Download Chapter 7 FACTOR ENDOWMENTS AND TRADE: THE 2X2

Chapter 7
FACTOR ENDOWMENTS AND TRADE:
THE 2X2 HECKSCHER-OHLIN MODEL
The simplest version of the Heckscher-Ohlin model is somewhat more difficult to analyze
than the three-factor specific factors model of the previous chapter. The reason is that
there is only one mobile factor in the specific factors model; in contrast, all (both) factors
of production are assumed to be mobile in the Heckscher-Ohlin model.
The main ingredients of the simple model are easily summarized. Two countries produce
two goods using two factors of production and identical techniques. (This version of the
Heckscher-Ohlin model is sometimes referred to as the 2x2x2 model.) Countries' factor
endowments contain different ratios of capital to labor, and goods differ in their input
requirements: at a given rental/wage ratio, one good requires more capital per manhour
than the other. The former good is said to be relatively capital-intensive, the latter
relatively labor-intensive.
The Stolper-Samuelson Theorem states that as the price of a good goes up, the return to
the factor used intensively in its production goes up by an even greater percentage, while
the return to the other factor of production falls.
Using "^" to denote percentage change and assuming that food production uses capital
intensively, this theorem can be stated as
^
r>
^
pF >
0=
^
pC >
^
w.
The proof is simple. When the price of food increases, firms in food production want to
expand. As there is full employment, they can do so only by attracting factors from the
clothing sector. Before the price change, however, clothing used less capital per worker
than the food sector. At the initial rental/wage ratio, the clothing industry would, in
shrinking, lay off more labor per unit of capital released than the food industry would
willingly hire. This would create a tendency to excess supply in the labor market and
excess demand in the capital market. To equilibrate both markets (by lowering desired
capital/labor ratios), the rental/wage ratio must rise. But does this mean w must fall in
absolute terms? Couldn't both r and w increase? No, because unit costs in clothing must
remain equal to the constant price of clothing, pC,
aLCw + aKCr = pC
where aLC and aKC are the labor/output and capital/output coefficients in clothing,
respectively.
The Rybczynski Theorem is concerned with unbalanced growth. Assuming that world
prices do not change, it states that if the endowment of one factor of production increases,
then output of the good using it intensively goes up by an even greater proportion, while
output of the other good falls.
Formally, if K is the capital stock, L the endowment of labor, and food production
relatively capital-intensive,
^
^
^
^
XF > K > 0 =
L > XC.
An unbalanced response to an addition to a factor endowment is not new, of course; we
saw it in the specific factors model when the supply of one of the specific factors
increased.
To prove the Rybczynski Theorem, suppose the capital stock grows. Supposing factor
prices constant (as we would if the country were small and if the Factor Price
Equalization Theorem held), output of food and clothing must adjust so that factor
proportions in the two industries remain unchanged. If the influx of capital locates in the
capital-intensive food sector, the capital/labor ratio in food rises, initially, above its
original level. As the labor-intensive clothing sector contracts, it releases capital and labor
to the food sector. This reallocation of factors brings the capital/labor ratio down to its
original level in the food industry, while the capital/labor ratio in the clothing sector is
unchanged. Food production expands because of the new capital in the economy plus the
capital and labor coming from clothing, while clothing production has contracted. (It is
easy to show that the influx of capital must locate in the capital-intensive industry; if it is
mistakenly installed in the clothing industry, the ratio of capital to labor released by the
food industry will be too high to restore the initial capital/labor ratios in the two
industries.)
The Heckscher-Ohlin Theorem, which states that a country has a comparative advantage
in, and thus exports, the good that uses its abundant factor intensively, follows from the
Rybczynski Theorem. Take two countries identical in all respects: factor endowments,
technologies, and preferences. (This implies that their autarky relative prices are the
same.) Now give one country a bit more capital, and the other a bit more labor. By the
Rybczynski Theorem, food production goes up in the first country, depressing the relative
price of food, while clothing output expands in the second country, depressing the relative
price of clothing or raising the relative price of food. When trade is permitted, the first
country exports food, and the second country clothing, thereby proving the HeckscherOhlin Theorem.
The final result, the Factor Price Equalization Theorem, states that if countries' factor
endowments are sufficiently similar and if they face the same commodity prices and have
the same technology, then their factor prices will be the same.
This is a surprising result. Even though factors are not internationally mobile, commodity
trade suffices to equalize their returns.
The proof involves realizing that the following two equations in the two unknowns, w and
r, have only one solution:
aLCw + aKCr = pC
aLFw + aKFr = pF.
When both equations apply to both countries, the Factor Price Equalization Theorem
holds.
SHORT-ANSWER QUESTIONS
1.
