International Economics Second Edition By Feenstra - Test Bank

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63
Movement of Labor and
Capital between Countries
Notes to Instructor
Chapter Summary
Chapter 5 studies the impact of immigration and foreign direct investment on
wages and returns on rental of land and capital to the foreign and host coun-
tries. Using the short-run specific-factors model, we examine how the move-
ment of labor between countries leads to a decline in the host country wage
following the inflow of labor. By contrast, the long-run model shows that the
increase in foreign labor supply does not result in a change in the host coun-
try wage. The short- and long-run models also explain the returns to capital
due to foreign direct investment.
Comments
This chapter covers the Rybczynski theorem and Factor Price Insensitivity,
which were not covered in the previous chapter. Note that Factor Price
Equalization is not dealt with except in problems 7 and 8.
This chapter bridges the gap between the short-run model (the specific-
factors from Chapter 3) and the long-run model (the Heckscher-Ohlin model
from Chapter 4). This allows an optional discussion of policies issues early on.
Immigration is not often discussed in textbooks and is exciting to teach. As
part of the lecture on foreign direct investment (FDI), it may be useful to read
out loud the article by Paul Krugman titled, “The Myth of Asia’s Miracle. ”
5
The students may think that the article is about Bill Clinton after he was
newly elected and the race between East and West, where the East is Asia.
However, toward the end they realize that it is actually in reference to John
Kennedy and the East is the Soviet Union. This leads to a discussion of how
Singapore, similar to the Soviet Union, experienced a depressed rate of return
to capital as a result of the inflow of FDI.
Lecture Notes
Introduction
During May and September, 1980, 125,000 Cubans left the port of Mariel,
Cuba, for Miami, which increased the host city’s population by about 7%.
Despite the large supply of low-skilled immigrants from Cuba, the wages of
low-skilled workers in Miami did not vary much relative to the national
trend.
Another example contradicting the fall in wages is the migration of
670,000 Russian Jews to Israel from late 1989 to 1996. The rise in the sup-
ply of highly skilled immigrants from Russia not only increased Israel’s pop-
ulation by 11% but also led to an increase in the wages of high-skilled work-
ers in Israel during the same period. A similar rise in the supply of highly
skilled workers occurred in Europe and the United States between the 1800s
and 1900s. In the following section, we examine whether these two cases pro-
vide evidence contrary to the basic principles of supply and demand.
1 Movement of Labor Between Countries
To understand the impact of migration on wages and rentals paid to capital
and land in the host country, we return to the specific-factors model presented
in Chapter 3. We begin with the short-run case in which capital and land are
fixed and labor is mobile between industries and countries. We assume that
the prices of goods, determined by the world markets, and wages are fixed.
Effects of Immigration in the Short Run: Specific-Factors Model
Similar to Chapter 3, we assume that the economy has two sectors: agricul-
ture, where land is the specific factor, and manufacturing, which uses capital
as the specific factor. Figure 5-1 shows that the total amount of labor in the
economy, L  LM  LA , is divided between the two industries, with the
amount of labor used in manufacturing, LM, measured from left (0M ) to right;
whereas the amount used in agriculture, LA , is measured from right (0A ) to
left.
Determining the Wage The curve representing the value of the marginal
product of labor in manufacturing (agriculture) comes from multiplying the
marginal product of labor in manufacturing (agriculture) with its price,
P M (PA ). The curve is downward (upward) sloping, reflecting the decline in
the marginal product of labor in manufacturing (agriculture) as we add more
labor to the sector, moving from left to right (right to left). The intersection
64 Chapter 5 ■ Movement of Labor and Capital between Countries
of the two marginal product curves gives the Home equilibrium wage and
shows that 0ML units of labor are used in manufacturing and 0A L units of la-
bor are used in agriculture. Because wages are equalized across the two sec-
tors, there is no incentive for labor to move between the industries.
Effect of Immigration on the Wage in Home As a contrast, we assume that
the wage in Foreign, W*, is less than that at Home, W. The higher wage entices
Foreign workers to move to Home, thereby increasing the Home workforce
by the number of immigrants, L. The increase in the amount of labor from
Foreign is shown as the expansion of the horizontal axis in Figure 5. 2, where the
origin for the agriculture industry shifts rightward from 0A to 0A by the amount
L. Coinciding with the rightward movement of the agriculture origin is
a parallel shift of the marginal product curve PA  MPLA to (P A  MPLA) by
the amount of the increase in Home workforce, L. The intersection of
(PA  MPLA ) and PM  MPLM gives the new equilibrium Home wage at point
B. Because both sectors absorb the additional workers (0ML  0ML and
0AL  0A L), the marginal product of labor in both industries declines, lead-
ing to a lower wage relative to premigration.
APPLICATION
Immigration to the New World
In 1870, the real wages of the “New World,” which included countries in North
and South America and Australia, were nearly three times higher than the “Old
World,” or Europe, as shown in Figure 5-3. Encouraged by the high wages and
new opportunities, about 30 million Europeans migrated to the New World be-
tween 1870 and 1913. Due to the large influx of new workers, the wages in the
New World grew slower relative to those of the Old World. By 1913, European
wages increased to half that of the New World. Figure 5-3 also shows forecasts
of the real wages without the immigration. The comparison of the estimated
wage growth with the actual indicates that wages in the New World grew slower
and wages in Europe increased faster due to emigration. ■
APPLICATION
Immigration to the United States and Europe Today
Immigration continues to take place today, but rather than from Europe to the
New World, workers are moving from developing countries to the richer in-
dustrialized countries. Policies toward immigration have changed over the
years in the wealthier host countries. For example, during the 1960s and
1970s, some European countries welcomed workers to fill shortages in un-
skilled jobs. The more recent policy in the European Union continues to re-
cruit workers but the aim is for high-skilled labor.
The policy toward immigration is also hotly debated in the United States.
Although most of the focus has been on the influx of illegal immigrants to the
country, many unskilled workers enter under the special visa programs to fill
voids in the agriculture sector as crop harvesters. In addition, a number of
skilled workers such as engineers and scientists are granted special privileges
to work in the United States.
The pattern between the number of immigrants and educational level is
shown in Figure 5-4 for the United States. The graphical analysis indicates
that contrary to the public debates, immigrants scarcely compete with most
Chapter 5 ■ Movement of Labor and Capital between Countries 65
domestic workers with mid levels of education. Instead, the foreign workers
vie for jobs primarily held by the lowest and highest ends of the educational
levels. In other words, although illegal immigrants may pose a threat to the
lowest-educated workers, those with the highest educational level are in com-
petition with legal migrants under the special H-1B visas.
Using an extension of the specific-factors model to accommodate for la-
bor with different educational levels, we find that between 1990 and 2004 the
inflow of workers to the United States resulted in a drop in wages of high-
school dropouts by 9%. The wages of college graduates fell by 5% whereas
most U. S. workers with mid-level educations saw their wages fall by 1% to
2. 4% for those with some college versus high school degree, respectively. ■
H E A D L I N E S
Europe Sours on Labor Migration
Following the expansion of the European Union in 2004 to include many Eastern European
countries, thousands of migrant workers from Asia found work in Eastern European countries
like Poland and the Czech Republic. These vacancies were created when countries like Great
Britain and Ireland welcomed the inflow of cheap Polish and Czech labor to work in indus-
tries like construction and services. Wages paid were modest by the standards of developed
Europe and yet were often three times as high as wages garnered back in Eastern Europe. A
system that worked so well for all involved has seen its first major test in the recent global
economic crisis. With high unemployment plaguing Great Britain, Spain, and other European
countries, governments are under pressure to limit if not reverse migrations flows.
