Factor Prices, Goods Prices, and Production Decisions

Factor Prices, Goods Prices,
and Production Decisions
In the main body of this chapter, we made three assertions that are true but that were
not carefully derived. First was the assertion, embodied in Figure 5-5, that the ratio of
labor to capital employed in each industry depends on the wage-rental ratio .
Second was the assertion, embodied in Figure 5-6, that there is a one-to-one relationship
between relative goods prices and the wage-rental ratio. Third was the
assertion that an increase in a country’s labor supply (at a given relative goods price
) will lead to movements of both labor and capital from the food sector to
the cloth sector (the labor-intensive sector). This appendix briefly demonstrates those
three propositions.
Choice of Technique
Figure 5A-1 illustrates again the trade-off between labor and capital input in producing
one unit of food—the unit isoquant for food production shown in curve II. It also, however,
illustrates a number of isocost lines: combinations of capital and labor input that cost
the same amount.
An isocost line may be constructed as follows: The cost of purchasing a given amount
of labor L is wL; the cost of renting a given amount of capital K is rK. So if one is able to
PC/PF
PC/PF
w/r
Units of capital
used to produce
one calorie of
food, aTF
1
II
Units of labor
used to produce
one calorie of
food, aLF
Isocost lines
Figure 5A-1
Choosing the Optimal
Labor-Capital Ratio
To minimize costs, a producer
must get to the lowest possible
isocost line; this means choosing
the point on the unit isoquant
(curve II) where the slope is equal
to minus the wage-rental ratio w/r.
108 PART ONE International Trade Theory
produce a unit of food using units of labor and units of capital, the total cost of
producing that unit, c, is
aLF aKF
Units of capital
used to produce
one calorie of
food, aTF
1
II
Units of labor
used to produce
one calorie of
food, aLF
2
slope =
–(w/r )2
slope =
–(w/r )1
Figure 5A-2
Changing the Wage-Rental Ratio
A rise in shifts the lowest-cost
input choice from point 1 to point
2; that is, it leads to the choice of
a lower labor-capital ratio.
w/r
c = waLF + raKF.
A line showing all combinations of aLF and aKF with the same cost has the equation
Goods Prices and Factor Prices
We now turn to the relationship between goods prices and factor prices. There are several
equivalent ways of approaching this problem; here we follow the analysis introduced by
Abba Lerner in the 1930s.
aKF = (c/r) - (w/r) aLF.
That is, it is a straight line with a slope of .
The figure shows a family of such lines, each corresponding to a different level of costs;
lines farther from the origin indicate higher total costs. A producer will choose the lowest
possible cost given the technological trade-off outlined by curve II. Here, this occurs at
point 1, where II is tangent to the isocost line and the slope of II equals . (If these
results seem reminiscent of the proposition in Figure 4-5 that the economy produces at a
point on the production possibility frontier whose slope equals minus , you are right:
The same principle is involved.)
Now compare the choice of labor-capital ratio for two different factor-price ratios. In
Figure 5A-2 we show input choices given a low relative price of labor, , and a high
relative price of labor, . In the former case, the input choice is at 1, in the latter case
at 2. That is, the higher relative price of labor leads to the choice of a lower labor-capital
ratio, as assumed in Figure 5-5.
(w/r)2
(w/r)1
PC /PF
-w/r
-w/r
CHAPTER 5 Resources and Trade: The Heckscher-Ohlin Model 109
Figure 5A-3 shows capital and labor inputs into both cloth and food production. In previous
figures we have shown the inputs required to produce one unit of a good. In this figure, however,
we show the inputs required to produce one dollar’s worth of each good. (Actually, any
dollar amount will do, as long as it is the same for both goods.) Thus the isoquant for cloth,
CC, shows the possible input combinations for producing units of cloth; the isoquant for
food, FF, shows the possible combinations for producing units of food. Notice that as
drawn, cloth production is labor-intensive (and food production is capital-intensive): For any
given , cloth production will always use a higher labor-capital ratio than food production.
If the economy produces both goods, then it must be the case that the cost of producing
one dollar’s worth of each good is, in fact, one dollar. Those two production costs will be
equal to one another only if the minimum-cost points of production for both goods lie on
the same isocost line. Thus the slope of the line shown, which is just tangent to both isoquants,
must equal (minus) the wage-rental ratio .
Finally, now, consider the effects of a rise in the price of cloth on the wage-rental ratio.
If the price of cloth rises, it is necessary to produce fewer yards of cloth in order to have
one dollar’s worth. Thus the isoquant corresponding to a dollar’s worth of cloth shifts
inward. In Figure 5A-4, the original isoquant is shown as , the new isoquant as .
Once again we must draw a line that is just tangent to both isoquants; the slope of that
line is minus the wage-rental ratio. It is immediately apparent from the increased steepness
of the isocost line that the new is higher than the previous one:
A higher relative price of cloth implies a higher wage-rental ratio.