HW4 Solution Key
UCDavis, 160a, Fall 2011
Prof. Farshid Mojaver
Factor Movement between Countries
1. In the short-run specific-factors model, examine the impact on a small country following a
natural disaster that decreases its population. Assume that land is specific to agriculture, capital is
specific to manufacturing, and labor is free to move between the two sectors.
a. In a diagram similar to Figure 5-2, determine the impact of the decrease in workforce on
the output of each industry and the equilibrium wage.
b. What happens to the rentals on capital and land?
Answer
a. The following diagram depicts a decrease in population (labor) in the specific-factors model.
The origin for agriculture shifts inward by exactly the amount of the change in population,
carrying with it the curve representing the marginal product of labor in agriculture. (Note: one
could equivalently shift the origin and MPL curve in manufacturing and arrive at the same result.)
The new equilibrium is determined at the intersection of PM MPLM and (PA MPLA)’, which
corresponds to a higher wage W’. In manufacturing, the amount of labor decreases from OML to
OML’ and the amount of capital remains the same. As a result, the output of manufacturing
decreases. In agriculture, the amount of labor has decreased from OAL to OA’L’ (note that (L’- L)
is necessarily less than (OA‘ - OA) and the amount of land remains the same. As a result, the
output of agriculture also decreases).
b. Because the quantity of labor in both industries decreases due to the natural disaster, the
marginal product of labor increases in both industries and the marginal products of the industryspecific factors decrease. Because it is a small country, the final output prices PA and PM remain
unchanged; hence, the rental rate for capital, PM MPK, decreases and the rental rate for land, PA
MPT, decreases.
2. How would your answer to problem 1 change if instead we use the long-run model, with shoes
and computers produced using labor and capital?
Answer: In the long-run model, a decrease in labor does not affect factor prices at all. Rather, the
output of shoes and computers adjust: according to the Rybczynski theorem, the output of the
labor-intensive industry (shoes) decreases and the output of the capital-intensive industry
(computers) increases. This point can be illustrated graphically as well, as in problem 3.
3. 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 5.11 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?
Answer
a).
Wage, W
A
W
B
W' P MPLA
A
PAMPL’A
OM
PMMPLM
L
L'
OA
L
b) With less land per laborer in the agriculture sector, MPLA decreases. This is represented by an
inward shift in the wage curve for agriculture and leads to a new equilibrium at point B. In words,
wages in the agriculture sector drop, drawing labor into the manufacturing sector. The increased
labor supply in the manufacturing sector puts downward pressure on the wage. In the new
equilibrium, wages are once again equalized across industries at W’< W, manufacturing labor
increases from OML to OML’, and agriculture labor decreases from OAL to OAL’.
c).
PAMPLA
Wage, W
A
C
W
W’
PAMPL'A
B
PMMPLM
OM
L
L’
L’’
OA
In the manufacturing industry, the quantity of labor increases and the amount of capital remains
the same (i.e., the labor/capital ratio increases). Therefore, the marginal product of capital
increases due to the natural disaster because each unit of capital has more laborers working with
it. As a result, the rental on capital, PM MPK, increases. In agriculture, the result seems
ambiguous at first.
On one hand, the natural disaster decreases the stock of land, which increases the marginal
product of land. On the other hand, the movement of labor from agriculture to manufacturing
decreases the marginal product of land. Which one of these effects is stronger? It is possible to
answer this question by looking at the move from A to B in steps. Consider the contraction in the
marginal product of labor in agriculture from A to C: The wage is held constant by (L’’ - L)
workers leaving the agriculture industry. Because the wage has not changed, nor has the
labor/land ratio or the rental on land. Then, allowing workers to migrate back into agriculture
holding the amount of land fixed, going from C to B, the wage is depressed to W’ and the
marginal product of land increases. Combining these steps, the land rental, PA MPT, increases
from A to B.
4. According to part A of Table 5-1, what education level loses most (that is, has the greatest decrease
in wage) from immigration to the United States? Does this result depend on keeping the rental on
capital constant? Explain why or why not.
Answer: Holding capital fixed, the table shows immigration has the greatest negative impact on
workers with very low or high levels of education and only a small negative impact on those workers
with mid-level education (12–15 years). The impacts are even smaller in the long run, when capital
adjusts to keep the real return to capital fixed in each industry: in that case, workers with very low or
high levels of education lose due to immigration, but workers with mid-level education gain due to the
immigration combined with the capital adjustment. The reason that the losses are smaller (and even
become gains) in the long run is that immigration leads to capital growth in industries.