Other Effects of Immigration in the Short Run
Rentals on Capital and Land We can compute the effect of immigration
on the earnings of capital and land by subtracting the payment to labor from
the revenue earned in each sector. Because wages are lower due to the influx
of foreign workers, the rentals to capital and land are higher. Additionally, the
rise in the rentals on capital and land occurs because the increase in labor
hired in each industry raises the marginal product of both capital and land.
Thus, owners of capital and land generally oppose policies that restrict immi-
gration for ones that would allow foreign workers to freely work in their in-
dustries, whereas workers, particularly unions, support stricter immigration
laws to lessen competition for jobs and decreases in their wages.
Effect of Immigration on Industry Output In addition to the impact on re-
turns to capital and land, the inflow of workers increases total output in both
agriculture and manufacturing as shown in Figure 5-5. Given our assumption
66 Chapter 5 ■ Movement of Labor and Capital between Countries
N E T W O R K
According to the U.S. Citizenship and Immigration Services, “the H-1B is a nonimmigrant
classification used by an alien who will be employed temporarily in a specialty occupation
or as a fashion model of distinguished merit and ability.” In fiscal year (FY) 2004, the law
limited the number of foreigners who may be issued an H-1B visa to 65,000.
of constant prices and fixed specific factors in the short run, Home will pro-
duce at point B on the new PPF.
Effects of Immigration in the Long Run
We will now determine the long-run effects of the movement of labor be-
tween countries. To simplify the model, we assume only two factors of pro-
duction (capital and labor), both of which are freely mobile between two in-
dustries (computers and shoes). The total amount of capital available at Home
is denoted by K, where KC units of capital are allocated to the production of
computers and KS units are used in producing shoes. Similarly, the total avail-
able labor at Home is represented by L, with LC employed in the production
of computers and LS devoted to shoe production. In addition, we assume that
shoe production is labor-intensive relative to computer production. Namely,
the labor/capital ratio in shoes is higher than that in computers (LS / KS 
LC / KC ). It follows that the capital/labor ratio is higher in the computer in-
dustry because the production of computers is capital-intensive as compared
with shoes (KC / LC  KS / LS ). Figure 5-6 shows Home’s PPF.
Box Diagram Figure 5-7 illustrates a “box diagram” where the horizontal
(vertical) axis measures the total amount of Home labor, L (capital, K). Read-
ing from the bottom left-hand corner, OSL units of labor and OSK units of
capital are employment in shoes production; whereas from the top right cor-
ner, O CL units of labor and O CK units of capital are used in the production
of computers. In other words, the line O SA represents the quantity of labor
and capital allocated to the production of shoes. Similarly the endowments al-
located to computer production are given by the line O CA. The line O CA is
steeper than the line OSA because the capital/labor ratio in shoes (OSK / OSL )
is lower than that in the computers industry (OCK / O CL).
Determination of the Real Wage and Real Rental The real wage and real
rental is given by the line along OSA because it represents the amount of la-
bor and capital used, namely the capital/labor ratio for shoe manufacture.
Increase in the Amount of Home Labor Suppose the inflow of foreign
workers is given by the amount L, then the total available labor at Home is
now higher at L   L  L  L. The increase in amount of labor is illus-
trated by the expansion of the horizontal axis in Figure 5-8. The additional
labor finds employment in the labor-intensive shoe industry. With the in-
crease in the number of workers available per unit of capital in the shoe in-
dustry, the marginal product of labor decreases but the marginal product of
capital rises. This leads to an increase in the rentals on capital in the shoe in-
dustry, which draws some capital away from the computer industry. The
movement of capital from computers to shoes raises the wage in the shoe in-
dustry. Consequently, some labor will also leave the computer industry. This
movement of labor and capital between the two industries continues until the
labor/capital ratio in each industry returns to the premigration level.
The new allocation of labor is illustrated in Figure 5-8, where the amount
of capital and labor devoted to the production of shoes are given by OSK
and OSL, respectively. Given the new equilibrium denoted by point B, the
endowments dedicated to shoes production has increased (OSK  OSK and
OSL  OSL). By contrast, the units of capital (OCK) and labor (O CL)
Chapter 5 ■ Movement of Labor and Capital between Countries 67
employed in the computer industry have declined (O CK  O CK and O CL
 OCL). Because the movement of labor and capital between shoes and com-
puters leaves the labor/capital ratio unchanged, the line OSB parallels the line
O SA and has the same slope. More important, the constant labor/capital ra-
tios across the two industries imply that the marginal products of labor and
capital remain unchanged. Thus, contrary to the short-run case, the inflow of
labor does not change wage and rentals on capital in the long run where all
factors of production are mobile.
Effect of Immigration on Industry Outputs Furthermore, in the short-
run, in which the specific factors are fixed, an increase in the supply of la-
bor leads to an increase in the output of both goods. By comparison, be-
cause the increase in labor endowment is absorbed entirely into the
labor-intensive industry in addition to some capital and labor from the cap-
ital-intensive industry, the output of shoes rises in the long run and com-
puter production falls. The increase in shoe output is reflected by the new
Home equilibrium at point B in Figure 5-9, where the unchanged relative
price of computers is just tangent to the outermost PPF. Note that this new
PPF is biased in the direction of shoes because of the increase in the en-
dowments devoted to the shoes industry. The long-run result of factor
movement on output is given by the following theorem:
Rybczynski theorem: An increase in the amount of a factor found in an economy
will increase the output of the industry using that factor intensively, and decrease the out-
put of the other industry.
Effect of Immigration on Factor Prices By absorbing additional units of the
increased factor via output expansion in the industry which uses the factor in-
tensively and contracting the output of the other industry, factor prices remain
unchanged. This result is referred to as:
Factor Price Insensitivity: In the Heckscher-Ohlin model with two goods and
two factors, an increase in the amount of a factor found in an economy can be absorbed by
changing the outputs of the industries, without any change in the factor prices.
APPLICATION
The Effects of the Mariel Boat Lift
on Industry Output in Miami
Recall that the Cuban refugees arriving in Miami in 1980 were predominately
less skilled relative to those in the Host city. With the large inflow in unskilled
workers, according to the Rybczynski theorem there should be an increase in the
outputs of the unskilled-labor–intensive industries in Miami and a fall in the pro-
duction of the skilled-intensive industries. Figure 5-10 shows the real-
value–added per capita for Miami and the average for comparison cities in the
apparel industry and high-skilled industries in panels (a) and (b), respectively.
Panel (a) provides some evidence of the results predicted by the Rybczynski
theorem. Namely, although the real-value–added per capita in the apparel in-
dustry fell between 1972 and 1996, the rate of decline was slower for Miami rel-
ative to the comparison cities after the boatlift in 1980. Support for the
Rybczynski theorem can also be found in panel (b), which shows that the
real-value–added per capita in skilled-intensive industries experienced a
greater drop in Miami after 1980 as compared with similar cities.
