Homework 3
UCDavis, 160a, Fall 2011
Prof. Farshid Mojaver
Heckshcer-Ohlin Model 2
1. This exercise uses the Heckscher-Ohlin model to predict the direction of trade.
Consider the production of hand-made rugs and assembly line robots in Canada and
India.
a. Which country would you expect to be relatively labor-abundant, and which capitalabundant? Why?
Answer Given Canada’s relatively small population (30 million compared with more
than 1 billion in India) and level of development, it is a safe assumption that L CAN / KCAN
< L IND / KIND. That is, there is more capital per worker in Canada, making it capitalabundant compared with India. Similarly, India would be labor abundant.
b. Which industry would you expect to be relatively labor-intensive, and which is capitalintensive? Why?
Answer: Given the amount of capital required to produce robots and the amount of labor
required to produce rugs, one would expect that LROBOT / KROBOT < LRUG / KRUG, making
robots capital intensive and rugs labor intensive.
c. Given your answers to (a) and (b), draw production possibilities frontiers for each
country. Assuming that consumer preferences are the same in both countries, add
indifference curves and relative price lines (without trade) to your PPF graphs. What do
the slopes of the price lines tell you about the direction of trade?
Answer:
Canada’s no-trade production and consumption of robots and rugs corresponds to a
relative price of robots that is lower than that in India. This is shown by the flatter sloped
relative price line in Canada.
d. Allowing for trade between countries, redraw the graphs and include a “trade triangle”
for each country. Identify and label the vertical and horizontal sides of the triangles as
either imports or exports.
Answer:
2. Leontief ’s Paradox is an example of testing a trade model using actual data
observations. If Leontief had observed that the amount of labor needed per $1 million of
U.S. exports was 100 instead of 182, would he have reached the same conclusion?
Explain.
Answer: If the amount of labor required for $1 million of U.S. exports was 100 personyears instead of 182, then the capital/labor ratio for exports would have been $25,500 per
person. Because this is larger than the corresponding ratio for imports, this test would
have provided support for the Heckscher-Ohlin theorem. That is, the United States
(which was assumed to be capital-abundant in both cases) would have been shown to
export capital-intensive goods. In actuality, however, Leontief ’s test showed exactly the
opposite.
3 According to the Heckscher-Ohlin model, two countries can equalize wage differences
by either engaging in international trade in goods or allowing skilled and unskilled labor
to freely move between the two countries. Comment.
Answer: Allowing skilled workers to migrate to skilled-labor scarce countries and
unskilled workers to migrate to unskilled-labor scarce countries reduces the ratio of
skilled/unskilled workers in the skilled-labor-abundant country and raises it in unskilledlabor-abundant country. This increases the wage ratio between skilled and unskilled labor
in the skilled-labor-abundant country and lowers it in the unskilled-labor-abundant
country. When the two countries trade in goods that embody these factors, the skilledlabor abundant country will export the skilled-labor-intensive good. By doing so, it
effectively sends a lot of skilled workers and a few unskilled workers to the unskilled
labor- abundant country. Likewise, when it imports the unskilled-labor-intensive good, it
effectively imports a few skilled workers and a lot of unskilled workers. The net effect is
skilled workers in the unskilled-labor-abundant country see a fall in their wage relative to
unskilled labor and unskilled workers experience a rise in their relative wage, similar to
that of migration.
4. According to the standard Heckscher-Ohlin model with two factors (capital and labor)
and two goods, movement of Turkish migrants to Germany would decrease the amount of
capital-intensive products produced in Germany. Discuss whether this is true or false, and
explain why.
Answer: An increase in a factor of production raises the production of the good that uses
that factor intensively and reduces the production of the other good.
5. Imagine a two good H-O economy which imports automobiles and exports wheat. Suppose the
production of these two goods use only capital and labor. If the government raises a tariff on the
import of automobiles it will raise the domestic price of autos. Suppose the price of wheat
remains constant. Explain as a result of this tariff who in the economy will gain and who will lose
in real terms?
Answer: With an increase in price of Auto relative demand shifts in favor of Auto
production and hence relative demand for Capital goes up (relative demand for labor goes
down). This will lead to a decrease in L-K ratio employed in the two sectors which
lowers real Wage rates and increases real rentals.
