HW3 Solution Key
UCDavis, 160a, Winter 2008
Prof. Farshid Mojaver
The Specific Factors Model and Factor Movement
1. Suppose that there are three factors: Capital, Labor, and Land. Bread requires inputs of land and labor, while steel requires
capital and labor.
a. Which factors are mobile and which are specific?
b. Assume that Canada’s endowments of land and capital are 10 units of capital and
100 land, while the U.S.’s are 50 units of capital and 100 land. Which good does each country export? Why?
c. How does trade affect the returns to land, labor, and capital in the U.S. and in
Canada? (Be sure to provide the details on whose real incomes go up or down,
which prices go up or down in which countries, and, if the effects are
indeterminate, then explain why.)
Answer Key to Q1
a. Labor is the “mobile” factor because it is used in both sectors. Therefore, it is assumed to be perfectly
mobile within the country. Capital is a specific factor for the steel-producing sector because it can only be
used to produce steel. Land is a specific factor in the bread-producing sector because it can only be used
to produce bread.
b. Canada is relatively land abundant because its ratio of the two specific factors, land to capital, is T/KCAN
= 100/10 = 10 > 2 = 100/5 = U.S.’s ratio of land to capital. The
U.S. is relatively capital abundant because its ratio of capital to land is K/TU.S. =
50/100 = ½ > 1/10 = 10/100 = Canada’s ratio of capital to land.
Therefore, Canada’s comparative advantage is in exporting of bread because it is the good that requires the
specific factor, land, in production and Canada has land in relative abundance to capital, as compared to the
U.S above. Likewise, the U.S. will export steel because its production requires the specific factor, capital,
which the U.S. has in relative abundance, compared to Canada.
c. In the U.S. trade implies the export of steel, raising the relative price of steel [(PS/PB)US increases]. In the
specific factors model, this implies that the mobile factor, labor, will move from bread production and into
steel production because it is more lucrative. This labor movement eventually equalizes wages at a higher
equilibrium wage rate (w* increases). However, the price of steel increases more than wages because the
labor demand schedules are downward sloping. Thus, capital owners increase the production of steel and
increase the productivity of these machines because they now have more laborers to work the night shift.
Therefore, the rate of return to owning a machine (MPK = rK) increases for these capitalists. Additionally,
the price of bread decreases (relatively) so capitalists enjoy both higher rental rates of capital ownership and
higher purchasing power (with respect to both goods but it is a bit more complicated with respect to steel).
Thus, U.S. capitalists are definitively better off.
Unfortunately, labor leaves the U.S. bread sector, making the land less productive with fewer itinerant
farmers to tend it. Therefore, the rate of return to owning land, or “land rents” (MPT = rT) decreases in the
U.S. Additionally, relative prices of steel have gone up so landowners’ real incomes fall. U.S. landowners
are definitively worse off.
In Canada, bread prices increase, relative to steel prices. [(PS /PB)CAN decreases.]
This draws Canadian labor out of the steel factories and into the fields to tend the
wheat crops. (Canadian workers cannot move to U.S.) This makes Canadian land more productive and land
rents (MPT = rT) go up in Canada. This, combined with a relative decrease in the Canadian price of steel,
due to competition with U.S. imports, and an increase in the price of bread that is not as great as the increase
in land rents, makes Canadian landowners definitively better off in terms of real income. Unfortunately,
Canadian capitalists are definitively worse off. The relative price of steel decreases and labor leaves,
leaving machines standing idle during the night shift. This decreases the productivity of those machines and
therefore decreases the rental rate of capital ownership (MPK = rK decreases). At the same time the price of
bread increases and the price of steel does not decreases as much as the rental rate of capital. Therefore,
Canadian capitalists have less purchasing power and lower real incomes with respect to both goods.
The effect of trade on laborers in both countries is indeterminate. For all workers, in both countries,
nominal wages have gone up (w* increases). However, for U.S. workers real incomes with respect to bread
have gone up [(w/PB)US increases], while real wages with respect to steel products have gone down [(w/PS)US
decreases]. For Canadian workers, real wages with respect to bread have gone down [(w/PB)CAN increases],
while real wages with respect to steel products have gone up [(w/PS)CAN increases]. So, the real effects on
their standard of living depend on the mix of these products that each group of workers consumes
(depends on their tastes or preferences). If Canadians consume very little bread, relative to steel, they can
still be better off. If Americans consume very little steel, relative to bread, they can be better off.
Unfortunately, if such is not the case then workers of either nationality may be worse off. (Note: Graphs,
like Figure 3-7 for each country, might be helpful in answering this question but they were not required.)