True or False:
In evaluating each of the following statements, assume that the two countries have
identical tastes and identical technology for producing food and clothing. Also
assume that the two countries are engaged in trade.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
When the price of the labor-intensive good rises, the return to capital
increases by more than the increase in the price.
Even though factors are immobile (i.e. countries cannot trade in factors of
production), countries can indirectly trade their factor endowments through
trade in goods.
As the price of the capital-intensive good rises, capital owners in the
country exporting the capital-intensive good are better off, while capital
owners in the country importing the capital-intensive good are worse off.
When capital is sector-specific in the short run but mobile across sectors in
the long run, an increase in the price of the capital-intensive good makes
labor worse off in the short run and better off in the long run.
Leontief concluded that the Stolper-Samuelson theorem does not hold for
the United States.
According to the Rybczynski theorem, if two countries face the same
terms-of-trade, the labor-abundant country will produce relatively more of
the labor-intensive good and relatively less of the capital-intensive good
than the capital-abundant country.
If two countries participating in international trade have identical
technologies and produce the same two goods, factor prices in the two
countries will be equalized.
As the price of the labor-intensive good increases, capital-owners in the
country which exports the labor-intensive good are worse off, while
capital-owners in the country which imports the labor-intensive good are
better off.
Trade flows are likely to decrease as the labor-abundant country receives
more capital.
(j)
Capital-owners favor a tariff on the labor-intensive good because as the
price of the labor-intensive good rises, workers will be attracted to that
industry, driving the wage rate down and the rental rate up.
2.
Identify which of the four trade theorems supports the following statements:
1.
2.
3.
4.
(a)
(b)
(c)
(d)
(e)
3.
The Heckscher-Ohlin Theorem
The Stolper-Samuelson Theorem
The Rybczynski Theorem
The Factor Price Equalization Theorem
An increase in the price of food will lead to an increase in the return to the
factor used intensively in the production of food and a decrease in the
return to other factors.
If a small country which participates in world markets experiences an
increase in its labor supply, domestic output of the labor-intensive good
will expand while output of the capital-intensive good will contract.
Reducing the tariff rate on the capital-intensive good will cause the wage
rate to rise.
The relatively labor-abundant country will import the relatively capitalintensive good.
When countries share the same technology and tastes and they trade in
international markets, capital gains from an increase in the price of the
capital-intensive good, regardless of its location.
Definitions:
(a)
(b)
Define what it means to say that the home country is relatively capitalabundant compared to the foreign country.
Define what it means to say that food is capital-intensive compared to
clothing.
4.
Consider a country that exports food and imports clothing. Would the owner of a
machine producing clothing favor or oppose a tariff if capital were sector-specific?
Assuming that clothing is relatively labor-intensive would his opinion about the
desirability of the tariff change if capital were mobile between sectors?
5.
Consider the 2x2 Heckscher-Ohlin model in which both countries produce clothing
and food using the same technology.
(a)
(b)
(c)
(d)
(e)
State the full employment conditions.
State the competitive profit conditions.
State in words what ?LC stands for.
Fill in the blank: ?LC + ?__ = 1. Why?
From the competitive-profit conditions, derive the following equation:
(?LC - ?LF) ( - ) = (C - F).
6.
Suppose that, at equilibrium prices pC = $45 and pF = $44, we observe that:
aLC = 5
aLF = 4
w = $6/hr
(a)
(b)
aKC = 3
aKF = 4
r = $5/hr.
Find ?LC, ?LF, ?KC, and ?KF. Which industry is labor-intensive?
Suppose the price of clothing increases by 20 percent while the price of
food is unchanged. What happens to the wage-rental ratio?
7.
Explain what is meant by the statement "Free trade in commodities can completely
substitute for international mobility of capital and labor." How does a capitalabundant country effectively trade its capital for labor?
8.
Which of the four trade theorems did Leontief's findings contradict?
9.
List some of the possible explanations for Leontief's result.
10.
The diagram below shows two possible unit isoquants.
(a)
(b)
(c)
Suppose the wage-rental ratio equals 2. Which industry is capitalintensive? Which industry is labor-intensive?
Suppose the wage-rental ratio equals 1/2. Now which industry is capitalintensive? Which industry is labor-intensive?
Isoquants like those shown in the diagram lead to "factor-intensity
reversals." How might this type of technology help us to explain the
Leontief paradox?
PROBLEMS
1.
Isoquants and Factor Intensity:
(a)
In a diagram with capital on the vertical axis and labor on the horizontal
axis, draw smoothly bowed-in isoquants which satisfy the following two
conditions:
(i)
the unit isoquants pass through the points given by:
aKC = 4,
aLC = 2,
(b)
(c)
2.
aKF = 2,
aLF = 4,
and the wage-rental ratio is the same in the two industries at these
points;
(ii)
no factor-intensity reversals.