Tariff on Auto imports  PA↑ >0 and so does the cost of production. Since Auto is
capital intensive  domestic QA ↑ demand for K↑ R↑ and R/PA↑ & R/PW↑
Similarly can show PA↑=> L/K↓ =>MPL↓ W↓ and W/PA↓ & W/PW↓
Rent earners win and Wage earners lose
6 Using a HO framework discuss the effects of U.S.-China trade on Skilled-Unskilled wage gap
in US and China. Do we actually see these predicted effects on skilled-unskilled wage gaps in the
two countries? Are you satisfied with this HO explanation of rising skilled-unskilled wage gap in
US?
Answer: HO would predict that as result of trade between skilled scarce China and
skilled abundant US, price of skilled intensive products increase in US (decrease in
China) according to SS this should lead to an increase in wages of skilled labor (a
reduction of wages of unskilled labor). We expect the opposite to happen in China. That
is as result of US-China trade we expect skilled-unskilled wage gaps to increase in US
and to decrease in China.
We observe the increase in skilled-unskilled wage gaps in US but we do not see the wage
gap reductions we expected to see in China. If anything this has actually increase in
China. HO explanation is not quite satisfactory because, first we are see conflicting effects,
second US trade with NIC’s constitutes only a small fraction of total U.S spending; this is too
small to explain the increased gap.
7. Laxland and Workland are two identical countries except that people in Workland
work twice as hard of those in Laxland. Under all the usual HO assumptions what would
be your prediction of the patterns of trade between these two countries? What do we
know about wage rates before and after trade in these two countries?
Answer)
Workland exports QL-int products to Laxland and imports QK-int products
QK-int
QL-int
(b) An increase in Capital
Endowment and the shift in PPF
FPE theorem tells us that with equal technology wages and rents would be equal across
countries. In Workland workers twice as hard as those in Laxland, this is as if they have
twice labor force. If wage rates in Laxland is W in Workland it would be 2W.
8. In 2008, the Ukraine successfully negotiated terms to become a member of the World
Trade Organization. Consequently, countries such as those in Western Europe are
shifting toward free trade with the Ukraine. What does the Stolper-Samuelson theorem
predict about the impact of the shift on the real wage of unskilled labor in Western
Europe? In the Ukraine?
Answer: According to the Stolper-Samuelson theorem, the real wage of unskilled labor
in Western Europe will experience a decrease in real earnings because Western
Europe is skilled-abundant relative to the Ukraine and will specialize in the skilled
intensive good. By trading with the Ukraine, the relative price of the skilled-intensive
good will rise. This leads to an increase in the real earnings of skilled labor and a
decrease in the real wage of unskilled labor. The situation would be opposite in the
Ukraine, where the real wage of unskilled labor would increase.
9. The following are data on U. S. exports and imports in 2007 at the two-digit
harmonized schedule (HS) level. Which products do you think support the HeckscherOhlin theory? Which products are inconsistent?
Exports
Products
($ billions)
Beverages
3.6
Pharmaceutical products
40.7
Cotton
4.9
Apparel
1.9
Footwear
1.0
Iron and steel
15.4
Copper
5.0
Electric machinery
124.9
Vehicles
73.6
Aircraft
83.0
Furniture
7.0
Toys
7.0
HS Code
22
30
52
61
64
72
74
85
87
88
94
95
Imports
($ billions)
14.7
55.6
0.8
33.3
17.6
12.4
6.4
212.1
131.9
18.4
30.1
27.6
Source: International Trade Administration, U.S. Department of Commerce.
Answer: Because the United States is relatively abundant in skilled labor and scarce in
unskilled labor, as predicted by the Heckscher-Ohlin model the U. S. imports unskilledlabor–intensive goods such as apparel, footwear, furniture, and toys. Assuming
pharmaceutical products use skilled labor, U. S. imports of these goods are contrary to
the prediction of the model. Both skilled labor and capital are used intensively in the
production of aircraft, and given that the United States has abundance in both factors, the
export of this good supports the Heckscher-Ohlin model. However, the model is
unsupported by the import of electric machinery and vehicles as both goods also use
intensively skilled labor and capital. The export of cotton is also likely to contradict the
Heckscher-Ohlin model because the United States is relatively land scarce.