2. In the specific factors model, again suppose that the relative price of manufactured goods decreases. That is, assume that the
price of agricultural goods increases while the price of manufactured goods is unchanged (i.e. ΔPA/PA > 0 and ΔPM/PM = 0).
Arrange the following terms in ascending order:
ΔRT/RT
ΔRK/RK
ΔPA/PA
ΔPM/PM
ΔW/W
Answer Key to Q2:Look at your lecture notes for the answer.
3.Make an argument that
a) there is tendency for labor to migrate from the rest of the world to US
b) migration improves US GDP but lowers the GDP of the ROW
c) migration is beneficial for the migrants but huts workers in the host country
d) owners of land/capital in the host country are better of as a result of labor migration
e) the world as a whole is better as a result of migration
f)
Answer Key to Q3: Look at Lecture notes
4. In the specific factors model for manufacturing goods and agriculture, consider a decrease in the stock of land. For example,
suppose natural disaster decreases the quantity of arable land for planting crops.
a) Redraw Figure 5.12 starting from the initial equilibrium point B.
b) What is the effect of this change on the quantity of labor in each industry and on the equilibrium wage?
c) Now suppose that international community wants to help the country struck by the natural disaster and decides to do so
by increasing its level of FDI. That is, the rest of the world increases its investment in physical capital in the stricken
country. What is the effect of this policy on the equilibrium wage? What is the total effect on the equilibrium wage of the
disaster and subsequent FDI investment (Increase, decrease or ambiguous)? Does the agriculture industry benefit or lose
from the FDI?
Answer Key to Q4
a).
Wage, W
B
W
W'
B’
PAMPLA
PAMPL’A
OM
LM
PMMPLM
L
L'
LA
PMMPL'M
L
b). As we could see from the figure, labor hired in Manufacturing industry increases, while labor in
agriculture industry decreases. The equilibrium wage also decreases.
c).
Wage, W
B
W''
W
W' PAMPLA
B’
PAMPL’A
OM
LM
PMMPL'M
PMMPLM
L
L'
LA
OA
L
Increasing the country’s FDI level would lead to an increase in wage level. While the total effect on the
equilibrium wage of the disaster and the subsequent FDI investment is ambiguous and depends on the
magnitude of the FDI. For example, when the new VMPL line for Manufacturing industry is the red dash
line, the new equilibrium wage W'' is lower than the original equilibrium wage W; when the new VMPL
line for Manufacturing industry is the purple dash line, the new equilibrium wage W'' is higher than the
original equilibrium wage W; finally when the new VMPL line is the blue solid one, the FDI exactly cancels
the negative impact of the disaster on wage, that is, the equilibrium wage keeps the same level as before the
disaster. In each case, it is clearly that the agriculture industry is further damaged by the inflow of FDI: its
production scale is further decreased because of loss of labor to manufacturing industry.
5. Now consider a long-run model for a country producing 2 products (digital cameras and baskets) using 2
factors (capital and labor).
a) Which good would you expect to be capital-intensive? Which good would you expect to be laborintensive? Why?
b) Suppose that foreign owners of domestic capital decide to decrease their investment. Illustrate the
effects of this change in a box diagram. Does output in each industry increase, decrease or stay the
same? Do wages increase, decrease, or stay the same in each industry?
Answer Key to Q5
a). Digital camera industry is capital-intensive while basket industry is labor-intensive. The former utilizes
much more complicated technology and therefore requires a much larger quantity of upfront investment in
research & development.
b).
Box Diagram:
Labor allocated to digital camera
 LC
L
The
withdrawn
FDI
OC
KC

Capital
allocated to
digital camera
Total
amount of
capital in
the
economy,
K
B
Capital
allocated
to basket
K
A
K

KS
Ob
L
LS 
Labor allocated to basket
Total amount of labor in the economy, L
Check the box diagram above, note the blue lines illustrates the new allocation of labor and capital between
the two industries after the decrease in FDI. That is: the capital intensive industry --- digital capital industry
--- is shrinking and uses less labor and capital. While on the other hand, the labor intensive industry --basket --- is expanding and uses more labor and capital than before the withdraw of FDI. The new
equilibrium point is at B instead of A.
Wage rate will keep at the same level as before since the world prices of products haven’t changed.
a). This is not a stable long-run outcome. Since the Home country still offers a higher wage than the
Foreign country, the migration will not stop, instead, workers will continue to immigrate to the Home
country.
Wage, W
Gains to
Home
World Amount of Labor
b). Yes, there are gains from immigration incurred to both Home country and Foreign country, which are
illustrated in the above graph (the purple area is gains to the Home country, while the yellow area is gains to
the Foreign country).