68 Chapter 5 ■ Movement of Labor and Capital between Countries
However, another reason why wages did not change in Miami could be that
the city adopted the use of computers more slowly relative to the rest of the
country during the period of “skill-biased technological change. ” Although
the national trend led to an increase in the demand for high-skilled workers
and a reduction in the employment of low-skilled workers in the 1980s, many
industries in Miami employed low-skilled workers such as the Mariel refugees
instead of moving to computer technologies. Therefore it is possible that the
absorption of the refugees in the apparel industry as well as other industries
such as manufacturing and services caused the wage to remain unchanged
rather than the explanation offered by the Rybczynski theorem. ■
APPLICATION
Immigration and U.S. Wages, 1990 to 2004
The impact of migrants on the wages of U. S. workers by education attain-
ment is presented in Table 5-1 for years 1990 to 2004. Part A gives the esti-
mated effect due to total migration and part B provides the estimates due only
to illegal immigrants. The findings offered in the first row of part A are cal-
culated based on the short-run specific-factors model, where capital and land
are fixed across industries. The estimates indicate that the inflow of foreign
labors have the largest negative impact on workers with less than 12 years of
education, followed by those with a college education. On average, the im-
pact of immigration on U. S. wages is 3. 2%.
The results are different when we remove the short-run assumption by al-
lowing capital to grow in each industry such that the real rental on capital re-
mains constant. By employing the additional workers with increased capital,
the estimated effect of immigration on U. S. wages is only negative on high-
school dropouts and those with a college education. More important, rather
than declining, U. S. wages increased by an average of 0. 3% as a result of the
immigration. These estimates are available in the second row of part A.
Turning to part B, the estimates suggest that only wages of those least educated
are negatively impacted by the inflow of illegal immigrants. With the absorption
of the illegal workers along with capital growth in each industry, all U. S. work-
ers with at least a high-school degree gain from illegal immigration. ■
2 The Movement of Capital between Countries:
Foreign Direct Investment
In this section we study the movement of capital across countries, also known
as foreign direct investment (FDI). A country experiences an inflow of FDI
when a foreign company builds or buys property including plant and equip-
ment in its land. FDI is considered greenfield investment when the foreign
company builds a plant in the host country. The investment is called acquisi-
tion when the foreign company buys an existing plant.
One motivation for companies investing abroad is to take advantage of
lower wages in the foreign country. By transferring some of their capital to
the Host country, companies from high-wage countries can combine their ex-
pertise to produce goods more cheaply using low-wage workers. Examples
include the purchase of plants by Western European firms that were once
state-owned in Eastern European countries such as the Czech Republic.
Chapter 5 ■ Movement of Labor and Capital between Countries 69
In addition, most of the FDI flowed into the manufacturing sector as shown in the follow-
ing table:
70 Chapter 5 ■ Movement of Labor and Capital between Countries
N E T W O R K
According to CzechInvest, the Investment and Business Development Agency, the Czech Re-
public has received approximately U.S. $40 billion in FDI since 1990. The following table
shows the inflow of FDI between 2003 and 2005. Most FDIs have been made by Western Eu-
ropean countries.
2006 2007 2008
$ % $ % $ %
WORLD 123,431.3 100% 211,943.7 100% 182,796.5 100%
EUROPE 122,832.1 100% 187,237.9 88% 168,684.2 92%
EU-27 110,429.7 89% 166,478.5 79% 157,439.3 86%
Belgium -606.3 0% 5,480.1 3% -6,713.6 -4%
France 6,044.4 5% 1,102.9 1% 7,585.5 4%
Italy -1,031.5 -1% 1,133.4 1% 2,477.6 1%
Germany 43,522.0 35% 24,471.9 12% 58,927.9 32%
Netherlands -9,698.1 -8% 45,007.6 21% 25,022.4 14%
Austria 22,567.7 18% 22,306.5 11% 35,646.1 20%
United Kingdom 5,936.0 5% -10,840.8 -5% -15,331.6 -8%
Sweden -4,363.1 -4% 6,891.1 3% 3,022.3 2%
Cyprus 4,826.6 4% 6,164.3 3% 17,730.6 10%
Hungary 873.8 1% 731.9 0% 1,280.8 1%
Poland 959.2 1% 3,425.5 2% 2,468.2 1%
Slovenia 31.2 0% 392.0 0% 235.4 0%
Slovakia 9,397.5 8% 7,770.1 4% 14,404.5 8%
EFTA 13,148.0 11% 21,296.5 10% 10,725.3 6%
Switzerland 12,008.5 10% 19,670.7 9% 6,907.8 4%
ASIA 1,087.8 1% 25,338.4 12% 3,356.4 2%
Source: http://www.czso.cz/csu/2009edicniplan.nsf/engkapitola/001-09-2009-0700
FDI into the Czech Republic by Country, 2006–2008
(millions of U.S. dollars)
2006 2007 2008
Economic Activity $ % $ % $ %
Total 123,431.3 100% 211,943.7 100% 182,796.5 100%
Agriculture, hunting
and forestry, fishing 1,466.3 1% 193.8 0% -480.8 0%
Mining and quarrying -1,879.1 -2% -12,438.7 -6% 753.2 0%
Manufacturing 38,306.1 31% 78,437.0 37% 61,248.0 34%
Electricity, gas, and
water supply -592.0 0% -4,658.7 -2% 9,412.7 5%
Construction 3,218.0 3% 716.5 0% 163.4 0%
Wholesale and retail
trade; repair of motor
vehicles, motorcycles, and
personal and household
goods 28,055.3 23% 22,427.3 11% 21,195.1 12%
Hotels and restaurants 1,227.7 1% 3,120.4 1% 1,782.9 1%
Transport, storage, and
communication -2,721.7 -2% 15,522.2 7% 6,171.5 3%
Financial intermediation 14,066.4 11% 46,841.9 22% 45,459.7 25%
Real estate, renting, and
business activities 32,573.7 26% 56,774.0 27% 31,951.1 17%
a
Source: http://www.czso.cz/csu/2009edicniplan.nsf/engkapitola/001-09-2009-0700
FDI into the Czech Republic by Sector, 2006–2008
(millions of U.S. dollars)
Greenfield Investment
In the following sections we focus on greenfield investments rather than ac-
quisitions. We treat the purchase of a new foreign building in the same way
as the movement of labor between countries. Doing so allows us to deter-
mine the impact of cross-country capital flows on the wage and rentals on
land and capital.
FDI in the Short Run: Specific-Factors Model
Effect of FDI on the Wage We begin with the short-run specific-factors
model in which labor is mobile and capital and land are used exclusively in
manufacturing and agriculture, respectively. Under these assumptions, the ad-
ditional capital is only employed in the manufacturing industry. The rise in the
amount of capital available per worker raises the marginal product of labor in
manufacturing. Holding prices constant, the inflow of capital shifts the PM 
MPLM curve rightward to PM  MPLM as illustrated in Figure 5-11. Due to the
shift, the equilibrium wage increases in the manufacturing sector, drawing out
some labor from agriculture. The labor movement between the two industries
continues until the wages are equalized across the two sectors at W  W.
Effect of FDI on the Industry Outputs The combination of increased capi-
tal and additional labor employed in the manufacturing sector means that the
output of manufactures increases after the inflow of FDI. In contrast, agricul-
ture production decreases because the amount of labor available to work on
the land has declined. The biased output growth cause by the inward FDI is
shown in Figure 5-11, where the equilibrium outputs shift from point A to
point B as prices are held constant.
Effect of FDI on the Rentals To determine the impact of FDI on the rental
on land, note that the decrease in workers employed in agriculture implies that
the marginal product of land falls. Consequently, the rental on land, R T 
PA  MPTA , drops because the price of agricultural goods is unchanged. For
the rental on capital, we use an alternative method that is measured by the dif-
ference between the revenue earned in manufacturing and payments to labor.
