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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.)
AK
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
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
AK: for these problems see your 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 A.
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?
AK
a).
Wage, W
A
W
B
W'
PAMPLA
PAMPL’A
OM
PMMPL'M
PMMPLM
LM
L
L'
LA
OA
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
A
W''
W
W'
B
PAMPLA
PAMPL’A
OM
LM
PMMPL'M
PMMPLM
L
L'
L
LA
OA
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?
AK
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

KS
Ob
L
LS 
Labor allocated to basket
Total amount of labor in the economy, L
K
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) Check the box diagram below, 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.
6. Figure 5.16 is a supply and demand diagram for the world labor market. Consider a situation where
Foreign workers immigrate to the home country, causing the Home wage to decrease to WNEW > W’, and
where the Foreign wage begins at W* and increases to WNEW > W’.
a) Is this a stable outcome in the long run? That is, would you expect this pattern of immigration to
stay the same, to reverse, or to stop at the new Home and Foreign wages?
b) Going from old wages to the new, are there gains that accrue to the Home country? Are there
gains that accrue to the Foreign country? If so, redraw the graph and identify the magnitude of the
gains for each country. If not, say why not.
AK
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.
Gains to
Home
Wage, W
W
WNew
W'
W*New
W*
Gains to
Foreign
O
Foreign
Wage
A
B
D
Home
Wage
A*
L
L'
O*
L  World Amount of Labor  L *
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).