10. Data for soybean yield, production, and trade are provided below for 2007.
Yield
Production
Exports
Imports
(metric ton/hectare) (100,000 metric ton)
Australia
Brazil
Canada
China
France
Ireland
Japan
Mexico
Russian Federation
United States
2.44
2.81
2.30
1.45
2.60
3.13
1.64
1.41
0.92
2.81
Source: Food and Agriculture Organization
3.2
5785.7
269.6
1272.5
8.5
40.8
22.7
8.8
65.0
7286.0
(100,000 metric ton) (100,000 metric ton)
0.3
2373.4
186.8
45.7
1.7
2.0
0.1
0.0
1.7
2984.0
1.0
9.8
21.3
3315.0
49.4
8.4
416.1
361.1
12.5
27.6
Suppose that the countries listed above are engaged in free trade and that soybean
production is land intensive. Then answer:
a. In which countries does land benefit from free trade in soybeans? Explain.
Answer: Landowners in the United States, Brazil, and Canada benefit from free trade
since the production of soybeans intensively uses land as a factor of production.
b. In which countries does land lose from free trade in soybeans? Explain.
Answer: Landowners in China, Mexico, Japan, Ireland, Russia, and France lose from
free trade because the world-relative price of soybeans is lower than each country’s notrade equilibrium price.
c. In which countries does the move to free trade in soybeans have little or no effect on
the land rental? Explain.
Answer: The move to free trade in soybeans is likely to have little or no effect on the
land rental in Australia and Russia because their import and export of the product is about
equal.
The Specific Factors Model
1. Starting from equilibrium in the specific-factors model, suppose the price of
manufactured goods falls so that wages fall from W’ to W in Figure 3.5 (below).
a. Show that the percentage fall in wages is less than the percentage fall in the price
of manufacturing, so that the real wage of labor in terms of manufactured goods
goes up.
Answer: As seen in the diagram, both the price of manufactured goods and the wages
decrease. The key to this exercise is to realize that the vertical distance of the decrease in
wage is less than the vertical distance of ∆PM . MPLM. Therefore:
∆PM . MPLM >∆W
where ∆W represents the change in wage. Dividing both sides by the initial wage
W = PM . MPLM
∆PM / PM >∆W / W
This is the desired result: the percentage fall in the wage is less than the percentage fall in
the price of manufacturing, so that the real wage of labor in terms of manufactured goods
goes up
b. What happens to the real wage of labor in terms of agriculture?
Answer: Because the wage decreases and the price of agricultural goods remains the
same, the amount of agricultural goods that can be bought by labor decreases.
That is, real wage decreases in terms of agriculture. Because the wage decreases and the
price of agricultural goods remains the same, the amount of agricultural goods that can be
bought by labor decreases. That is, real wage decreases in terms of agriculture.
c. Are workers better off, worse off, or is the outcome ambiguous?
Answer: Because the real wage increases with respect to manufactured goods and
decreases with respect to agriculture, the outcome will be ambiguous for workers. For
some, who prefer to purchase a lot of agriculture, the price change means an overall loss
in terms of how much they can buy. Others, who prefer to buy mainly manufactured
goods, gain in terms of how much they can buy.
2. Read the article by Lori G. Kletzer and Robert E. Litan,“ A Prescription to Relieve
Worker Anxiety,” Policy Brief 01-2, Institute for International Economics, Washington,
DC, www.iie.com/publications/pb/pb01-2.htm. Then answer the following questions.
a. Under the version of the Trade Adjustment Assistance (TAA) Act in the United States
that they refer to, how many extra weeks of unemployment insurance are workers eligible
for? What two criteria must they meet to qualify for this extra unemployment insurance?
Answer: Qualified workers may gain an additional 52 weeks of unemployment insurance
UI payments, provided they are enrolled in an approved training program. A similar
program, the North American Free Trade Agreement Transitional Adjustment Assistance
(NAFTA-TAA) program, was created in 1993. For eligibility, workers must prove that
they lost their job because of increased imports from, or a shift in production to, either
Canada or Mexico.”
b. Consider the proposal for “wage insurance” that Kletzer and Litan make in their
article. What criteria would a worker need to meet to qualify for this insurance?
What amount of extra income would they receive from the insurance?