I. MC Question: 1.D, 2.B, 3.D, 4.C, 5.C, 6.B, 7.B
II. Essay Type Questions
Problem 1:
According to the Heckscher-Ohlin Theorem: “A country will export goods that use its relatively abundant
factor more intensely in production, when that country opens up to trade” (paraphrased). Developing
countries can produce more labor-intensive goods, like clothing, and export them for a higher price than
would be paid in autarky. By inspection of Figure Unit-Isoquant, one can see that W/R increases more than
PC/PF. That is, W actually increases more than either PC or PF so that real wages with respect to all goods
increases. Therefore, the standard of living improves for developing countries with the opening up of trade,
according to the Heckscher-Ohlin model.
Note: One could have used the Stolper-Samuelson
If ∆PF/PF < ∆PC/PC then ∆W/W > ∆PC/PC > ∆PF/PF > ∆R/P
Therefore, W/PF increases and W/PC increases in the developing country. However, neither of these things
was required to get full credit for your answer.
Problem 2
Consider the following information on the factor endowments of two countries:
Factor Endowments
Labor Force
Capital Stock
United States
30 million workers
200,000 machines
Austria
15 million workers
400,000 machines
a. The capital to labor ratios are U.S.: 200,000/30,000,000 = 2/300
Austria: 400,000/15,000,000 = 4/150 = 8/300
Since 8/300 > 2/300, Austria is relatively capital abundant.
b. The labor to capital ratios are U.S.: 30,000,000/200,000 = 150
Austria: 15,000,000/400,000 = 150/4
Since 150 > 150/4, U.S. is relatively labor abundant.
c. Austria has the comparative advantage in the production of steel, according to the
Heckscher-Ohlin Theorem, “Because steel uses Austria’s relatively abundant factor
(capital) more intensely in its production than do textiles. Therefore, Austria should produce and export
steel (although it may still produce some textiles as well, according to H-O theory).
Problem 3
Explain why/whether each of the following conditions might prevent factor prices from being equalized across countries in a
Heckscher-Ohlin world.
a. One country subsidizes the production of one of its goods
Say production of good X is subsidizes at a rare s. This increases the price producers receive for their
product to PX (1+ s). Therefore the domestic price ratio at the point of production will exceed that of
international price ratio [PX (1 +s)/PY] domestic > [PX/PY] world. This will increase the return to factors
used intensively in production of X relative to that of Y.
b. One country imposes environmental regulations that reduce the productivity of capital
in the country's capital intensive sector.
Then imposition of an environmental regulation that reduces the productivity of K in the capital intensive
sector Y reduces return to K thereby reducing return to K relative to L.
c. One country has a smaller labor force.
Lower Labor force has no effect on TFP.
4. 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?
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
Problem 5 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 skilledunskilled wage gap in US?
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.
True False questions
Question1
“Opening up free trade does hurt people in import-competing industries in the short run. But in the long run, when people and
resources can move between industries, everybody ends up gaining from free trade.”
False – Opening up free trade is likely to hurt some people. Owner of specialized factors in importcompeting industries and owners of factors used intensively in import-competing industries will lose from
free trade both in the short and in the long run.
Question2
“American workers gain from free trade with China because free trade lowers prices of clothing in the United States and
American workers spent very large portion of their income on clothing”
False – Free trade lowers clothing prices in the United States but it lowers real wage of American worker
too. Since wage income is the main source of American workers we may conclude that their income goes
down with opening up trade with China.
Jeopardy Answers
1.
term used to describe Argentina if Argentina has more land per unit of capital than Brazil.
Land abundant country
2.
term used to describe aluminum production when aluminum production requires more energy per unit of capital than steel production.
Aluminum is an energy intensive industry
3.
general term used to describe the amount of a factor needed to produce one unit of a good.
Unit Factor Requirement
4.
the two key terms used in the Heckscher-Ohlin model; one to compare industries, the other to compare countries.
Labor (capital) intensive industry; labor (capital) abundant country
5. term used to describe when the capital-labor ratio in an industry varies with changes in market wages
and rents
Variable factor proportions
6.
term describing the ratio of the unit-capital requirement and the unit-labor requirement in production of a good.
Capital intensity
7.
8.
the assumption in the Heckscher-Ohlin model about unemployment of capital and labor.
interpretation given for the slope of the production possibility frontier.
Zero
Opportunity cost of production (Y in terms of X)
9.
the H-O model theorem that would be applied to identify the effects of a tariff on the prices of goods and factors.
Samuelson Theorem
Stolper-