Which industry uses labor relatively intensively?
In your diagram, show that for any change in the wage-rental ratio, the
industry you chose in part (b) is always the labor-intensive industry. Show
also that when the wage-rental ratio rises, both industries choose more
capital-intensive techniques.
Goods Prices and Factor Prices under Fixed Coefficients:
Consider a country that produces clothing and food using capital and labor. The
techniques of production in each industry are fixed and are given by:
aKC = 2,
aLC = 2,
(a)
(b)
(c)
(d)
(e)
(f)
3.
aKF = 3,
aLF = 2.
What do the isoquants look like in each industry? How does the capitallabor ratio depend on the wage-rental ratio?
Find the capital-labor ratio in each industry. Which industry is capitalintensive?
Suppose that the world price of clothing is $12 and the world price of food
is $16. Assume that the country produces both goods. Find the wage rate,
the rental rate, and the wage-rental ratio.
Find the cost shares of labor and capital in each industry.
Suppose the world price of food falls to $14. What is the new wage-rental
ratio? What theorem could you have used to predict this result?
What happened to the factor cost shares in the two industries?
Proving the Factor Price Equalization Theorem:
Use the competitive profit conditions to show that factor prices must be equal in
the two countries if technology is the same and both countries produce both
goods.
4.
Changing Factor Use:
Consider two countries with the technology shown in the two figures and assume
that the (initial) equilibrium world price is (pC/pF).
(a)
(b)
(c)
5.
Suppose the world price of clothing rises by 10 percent while the price of
food remains constant. Draw in the new production point on the
production possibilities frontier.
Applying the Stolper-Samuelson Theorem, what should happen to the
wage-rental ratio? Draw in the tangencies along the unit isoquants at the
new wage-rental ratio. What happens to the capital-labor ratio in each
industry?
Draw in the new allocation of labor and capital between the two industries
in the production box. (Make sure that the slope along the unit isoquants
is the same in both diagrams.) Draw in the capital-labor ratios at the new
equilibrium point and the contract curve.
Comparative Advantage in the Heckscher-Ohlin Model:
The amount of capital and labor required to produce a unit of food and a unit of
clothing are given by:
aKC = 1,
aLC = 3,
aKF = 2,
aLF = 2.
Assume that the techniques of production are invariant to the wage-rental ratio.
(a)
(b)
(c)
(d)
6.
Suppose the home country is endowed with 160 units of labor and 100
units of capital. Draw the labor and capital constraints in output space.
(Put xC on the horizontal axis, xF on the vertical axis.) Identify the slopes
of the two constraints. At full employment, how much clothing and food
does the home country produce?
Suppose the foreign country is endowed with 120 units of labor and 80
units of capital. Draw in the labor and capital constraints for the foreign
country in the diagram for part (a). How much food and clothing does the
foreign country produce?
Compare the outputs of the two countries. What theorem would have
predicted this pattern of production?
Assume that the two countries have the same tastes. Which country will
export food? Clothing? Could you have predicted this result on the basis
of factor endowments and the factor-intensities of the two industries?
What theorem are you using to make this prediction?
Relative Factor Abundance and Trade Patterns:
The production possibilities frontiers below are drawn under the assumption that
the home country is endowed with a higher proportion of capital to labor than the
foreign country. Capital is used relatively intensively in the production of food.
Preferences in the two countries are identical and homothetic.
(a)
Suppose these countries begin to trade. Draw in the new production and
consumption points for each country.
(b)
(c)
(d)
7.
What happened to the pattern of production? Have the countries become
more or less specialized as a result of trade?
What happened to the pattern of consumption? Have the bundles in the
home and foreign countries become more or less similar as a result of
trade?
What do you think happened to the wage-rental ratio in each country?
Consider a country that produces food with relatively labor-intensive techniques
and clothing with relatively capital-intensive techniques. In the short run, capital is
specific to each sector, but in the long run capital is mobile between the sectors.
(a)
Suppose the price of clothing rises relative to the price of food. Draw in
the new value of the marginal product of labor curve in the clothing
industry (LC). What happens to the wage rate? What happens to the
(b)
(c)
(d)
return to capital in each industry? (Hint: Go back to the cost conditions in
each industry.)
Draw in the new distribution of labor and capital in the short run.
(Remember that the capital stock in each industry is fixed in the short run.)
In the long run, the discrepancy in the rental rates will lead to a reallocation
of capital between the industries. Draw in the new value of the marginal
product of labor curves for each industry. Since clothing is capital
intensive, what must happen to the wage rate in the long run? What
happens to the rental rate?
Draw in the long-run allocation of capital and labor and draw in the wagerental ratio at that point.