forgone. Hence migration, for the world as a whole, is unambiguously
welfare improving. Exactly the same analysis would hold for movements
of capital, save that ex ante capital would have the higher return in the less capitalabundant
(i.e. poorer) country and would migrate from rich countries to poor ones.
Less often noted, however, is that in advanced economies not just the wages of
the unskilled, but per capita income, can fall as a result of migration and foreign
investment; that is, the losses to the scarce factor can actually outweigh the gains to
the abundant one(s). Again, this can readily be seen in the simple terms of Figure 45.1.
Recall that total product in each country is the area under the MPL (marginal product
of labor) line: the MPL tells us how much additional product we get from each new
unit of labor, and the sum of all those marginal products is the total product. 4 Then
per capita total product in each country is just that area under the MPL curve divided
by the population segment (represented, remember, by the x-axis). This is the same
thing as the average height of the trapezoid composed of (for our high-wage country
in Figure 45.1) the medium-shaded triangle and the dark-shaded rectangle on the lefthand
side. As population moves from country B to country A, per capita product—
the average height of this trapezoid—must fall in A and rise in B. The point can be
generalized: in the simplest Cobb–Douglas production function, with only capital
and labor as inputs, per capita output y(= Y/L) is always increasing in the capital–
labor ratio k(= K /L). 5 As trade in factors opens, capital-abundant countries export
capital and import labor, decreasing k. Since, in the model, the marginal gain in
productivity in the capital-scarce countries outweighs the marginal loss in the capitalabundant
ones, world welfare improves; 6 but, in theory, developed-country welfare
can easily decline.
⁴ Similarly, if we graphed each student’s weight against her or his height, we would have a “marginal”
curve; if we take the sum of all those weights—i.e. the area under the weight–height curve, or the
cumulative distribution—we will know the total poundage of all students below a specific height.
⁵ In the standard Cobb–Douglas notation, Y = AK · L 1−·; · O (0, 1); hence, where y = Y/L and
k = K /L , y = Ak·. Whatever decreases the capital–labor ratio must decrease per capita output.
⁶ In the notation used immediately above, dy/dk = A· ; i.e. the marginal per capita gain in output
k 1−·
from any given increase in the capital–labor ratio will be higher, the lower is the initial capital–labor
ratio.