In Figure 5-12, we hold wage constant and let the amount of capital and la-
bor used in manufacturing increase in equal proportions from points A to C.
Given that the labor/capital ratio in manufacturing, LM / KM, is the same at
points A and C, then the rental on capital is also fixed. Next, we will con-
tinue to hold the capital usage constant but allow the wage to increase from
points C to B along the PM  MPLM curve. With higher payments to labor,
the rental on capital falls as the marginal product of capital decreases.
FDI in the Long Run
To examine the effect of FDI in the long run, we return to the simplified
model with two industries (computers and shoes) using two factors of pro-
duction (labor and capital), where computers are capital-intensive and shoes
are labor intensive (i. e. , KC / LC  KS / LS ). Point A of the “box diagram”
illustrated by Figure 5-13 gives the initial allocation of endowments between
the two industries. In particular, the lower left corner shows that O SL units
of labor and O SK units of capital are used in the production of shoes, whereas
Chapter 5 ■ Movement of Labor and Capital between Countries 71
the upper right corner denotes that the amount of labor and capital devoted
to computers is measured by O CL and O CK, respectively.
Suppose that the amount of capital in the economy increases due to an in-
flow of FDI. The increase expands the right and left sides of the box in panel
(a) of Figure 5-13 and shifts the origin up to O C . The new allocation of fac-
tors between the industries is shown at point B. Now the labor and capital
used in the shoe industry are measured by OSB, which is shorter than the line
O SA. Therefore, less labor and less capital are used in the production of
footwear, and shoe output falls. The labor and capital used in computers are
measured by O C B, which is longer than the line OCA. Therefore, more la-
bor and more capital are used in computers, and the output of that industry
rises.
Effect of FDI on Outputs and Factor Prices The increase in the amount of
capital due to inward FDI is represented by the expansion of the vertical axis
where the origin for the computer industry shifts upward from OC to O C .
The new allocation of factors between the industries given by point B corre-
sponds to greater amounts of labor and capital dedicated to the capital-
intensive computer industry and a reduction in the endowments devoted to
the labor-intensive shoe industry. As predicted by the Rybczynski theorem,
the output in shoes falls and computer production enlarges, as shown in panel
(b) of Figure 5-13. Moreover, with no change in the capital/labor ratios across
the two industries, the wage and the rental on capital remain unchanged.
Similar to the inflow of labor, the results of the long-run model show that an
increase in capital does not impact the price of either factor.
APPLICATION
The Effect of FDI on Rentals and Wages in Singapore
Many countries have policies to attract foreign investments. One such coun-
try is Singapore, which for many years encouraged foreign firms to invest in
its electronics industry through the establishment of subsidiaries within its
borders. Table 5-2 presents the estimated effect of the inflow of FDI on the
real rental and wages in Singapore for 1970 to 1990. Over this period, the
overall capital/labor ratio grew about 5% per year. With the increase in cap-
ital relative to labor, the real rental on capital fell by 3. 4% each year as shown
in part A. On the flip side, the boost in capital available to each worker in-
creased the marginal product of labor such that the real wage grew by 1. 6%
per year. More specifically, these estimates are consistent with the short-run
specific-factors model, which predicts that the increase in capital due to FDI
would lead to a fall in the rental on the specific factors (capital) and an in-
crease in the wage paid to the mobile factor (labor).
Alternatively, the rental on capital can be measured as the price, PK, of the
capital equipment multiplied by the interest rate, i, earned had the capital
been invested in other forms of asset plus its rate of depreciation, d. Namely
the rental on the capital equipment calculated as PK  (i  d) is equivalent to
the return on a financial asset from renting out the equipment. Part B gives
the estimates on the growth rate in the real rental using three different inter-
est rates. The real rental is given by the following formula:
 (i  d)
R
P
PK
P
72 Chapter 5 ■ Movement of Labor and Capital between Countries
where P is the overall price index. Using the bank lending rate for i, the real
rental is estimated to grow by 1. 6% per year as shown in the first row. With
the return on equity as the interest rate, the second row shows that the real
rental to fall by 0. 2% each year between 1971 and 1990. The third row shows
the real rental to decline by 0. 5% each year when the earnings–price ratio is
used as the interest rate.
Altogether the alternative calculations for the rental on capital contradict
the results of part A, suggesting a lack of evidence that the rental on capital fell
as predicted by the short-run specific-factors model. However, these results
do not clearly verify the long-run specific-factors model. In particular, part B
also shows the real wage in Singapore over the same period. Contrary to the
predictions of the long-run specific-factors model, instead of remaining con-
stant, real wages grew between 2. 7% and 3. 6% per year, varying by the in-
terest rate used. The growth of the real wages coupled with the relatively sta-
ble real rental on capital may indicate that productivity growth occurred in
Singapore, which increased the marginal product of labor. ■
H E A D L I N E S
“The Myth of Asia” Miracle
The article gives the reader the impression that the United States and Europe are concerned
about rising competition from Asia due to the amount of capital accumulation in the region.
In addition, it alludes to a pledge made—possibly by Bill Clinton—to meet the new chal-
lenge. However, it turns out that the Eastern economy is the Soviet Union and the technol-
ogy challenge resulting from the launch of Sputnik. Moreover, the president in reference is
John Kennedy. From this, Krugman drives the point that the competition facing the Western
economies resulting from the economic growth of the Asian countries is not new.
3 Gains from Labor and Capital Flows
Most countries have restrictions on foreign investment and immigration, par-
ticularly the latter. These limitations include a quota on the number of indi-
viduals allowed from each country, such as the Quota Law of 1921 in the
United States. The restrictions are supported by groups opposed to public
spending on services available to immigrants (e. g. , school, medical care, and
welfare) as well as individuals in fear of job competition. However, as the spe-
cific-factors model shows, in the Host country, certain groups benefit from
the inflow of workers, which lowers wages, particularly owners of the inten-
sively used factor. Moreover, the movement of capital and labor provide po-
tential gains to the Foreign country.
Gains from Immigration
Wages at Home and Abroad The specific-factors model for the world is il-
lustrated in Figure 5-14, in which the horizontal axis measures the number of
workers at Home, L, from left to right, and the number of workers in Foreign,
L*
, is measured from right to left, giving the total amount of workers in the
world, L  L *. The labor demand curve for Home is downward sloping, with
Chapter 5 ■ Movement of Labor and Capital between Countries 73
OL workers employed prior to immigration at the equilibrium wage of W given
by point A. With additional workers entering from the Foreign country, Home
increased employment to OL, which reduces the Home wage to W, at point
B. For Foreign, the labor demand curve is upward sloping because its endow-
ment is measured from right to left. Before the movement of labor, the number
of workers employed in Foreign is equal to O*L, where the equilibrium wage,
W *, at point A* is lower than that at Home. The higher Home wage entices
some workers to leave Foreign, which reduces the number of labor to O*L, dri-
ving up the Foreign wage to W, at point B. Note that wages are equalized
across the two countries at point B or the equilibrium with full migration.
Gains for the Home Country We are now ready to determine whether
there are overall gains to Home from immigration. Recall that wage is equal
to the marginal product of labor in the respective industry multiplied by the
price of its good. Therefore, the marginal product of the first Foreign worker
to migrate equals the Home wage, W. As each additional Foreign worker en-
ters the Home workforce, the marginal product of labor at Home falls given
the law of diminishing returns and our assumption of fixed land and capital in
the short run. The decrease in marginal product due to the inflow of immi-
grants causes the Home wage to decrease from W to W along the Home
wage curve from points A to B.
