More on Resources and Output

More on Resources and Output
We now examine more rigorously how a change in resources—holding the prices of cloth
and food constant—affects the allocation of those factors of production across sectors and
how it thus affects production responses. The aggregate employment of labor to capital
can be written as a weighted average of the labor-capital employed in the cloth sector
and in the food sector :
(5A-1)
L
K =
KC
K
LC
KC
+
KF
K
LF
KF
(LC/KC) (LF/KF)
L/K
(slope = - (w/r)2) w/r
CC1 CC2
w/r
w/r
1/PF
1/PC
FF
Labor input
slope =
–(w/r)
Capital input
CC
Figure 5A-3
Determining the Wage-Rental
Ratio
The two isoquants CC and FF
show the inputs necessary to produce
one dollar’s worth of cloth
and food, respectively. Since price
must equal the cost of production,
the inputs into each good must
also cost one dollar. This means
that the wage-rental ratio must
equal minus the slope of a line
tangent to both isoquants.
110 PART ONE International Trade Theory
Note that the weights in this average, and , add to 1, and are the proportions of
capital employed in the cloth and food sectors. We have seen that a given relative price of
cloth is associated with a given wage-rental ratio (so long as the economy produces both
cloth and food), which, in turn, is associated with given labor-capital employment levels in
both sectors . Now consider the effects of an increase in the economy’s
labor supply L at a given relative price of cloth: increases while and both
remain constant. For equation (5A-1) to hold, the weight on the higher labor-capital ratio,
, must increase. This implies an increase in the weight and a corresponding
decrease in the weight . Thus, capital moves from the food sector to the cloth sector
(since the total capital supply K remains constant in this example). Furthermore, since
remains constant, the decrease in must also be associated with a decrease in labor
employment in the food sector. This shows that the increase in the labor supply, at a
given relative price of cloth, must be associated with movements of both labor and capital
from the food sector to the cloth sector. The expansion of the economy’s production
possibility frontier is so biased toward cloth that—at a constant relative price of cloth—the
economy produces less food.
As the economy’s labor supply increases, the economy concentrates more and more of
both factors in the labor-intensive cloth sector. If enough labor is added, then the economy
specializes in cloth production and no longer produces any food. At that point, the one-toone
relationship between the relative goods price and the wage-rental ratio is
broken; further increases in the labor supply L are then associated with decreases in the
wage-rental ratio along the CC curve in Figure 5-7.
A similar process would occur if the economy’s capital supply were to increase—again
holding the relative goods price fixed. So long as the economy produces both cloth
and food, the economy responds to the increased capital supply by concentrating production
in the food sector (which is capital-intensive): Both labor and capital move to the food
sector. The economy experiences growth that is strongly biased toward food. At a certain
point, the economy completely specializes in the food sector, and the one-to-one relationship
between the relative goods price and the wage-rental ratio is broken once
again. Further increases in the capital supply K are then associated with increases in the
wage-rental ratio along the FF curve in Figure 5-7.
PC/PF w/r
PC/PF
PC/PF w/r
LF
LF/KF KF
KF/K
LC/KC KC/K
L/K LC/KC LF/KF
(LC/KC and LF/KF)
KC/K KF/K
FF
Labor input
slope =
–(w/r )2
Capital input
CC
2
CC
1
slope =
–(w/r )1
Figure 5A-4
A Rise in the Price of Cloth
If the price of cloth rises, a smaller
output is now worth one dollar;
so is replaced by . The
implied wage-rental ratio must
therefore rise from (w/r)1 to (w/r)2.
CC1 CC2