5. In Table 5-2, we show the growth in the real rental and real wages in Singapore, along with the
implied productivity growth. One way to calculate the productivity growth is to take the average
of the growth in the real rental and real wage. The idea is that firms can afford to pay labor and
capital more if there is productivity growth, so in that case, real factor prices should be growing.
But if there is no productivity growth, the average of the growth in the real rental and real wage
should be close to zero.
To calculate the average of the growth in the real factor prices, we use the shares of GDP going to
capital and labor. Specifically, we multiply the growth in the real rental by the capital share of
GDP, and add the growth in the real wage multiplied by the labor share of GDP. Then answer:
a. For a capital-rich country like Singapore, the share of capital in GDP is about one half
and the share of labor is also one half. Using these shares, calculate the average of the
growth in the real rental and real wage shown in each row of Table 5-2. How do your
answers compare with the productivity growth shown in the last column of Table 5-2?
b. For an industrialized country like the United States, the share of capital in GDP is about
one third, and the share of labor in GDP is about two thirds. Using these shares, calculate
the average of the growth in the real rental and real wage shown in each row of Table 52. How do your answers now compare with the productivity growth shown in the last
column?
Answer:
a. As shown in column (3) of the table, when using a capital share of 0.5, as applies for a country
like Singapore, the implied productivity growth is close to that in Table 5-2, shown in column (5).
b. As shown in column (4) of the table, when using a capital share of 0.33, as applies for a
country like the United States, the implied productivity growth is not as close to that in Table 5-2,
shown in column (5).
6. Figure 5-14 is a supply-and-demand diagram for the world labor market. Starting at points A
and A*, consider a situation where some Foreign workers migrate to Home, but not enough to
reach the equilibrium with full migration (point B). As a result of the migration, the Home wage
decreases from W to W”> W’, and the Foreign wage increases from W* to W**< W’.
a. Are there gains that accrue to the Home country? If so, redraw the graph and identify the
magnitude of the gains for each country. If not, say why not.
b. Are there gains that accrue to the Foreign country? If so, again show the magnitude of
these gains in the diagram and show the world gains.
Answer
a) Home GDP is higher because of higher employment (by the extra area under demand
curve LL’). But if the migrant workers send some of their wages home not all of this gain
belongs to Home.
Gains to
Home
Wage, W
W
W”
W'
W**
W*
Gains to
Foreign
O
Foreign
Wage
A
B
D
Home
Wage
A*
L
L'
O*
L  World Amount of Labor  L *
b) If migrant workers send remittances back home Foreign is better off too. If Foreign
workers send all their extra earnings back home then we would have the situation like the
figure above where the purple area is gains to the Home country, while the yellow area is
gains to the Foreign country.
7. A housekeeper from the Philippines is contemplating immigrating to Singapore in search of higher
wages. Suppose that the housekeeper earns approximately $2,000 annually and expects to find a job in
Singapore worth approximately $5,000 annually for a period of 3 years. Furthermore, assume that the cost
of living in Singapore is $500 more per year than at home.
a. What can we say about the productivity of housekeepers in Singapore versus the Philippines?
Explain.
b. What is the total gain to the housekeeper from migrating?
c. Is there a corresponding gain for the employer in Singapore? Explain.
d. Suppose that the housekeeper is unable to obtain a work visa abroad and faces a payment schedule
for illegal trafficking as outlined in Table 5-4.The housekeeper intends to enter Singapore via
Indonesia. Now what are the gains to the migrant? Is it still worth moving?
Answer
a. Assuming that housekeeping is a perfectly competitive industry, housekeepers’ wages are
equal to their marginal product of labor. Because wages are higher in Singapore,
housekeepers there are more productive.
b. The total gains from migrating are the net benefits relative to staying in the Philippines—
that is, salary of $5,000 minus the opportunity cost of working in the Philippines of
$2,000, minus the extra costs of living in Singapore of $500. Annual gains from
migrating (over the first 3 years) are $2,500.
c. The gains to the employer in Singapore depend on whether the wage is driven down by
the migration.
d. The trafficking costs from Indonesia to Singapore are $3,500, which is higher than the
annual net gain from migration of $2,500 but lower than the gain over 2 years of
$5,000.Thus, the housekeeper has to work at least 2 years in Singapore to make migrating
worthwhile.