After migration all workers are paid the Home wage of W, which equals
the marginal product of the last worker multiplied by the goods price in each
industry. However, the marginal product of labor of all the Foreign workers
with the exception of the last to migrate is higher than the wage paid. There-
fore, the contribution of each Foreign worker to Home production is equal to
the individual’s marginal product minus the wage received. Namely, Home
benefits W  W from the first Foreign migrant, and so on. Summing up the
benefits from each Foreign worker, the overall gains to the Home economy
from immigration is denoted by the triangle ABC.
Gains for the Foreign Country In the Foreign country, the wage absence of
emigration is W* at point A*. As each worker leaves, the Foreign marginal
product of labor improves, causing the wage to rise from W* to W. In addi-
tion to workers in the Foreign country receiving the higher wage, emigrated
Foreign workers are also paid W in the Home country under full migration.
However, because the wage earned, W, at Home is higher than the Foreign
marginal product of labor (i. e. , between W and W* ), the Foreign country
benefits from the earnings sent back by migrated workers. Adding up the dif-
ferences between the wage earned by the migrants and their Foreign marginal
products gives the overall Foreign gains represented by triangle A*BC.
74 Chapter 5 ■ Movement of Labor and Capital between Countries
S I D E B A R
Immigrants and their Remittances
For some countries, remittances or earnings sent back to Home
by immigrants are an important source of income. The estimated
remittances in 2008 were $336 billion, up from $289 billion in
2007. World remittances then declined to $316 billion in 2009
due in part to the global recession. Table 5-3 shows the remit-
tances versus net foreign aid received by some developing coun-
tries in 2007. For these countries, remittances accounted for a
larger source of income than official aid.
World Gains from Migration The sum of triangles ABC and A*BC rep-
resenting Home and Foreign gains, respectively, gives the larger triangle
A*AB, which denotes the increase in the world gross domestic product
(GDP) due to immigration. For example, when the first migrant leaves
Foreign for Home, the GDP in the former country falls by W* whereas
that in the latter increases by W. The gain in world welfare due to the
movement of the first migrant is equal to the difference between the Home
and Foreign wages.
APPLICATION
Gains from Migration
It is estimated that the net gain due to immigration is about 0. 1% of GDP
where the migrants are assumed to make up approximately 10% of the U. S.
workforce and compete for domestic jobs. The 0. 1% net GDP gain trans-
lates into an estimate of 2% gains for capital and 1. 9% loss for domestic la-
bor. The relatively small size in GDP gain compared with the transfer of
income from labor to capital helps to explain the focus on potential harm
to labor instead of overall increases in welfare in debates over immigration
policies.
The first row of part A in Table 5-4 shows that the gains are higher (0. 4%
of GDP) if we assume the low-skilled work provided by the immigrants com-
plements those of the higher-skilled U. S. population. The gains are even
higher using estimates from household workers as shown in the second row.
More specifically, the net GDP gain would be about 1. 2% to 1. 4% if low-
skilled foreign labors substitute high-skilled domestic individuals by perform-
ing household work.
The estimated worldwide gains due to immigration are shown in part B.
The result in the first row indicates that a 3% flow of workers from develop-
ing to developed countries increases world GDP by 0. 6%. The remaining
findings in part B consider the enlargement of the European Union (EU), tak-
ing into account differences in technology across countries and allowing for
full mobility. The estimates suggest that the original 15 EU countries double
in productivity with the addition of the new members. Over time, the ben-
efits to the EU countries continue to rise due to the movement of capital and
labor from Eastern Europe. ■
Gains from Foreign Direct Investment
To determine the overall gains from FDI we present in Figure 5-15 the total
world capital on the horizontal axis and the rental earned in each country on
the vertical axis. The amount of capital used at Home, measured from left to
right, is denoted by OK. Prior to FDI, the Home rental is R at point A. The
units of capital employed in Foreign, measured from right to left, equals O*K,
with the Foreign rental R* determined at point A*. With capital mobility, FDI
flows from Home to Foreign because the rental is higher in the latter. The in-
crease in available capital decreases the marginal product of capital in Foreign,
which drives down the Foreign rental although raising the Home rental due
to the rise in the marginal product of capital at Home. The rental on capital
is equalized across the two countries at point B at which capital ceased to
Chapter 5 ■ Movement of Labor and Capital between Countries 75
move from Home to Foreign. Due to reasoning similar to that of the move-
ment of labor, the benefits to Home (Foreign) from the capital outflow (in-
flow) can be illustrated by the triangle ABC (A*BC). The sum of Home and
Foreign gains gives the world welfare improvement due to foreign direct in-
vestment, denoted by triangle A*BA.
5 Conclusion
This chapter examines the impact of labor and capital mobility on the Home
and Foreign country in the short and long run using the specific-factors
model. In the short run, the inflow of foreign workers reduces the marginal
product of labor, which in turn decreases wage in the host country. However,
due to the decrease in the payment to labor, the rentals on capital and land
rise. These results explain the opposition to immigration by labor groups, al-
though policy toward fewer labor restrictions are supported by landowners
and capital owners. In the long run, when labor as well as capital is mobile
between the industries, the wage does not necessary fall in contrast to the
short-run case. The reason is that there is an expansion in the output of the
industry that uses the labor intensively and a contraction in the other indus-
try leading to full employment without a change in the labor/capital ratio.
The cross-border movement of capital, also known as foreign direct invest-
ment (FDI), leads to an analogous effects on the Home and host countries as
immigration. Namely, the increased supply of capital from abroad lowers the
rental on capital in the short run. At the same time, the rental on land de-
creases and the surge in capital raises the marginal product of labor, which
causes wage to rise. However, as in the case with immigration, capital mobil-
ity does not lead to changes in wage and the rental on capital in the long run.
There are gains to the host country from the movement of labor and cap-
ital across borders. The gains to the home country result from paying the fac-
tors of production less than its full contribution to GDP. The source country
also benefits from the remittances or earnings received by the factors in the
host country. The overall gains in the world are the sum of the welfare in-
creases across the countries.
TEACHING TIPS
Tip 1: Differences in the Short- and Long-Run Model
This chapter deals with the affects of factor movements on factor returns in
both the short- and long-run models. This is important because it demon-
strates the differences between these two models. In teaching this chapter, it
is important to stress the differences in factor returns and their link to factor
mobility. In-Class Problems 9 and 10 demonstrate this difference. Ask stu-
dents to complete these problems and comment on the difference in output
and factor prices in these two problems.
Tip 2: Discussion and Debate Migration
Ask students to use information from this chapter (we suggest students read
SIDEBAR: Immigrants and their Remittances and APPLICATION:
76 Chapter 5 ■ Movement of Labor and Capital between Countries
Gains from Migration), as well as independent research, to prepare to dis-
cuss the consequences of migration for both countries involved. Given that
the short-run model predicts that both countries gain from migration only in
the presence of remittances, have students investigate recent developments in
remittance flows. Here are some potential data sources to get students started:
Data on world migration:
UN International Migrant Stock: http://esa. un. org/migration/
Data source for remittance flows:
Time series data: Go to http://data. un. org/Default. aspx and search for
“remittances. ”
Most recent data and projections: Search for “World Bank migration and
remittances” to find the World Bank’s Prospects for Migration and Remit-
tances, which provides the most recent data on remittance flows.
