HW3 Solution Key
UCDavis, 160a, Winter 2008
Prof. Farshid Mojaver
The Specific Factors
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.)
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 >
ΔPA/PA > ΔW/W > 0 =
ΔPM/PM > ΔRK/RK
3. In the (standard) Specific Factors Model, analyze the effects on factor prices of an increase in
the relative price of good X. That is,
a. Show how a rise in the price of good X, holding the nominal price of good Y constant,
would change the market equilibrium values of the
i. nominal wage
ii. nominal rental on capital employed in X
iii. nominal rental on capital employed in Y
iv. real wage
v. real rental on capital employed in X
vi. real rental on capital employed in Y
Use the usual Specific Factors diagram to help you get your results, together with other
relationships that you know must hold, but also be sure to say explicitly what you have
found and why.
Holding the price of good Y constant, the rise in price of good X shifts the W = PXMPLX
curve (labor demand curve for the X sector) upward, as shown below:
W
W
W3
W2
W1
PY MPLY
PX'MPLX
PXMPLX
OX
L X L X'
OY
Thus, the rise in PX causes more labor to be employed in the X sector (LX rises) and less
in the Y sector (LY falls). These changes in turn, since capital stocks in the sectors are
fixed in the specific factors model, mean that the ratios of capital to labor, on which
marginal products depend, change as follows:
KX/LX falls
KY/LY rises.
It follows, since in each sector MPL rises with K/L and MPK falls with K/L, that
MPLX falls
MPLY rises
MPKX rises MPKY falls
From the figure we see immediately that the nominal wage rises, from W1 to W2, as does
the nominal rental price of capital in the X sector (since the triangle above W2 and below
PX'MPLX is larger, meaning that payments to X-sector capital increase, while the quantity
of capital there has not changed), while the nominal rental price of capital in the Y sector
falls (the triangle for it gets smaller).
As for real factor prices, these can be inferred from the ratios of their nominal prices to
goods prices, which are equal to marginal products, as shown in the list below.
W = PXMPLX = PYMPLY rises, from figure
RX = PXMPKX rises, from figure, or because PX and MPKX both rise
RY = PYMPKY falls, from figure, or because MPKY falls
W/PX = MPLX falls
W/PY = MPLY rises
hence effect on real wage is ambiguous
RX/PX = MPKX rises
RX/PY = (RX/PX)(PX/PY) rises, since both terms rise
hence real rental on X-sector capital rises
RY/PY = MPKY falls
RY/PX = (RY/PY)/(PX/PY) falls, since numerator falls and denominator rises
hence real rental on Y-sector capital falls
b. We still assume that the relative price of good X increases due to trade. Which of
your answers would be changed if it was the nominal wage that was fixed, instead
of the nominal price of Y? (Hint: in this case, since W = PXMPLX = PYMPLY, and
since the shift of labor into the X sector has caused MPLX to fall and MPLY to
rise, the constant wage requires that PX rises while PY falls.
Now the figure is a little bit more complicated. In addition to what is shown above, we
would need to lower the price of good Y to get W back where it started. Just note that
real variables are unaffected by nominal ones, so the answers for real factor prices must
be the same as above. (Each ratio of a factor price to a goods price depends just on a
real marginal product and, in some cases, the relative prices of the goods, but never on
any nominal prices alone.)
W = PXMPLX = PYMPLY, and since the shift of labor has caused MPLX to fall and MPLY
to rise, the constant wage requires that PX rise while PY falls. Thus RX = PXMPKX rises,
since both PX and MPKX rise, and RY = PYMPKY falls, since both PY and MPKY fall.
Hecksher_Ohlin Model
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. Stolper-Samuelson Theorem
I. MC Question: 1.D, 2.B, 3.D, 4.C, 5.C, 6.B, 7.B
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 import-competing industries and owners of factors used intensively in importcompeting 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.