Answer: “Wage insurance would work as follows: Eligible workers would receive some
fraction of their wage loss, which could vary by age and tenure of the worker for up to 2
years following the initial date of job loss, but would begin to be paid only when workers
found a new job.”
“To qualify for our proposed supplemental wage insurance benefit, workers need only
document that they have been ‘displaced’ according to criteria similar to the operational
definition of displacement used by the BLS in its Displaced Worker Surveys (plant or
company closed or moved, elimination of position or shift, insufficient work); that they
had served at their previous job for a minimum period of time: we suggest 2 years; and
that they have suffered an earnings loss (from old job to new job) . . .”
c. If Kletzer and Litan’s new plan for “wage insurance” had been adopted by the
United States, what would have been the budgetary cost in 1999 when unemployment
was 4.2%? How does this compare with the amount that is now spent on unemployment
insurance?
Answer: “Assuming a 50% replacement and subsidy rate, the table indicates that our
wage insurance and health insurance program would have cost about $2.9 billion in 1999,
when the national unemployment rate averaged 4.2%.
“The total cost, less than $4 billion, might have been a major obstacle when federal
deficits were high and growing but is not a problem now, and in any event would be
small in relation to the more than $20 billion that is now spent on unemployment
insurance . . .”
3. Suppose two countries, Canada and Mexico, produce two goods, timber and
televisions. Assume that land is specific to timber, capital is specific to televisions, and
labor is free to move between the two industries. When Canada and Mexico engage in
free trade, the relative price of televisions falls in Canada and the relative price of timber
falls in Mexico.
a. In a graph similar to Figure 3-5, show how the wage changes in Canada because of a
fall in the price of televisions, holding constant the price of timber. Can we predict that
change in the real wage?
Answer: As shown by the following figure, real wage falls but by less than the
percentage decrease in the price of televisions.
b. What is the impact of opening trade on the rentals on capital and land in Canada?
Can we predict that change in the real rentals on capital and land?
Answer: Because capital is specific to the television sector, the drop in the relative price
of television will lead to a fall in the rental on capital. With Canada exporting timber,
rental on land will rise because land is specific to the timber industry.
c. What is the impact of opening trade on the rentals on capital and land in Mexico? Can
we predict that change in the real rentals on capital and land?
Answer: Through the exports of televisions, the relative price of televisions will rise in
Mexico, which will lead to an increase in the rental on capital. By contrast, the rental on
land will fall.
d. In each country, has the specific factor in the export industry gained or lost, and has
the specific factor in the import industry gained or lost?
Answer: In both cases, the specific factor in the export industry (i.e., land in
Canada and capital in Mexico) gained whereas the factor specified to the import industry
(i.e., capital in Canada and land in Mexico) loses when the two countries engage in trade.
4. Home produces two goods, computers and wheat, where capital is specific to
computers, land is specific to wheat, and labor is mobile between the two industries.
Home has 100 workers and 100 units of capital, but only 10 units of land.
a. Draw a graph similar to Figure 3-1, with the output of wheat on the vertical axis and
the labor in wheat on the horizontal axis. What is the relationship between the output of
wheat and the marginal product of labor in the wheat industry as more labor is used?
Answer
As more labor is added to the production of wheat, the marginal product of labor declines
so that although the output of wheat continues to increase, the output is increasing at a
decreasing rate.
b. Draw the production possibilities frontier (PPF) for Home with wheat on the horizontal
axis and computers on the vertical axis.
Answer: See the following graph.
c. Explain how the price of wheat relative to computers is determined in the absence of
trade.
Answer: In the absence of international trade, the relative price of wheat is the slope of
the line tangent to the PFF and Home’s indifference curve.
d. Reproduce Figure 3-4 with the amount of labor used in wheat measuring from left to
right along the horizontal axis, and the amount of labor used in computers moving in the
reverse direction.
Answer: See graph below.
e. Assume that because of international trade, the price of wheat rises. Analyze the effect
of the increase in the price of wheat on the allocation of labor between the two sectors.
The increase in the price of wheat shifts the PW MPLW curve upward to PW'MPLW so
that the new equilibrium is at point B. The amount of labor used in wheat increases from
0WL to 0WL', although the amount of labor devoted to computer decreases from 0CL to
0CL'. Although the wage rises from W to W', the increase is less than the vertical shift of
the PW MPLW curve given as ∆PW MPLW.