Tip 3: FDI Data Exercise
To familiarize students with data sources, ask students to look up the most re-
cent U. S. direct investment data, as seen in In-Class Problems 1–3. Instruct
students to go to http://www. bea. gov, and then proceed to the section la-
beled “International Economic Accounts. ” Scroll down to “Operations of
Multinational Companies” and click on the “Selected Tables” link for U. S.
direct investment abroad and foreign direct investment in the United States.
Here students will find country-by-industry tables on historical cost basis for
FDI in the United States and the U. S. direct investment position abroad (as
is reported in the in-class problems).
Ask students to investigate the latest available industry level data and discuss
whether it remains consistent with previous data or if there have been any ma-
jor changes. Additionally, you may want to ask students to investigate the data
by source and destination country (as in Problems 1 and 2). Which countries
does the United States invest in most heavily, and in which industries? Which
countries invest most heavily in the United States, and in what U. S. indus-
tries? Ask students to compile this information and discuss.
Chapter 5 ■ Movement of Labor and Capital between Countries 77
78 Chapter 5 ■ Movement of Labor and Capital between Countries
I N – C L A S S P R O B L E M S
1. Obtain information pertaining to the U. S. Direct
Investment Position Abroad on a Historical-Cost
Basis from the Bureau of Economic Analysis
(http://www. bea. gov/). Name the top ten coun-
tries receiving FDI from the United States. Com-
ment on your list. Are the countries the same over
the years?
Answer: The top ten countries receiving FDI
from the United States from 1990 to 2005 are
given in the table below. For the most part, the
top ten countries are the same over the years. All
the countries on the list, with the exception of
Bermuda, are industrialized countries. The invest-
ment in Mexico is considered vertical FDI, in
which U. S. multinationals move production
within the borders of its southern neighbor to cut
costs by using lower Mexican wages. By contrast,
Bermuda receives FDI from the United States be-
cause of its tax policies.
2. Name the top nine countries investing in the
United States using data from the Historical-Cost
Basis. Is your list of countries the same as that of
problem 1? What may account for the differences?
Answer: The top nine countries investing in the
United States from 1990 to 2005 are given in the
table below. Most countries receiving FDI from
the United States as listed in problem 1 are also the
top ten countries investing in the United States.
As mentioned in this chapter, this type of invest-
ment is called horizontal FDI. Note that Bermuda
and Mexico are replaced by Sweden and France.
Country 2009
World 3,508,142
Netherlands 471,567
United Kingdom 471,384
Canada 259,792
Bermuda 245,671
Luxembourg 174,092
Ireland 165,924
Switzerland 148,239
United Kingdom Islands, Caribbean 141,527
Germany 116,832
Australia 106,370
U.S. Direct Investment Abroad
on a Historical-Cost Basis
Country 2009
World 2,319,585
Japan 271,883
Germany 259,612
Canada 251,162
France 212,614
Netherlands 118,984
Bermuda 92,588
Switzerland 88,448
Australia 48,353
Spain 47,480
FDI into the U.S. by Country
on a Historical-Cost Basis
Chapter 5 ■ Movement of Labor and Capital between Countries 79
3. In which industries is the U. S. investment abroad
the largest? In what industries are foreign invest-
ments in the U. S. most concentrated?
Answer: U. S. investment is largest in manufac-
turing as well as services such as “holding compa-
nies (nonbank)” and “finance and insurance. ” For-
eign investment in the United States is most
concentrated in the manufacturing sector.
2005 2006 2007 2008 2009
All Industries 2,241,656 2,477,268 2,993,980 3,219,725 3,508,142
Mining 109,280 121,006 141,299 153,442 171,106
Manufacturing 430,737 441,724 484,839 484,596 541,080
Food 27,638 31,215 40,588 41,201 45,247
Chemicals 106,975 94,519 95,915 114,171 129,529
Primary and Fabricated metals 23,013 18,773 22,244 20,078 23,186
Machinery 26,433 29,136 31,257 39,093 43,612
Computers and electric products 50,773 63,113 69,467 65,530 65,598
Electrical equipment, appliances, and components 15,449 16,293 19,979 23,582 24,694
Transportation equipment 50,739 50,663 60,612 45,456 47,235
Wholesale trade 132,915 138,211 150,089 176,869 198,985
Information 102,848 100,445 116,923 135,037 149,826
Finance and insurance 463,981 514,462 649,773 688,160 746,993
Professional, scientific, and technical services 57,164 69,213 81,344 74,691 77,474
Holding companies (nonbank) 710,386 838,566 1,039,045 1,181,323 1,279,952
Source: Bureau of Economic Analysis
U.S. Direct Investment Abroad by Industry on a Historical-Cost Basis, millions of U.S. dollars (2005–2009)
2005 2006 2007 2008 2009
All Industries 1,634,121 1,840,463 2,055,176 2,165,748 2,319,585
Manufacturing 499,851 569,324 684,555 746,475 790,568
Food 45,217 50,339 26,903 23,849 20,004
Chemicals 123,784 135,054 190,049 187,332 203,760
Primary and Fabricated metals 27,164 34,812 42,453 47,645 48,693
Machinery 46,433 41,600 93,091 88,730 95,585
Computers and electric products 31,298 48,944 44,410 59,757 55,349
Electrical equipment, appliances, and components 11,037 25,537 20,112 20,561 24,004
Transportation equipment 74,485 67,505 93,053 83,907 96,872
Wholesale trade 235,508 255,590 294,697 316,581 328,430
Retail trade 30,934 31,677 31,363 40,129 44,330
Information 102,584 135,986 155,704 164,491 146,114
Depository Institutions (banking) 130,184 135,391 107,242 92,565 111,913
Finance and insurance 214,623 283,364 275,722 238,875 293,204
Real estate, rental, and leasing 37,341 41,924 53,780 57,459 54,539
Professional, scientific, and technical services 51,546 47,597 55,201 62,934 46,087
FDI in the United States by Industry on a Historical-Cost Basis, millions of U.S. dollars (2005–2009)
4. Why might a labor group support limitations on
the outflow of FDI?
Answer: In the short run, an outflow of FDI decreases
the amount of capital available per worker. This lowers
the marginal product of labor resulting in a fall in the
equilibrium wage.
80 Chapter 5 ■ Movement of Labor and Capital between Countries
5. According to Table 5-3, for some countries remit-
tances account for a larger source of income than
foreign aid. Should these countries have policies
to encourage emigration? Explain.
Answer: In the short run, emigration would de-
crease the available labor leading to a higher mar-
ginal product of labor and higher wages in the for-
eign country. In addition, if remittances are a
significant source of income for the foreign coun-
try, then it is likely that emigration policies would
be encouraged.
6. Assume that Mexico receives an inflow of FDI.
Suppose two factors (labor and capital) are used in
the production in two industries (food and televi-
sions). Further assume that televisions are capital-
intensive as compared with food. Use the long-
run specific-factors model to answer the following
questions.
a. Show the impact of the inflow of FDI on
Mexico in an illustration similar to Figure
5. 13 with output of food (televisions) on the
vertical (horizontal) axis. What happens to the
output of each good?
Answer: Due to the inflow of FDI, more la-
bor and more capital are in televisions so that
the output of that industry goes up. By con-
trast, less labor and less capital are devoted to
the production of food, leading to a fall in the
output in this industry. As predicted by the
Rybczynski theorem, the additional capital in-
creased the output of the capital-intensive in-
dustry (televisions) and decreased the output
of the labor-intensive industry (food).
b. How has wage changed in terms of food and
televisions?
Answer: Because the capital-intensive indus-
try (televisions) absorbed the additional capital
along with the shift of labor from the labor-
intensive industry, the capital/labor ratios re-
mained constant. With the capital/labor ratios
unchanged across the two industries, the wage
is also unchanged. With constant factor prices,
wage does not change in terms of either food
or televisions.
7. Only developing countries compete for FDI.
Comment.
Answer: Competition for FDI takes place among
developing as well as developed countries. An ex-
ample is the generous incentive package offered by
Kentucky to Toyota Motor Corporation in 1985.
Output of
food, QF
Output of
televisions,
Q TV
Relative price of
televisions, P TV / PF
Shift in Mexico
PPF due to FDI
Mexico PPF
A
B
Chapter 5 ■ Movement of Labor and Capital between Countries 81
8. The following table shows the flow of FDI for se-
lect countries between 1985 and 2008. Over this
period, the inflow of FDI to China increased sub-
stantially. What is the impact of this flow of capi-
tal on wages in China according to the short-run
specific-factors model?
Answer: In the short run, the inflow of capital
raises the marginal product of labor in the capital-
specific industry. With prices held constant, the
equilibrium wages in China increase initially in
the capital-specific industry and eventually across
both sectors as wages become equalized.
9. Consider a long-run model for a country produc-
ing two products (digital cameras and baskets) us-
ing two factors (capital and labor).
a. Which good would you expect to be capital-
intensive? Which good would you expect to
be labor-intensive? Why?
Answer: We define a capital-intensive good
(in contrast to a labor-intensive good) as the
one having a higher capital/labor ratio. One
would expect digital cameras to be capital-
intensive due to the relatively high proportion
of machinery, knowledge, and technology that
combine to produce the final good. Con-
versely, baskets typically require more manual
skill; hence, we would expect them to be
labor-intensive relative to digital cameras.
b. Suppose that foreign owners of domestic cap-
ital decide to decrease their investment. Illus-
trate the effects of this change in a box dia-
gram. Does output in each industry increase,
decrease, or stay the same? Do wages increase,
decrease, or stay the same in each industry?
Answer: The effect of decreasing FDI is
equivalent to a decrease in capital in this
model of two products and two factors. To as-
certain changes in industry output, recall the
Rybczynski theorem: A decrease in a factor
will decrease the output of the industry for
which that factor is intensive and increase the
output of the other industry. In this case, the
decrease in FDI decreases the output of capital-
intensive digital cameras and increases the out-
put of labor-intensive baskets. Because wage is
determined in each industry by the ratio of
marginal products of labor (which are un-
changed because the capital/labor ratio does
not change), there is no change in wages due
to the decrease in capital in this model.
1985–2004
(Annual
Flow Average) 2005 2006 2007 2008
World Inflows 439,007 973329 1461074 1978838 1697353
Outflows 443,885 878988 1396916 2146522 1857734
Developed Countries Inflows 312,072 613089 972762 1358628 962259
Outflows 395,122 741972 1157910 1809531 1506528
United Kingdom Inflows 33,530 176006 156186 183386 96939
Outflows 60,078 80833 86271 275482 111411
Japan Inflows 3,238 2775 -6506 22549 24426
Outflows 226,874 45781 50266 73549 128020
United States Inflows 93,586 104809 237136 271176 316112
Outflows 90,779 15369 224220 378362 311796
Developing Countries Inflows 120,841 329292 433764 529344 620733
Outflows 46,412 122707 215282 285486 292710
India Inflows 2,036 7606 20336 25127 41554
Outflows 419 2978 14344 17281 17685
China Inflows 27,900 72406 72715 83521 108312
Outflows 2,263 12261 21160 22469 52150
Mexico Inflows 10,492 21922 19316 27278 21950
Outflows 908 6474 5758 8256 686
Source: UNCTAD, Interactive Database
FDI Flow by Country, millions of U.S. dollars, 1985 to 2008
82 Chapter 5 ■ Movement of Labor and Capital between Countries
K
K
O B
K B
LB
L DC O DC
A B
K 
K
O DC
K DC
L
K 
L

L

10. Suppose a country has two specific factors, land
and capital. Land is an input in the production of
corn. Capital is used only in the production of
rockets. A third factor, labor, is mobile between
the two sectors. Holding all else constant, what is
the effect of an increase in the amount of available
capital
a. on the real return on capital?
Answer: The increase in capital leads to a de-
crease in its real return in the short run be-
cause there is more capital available per unit of
labor, which lowers the marginal product of
capital.
b. on the real return of the mobile factor of pro-
duction?
Answer: Wages increase because the addi-
tional capital raises the marginal product of
labor.
c. on the output of corn and rockets?
Answer: According to the Rybczynski theo-
rem, an increase in the amount of capital will
raise the output of the industry using that fac-
tor (rockets) and decrease the output corn,
which is land specific.

Movement of Labor and Capital
between Countries
1. In the short-run specific-factors model, examine the impact on a small country fol-
lowing 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 work-
force on the output of each industry and the equilibrium wage.
Answer: 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 OAL (note that (L  L) is necessarily less than
(OA  O A ) and the amount of land remains the same. As a result, the output of
agriculture also decreases).
S-39
5
b. What happens to the rentals on capital and land?
Answer: Because the quantity of labor in both industries decreases due to the nat-
ural disaster, the marginal product of labor increases in both industries and the mar-
ginal products of the industry-specific factors decrease. Because it is a small coun-
try, 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 adjusts: 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. Consider an increase in the supply of labor due to immigration, and use the long-run
model. Figure 5-8 shows the box diagram and the leftward shift of the origin for the
shoe industry. Redraw this diagram, but instead, shift to the right the origin for comput-
ers. That is, expand the labor axis by the amount L, but shift it to the right rather
than to the left. With the new diagram, show how the amount of labor and capital
in shoes and computers is determined, without any change in factor prices. Carefully
explain what has happened to the amount of labor and capital used in each industry
and to the output of each industry.
Answer: Keeping factor prices constant (i. e. , W and RK constant), the K/L ratio in
each industry remains unchanged. In the diagram below, this means that the slope of
the arrows emanating from each origin stays the same even when the total endow-
ments of capital or labor change. Shifting the origin for computers to the right ex-
pands the horizontal axis and signifies the increase in labor due to immigration.
Finding a new equilibrium involves scaling the arrows up or down from their re-
spective origins to find a unique intersection. In this case, the only possible intersec-
tion involves lengthening the shoes arrow and contracting the computers arrow. This
illustrates the Rybczynski theorem: the output of the labor-intensive industry in-
creases with additional labor in the economy (vice versa for the capital-intensive in-
dustry). The new equilibrium is identical to that in Figure 5-8, so it does not matter
to which industry the extra labor is initially added.
S-40 Solutions ■ Chapter 5 Movement of Labor and Capital between Countries
Wage, W
P A · MPL A
(PA · MPL A )
PM · MPL M
A
B
W 1
W
O M O AL L
L
O A
4. In the short-run specific-factors model, consider a decrease in the stock of land. For
example, suppose a natural disaster decreases the quantity of arable land used for
planting crops.
a. Redraw panel (a) of Figure 5-11 starting from the initial equilibrium at point A.
Answer:
b. What is the effect of this change in land on the quantity of labor in each indus-
try and on the equilibrium wage?
Answer: 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
Solutions ■ Chapter 5 Movement of Labor and Capital between Countries S-41
K
O S LS
K S
K C
O CLC O C
K
L
K
K
B
A
L
LL
Wage, W
PA · MPL A
PA · MPL A
PM · MPLM
A
B
W
O M O AL
W 
L
manufacturing sector puts downward pressure on the wage. In the new equilib-
rium, wages are once again equalized across industries at W  W, manufactur-
ing labor increases from O ML to OML, and agriculture labor decreases from O A L
to O A L.
c. What is the effect on the rental on land and the rental on capital?
Answer: In the manufacturing industry, the quantity of labor increases and the
amount of capital remains the same (i. e. , the labor/capital ratio increases). There-
fore, 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 agri-
culture 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.
d. Now suppose that the international community wants to help the country struck
by the natural disaster and decides to do so by increasing its level of FDI. So the
rest of the world increases its investment in physical capital in the stricken coun-
try. Illustrate the effect of this policy on the equilibrium wage and rentals.
Answer: An increase in FDI increases the amount of capital in manufacturing,
shifting out the wage curve in that sector. This has the effect of raising MPLM
and hence wages, drawing additional labor into that sector. The new equilibrium
occurs at a higher wage than after the disaster. (The total effect as compared with
before the disaster will depend on the relative magnitude of the loss in land and
inflow of capital, and is therefore ambiguous. ) The agriculture sector shrinks fur-
ther due to the capital inflow, but those still employed in it enjoy a higher wage
than after the disaster. (We do not know if the wage is higher or lower than be-
fore the disaster. )
S-42 Solutions ■ Chapter 5 Movement of Labor and Capital between Countries
Wage, W
PA · MPL A
PA · MPL A 
PM · MPLM
A
B
CW
O M O AL L
W 
L
5. 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 nega-
tive 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 cap-
ital fixed in each industry: in that case, workers with very low or high levels of edu-
cation 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.
6. Suppose that computers use 2 units of capital for each worker, so that KC  2  LC ,
whereas shoes use 0. 5 units of capital for each worker, so that KS  0. 5  LS. There
are 100 workers and 100 units of capital in the economy.
a. Solve for the amount of labor and capital used in each industry. Hint: The box
diagram shown in Figure 5-7 means that the amount of labor and capital used in
each industry must add up to the total for the economy, so that:
KC  KS  100, and LC  LS  100
Use the facts that KC  2  LC and KS  0. 5  LS to rewrite these equations as:
2  LC  0. 5  LS  100, and LC  LS  100
Use these two equations to solve for LC and LS, and then calculate the amount
of capital used in each industry using KC  2  LC and KS  0. 5  LS.
Answer: The above two equations can be solved as:
2  LC  0. 5  LS  100
2 LC  2 LS  200
1. 5  LS  100
so that LS  100 / 1. 5  66. 7. It follows from the same equations that LC 
33. 3, and that KC  2  LC  66. 7 and KS  0. 5  LS  33. 3.
b. Suppose that the number of workers increases to 125 due to immigration, keep-
ing total capital fixed at 100. Again solve for the amount of labor and capital used
in each industry. Hint: Redo the calculations from part a, but using LC  LS 
125.
Answer: The labor equations are now solved as:
2  LC  0. 5  LS  100
2  LC  2  LS  250
1. 5  LS  150
so that LS  150 / 1. 5  100. It follows from the same equations that LC  25,
and that KC  2  LC  50 and KS  0. 5  LS  50.
Solutions ■ Chapter 5 Movement of Labor and Capital between Countries S-43
c. Suppose instead that the amount of capital increases to 125 due to FDI, keeping
the total number of workers fixed at 100. Again solve for the amount of labor
and capital used in each industry. Hint: Redo the calculations from part (a), us-
ing KC  KS  125.
Answer: The first labor equation is now 2  LC  0. 5  LS  125, so the labor
equations are solved as:
2  LC  0. 5  LS  125
2  LC  2  LS  200
1. 5  LS  75
so that LS  75 / 1. 5  50. It follows from the same equations that LC  50,
and that KC  2  LC  100 and KS  0. 5  LS  25.
d. Explain how your results in parts (b) and (c) are related to the Rybczynski the-
orem.
Answer: Comparing part (a) with part (b), the increase in the amount of labor
in the economy has increased the amount of labor and capital devoted to shoes
(from LS  66. 7 and KS  33. 3 to LS  100 and KS  50) and decreased the
amount of labor and capital devoted to computers (from LC  33. 3 and KC 
66. 7 to LC  25 and KC  50). Therefore, the output of shoes increases and the
output of computers decreases, due to the overall increase in labor. Shoes are la-
bor-intensive because they use 0. 5 units of capital per unit of labor, computers
are capital-intensive because they use 2 units of capital per unit of labor. So the
change in outputs is in accordance with the Rybczynski theorem: the increase in
labor has increased the output of the labor-intensive good and decreased the out-
put of the other good.
Conversely, comparing part (b) with part (d), there has been an increase in the
amount of capital in the economy. Consistent with the Rybczynski theorem,
there has been a rise in the amount of labor and capital devoted to computer pro-
duction (from LC  33. 3 and KC  66. 7 to LC  50 and KC  100) and a fall
in the amount of labor and capital devoted to shoe production (from
LS  66. 7 and KS  33. 3 to LS  50 and KS  25).
The following two questions explore the implications of the Rybczynski theorem and the
Factor Price Insensitivity result for the Heckscher-Ohlin model, from Chapter 4.
7. In this question we use the Rybczynski theorem to review the derivation of the
Heckscher-Ohlin theorem.
a. Start at the no-trade equilibrium point A on the Home PPF in Figure 4-2, panel
(a). Suppose that through immigration, the amount of labor in Home grows.
Draw the new PPF and label the point B where production would occur with
the same prices for goods. Hint: You can refer back to Figure 5-9 to see the ef-
fect of immigration on the PPF.
Answer: Figure 5-9, reproduced below, shows the shift in the Home PPF due to
the inflow of labor. With the same prices for goods, production occurs at point
B, with greater output of shoes and less output of computers, in accordance with
the Rybczynski theorem.
S-44 Solutions ■ Chapter 5 Movement of Labor and Capital between Countries
b. Suppose that the only difference between Foreign and Home is that Foreign has
more labor. Otherwise, the technologies used to produce each good are the same
across countries. Then how does the Foreign PPF compare with the original
Home PPF (without immigration) that you drew in part (a)? Is point B the no-
trade equilibrium in Foreign? Explain why or why not.
Answer: The Foreign PPF is shifted out and upward as compared with the orig-
inal Home PPF, just like immigration shifted out the Home PPF. This result fol-
lows because the only difference between Home and Foreign is that Foreign has
more labor (but has the same technologies for producing the two goods as at
Home). Therefore, the Foreign PPF is shifted out as compared with the original
Home PPF, and is, in fact, identical to the Home PPF inclusive of the immigra-
tion inflow. Assuming that point A is the no-trade equilibrium at Home, and
that the two countries have the same tastes, then point B cannot be the no-trade
equilibrium in Foreign. The reason for this is that because an indifference curve
is tangent to the Home no-trade equilibrium at point A, then an indifference
cannot also be tangent to point B.
c. Illustrate a new point, A*, that is the no-trade equilibrium in Foreign. How do
the relative no-trade prices of computers compare in Home and Foreign? There-
fore, what will be the pattern of trade between the countries, and why?
Answer: The Foreign no-trade point A* is shown with an indifference curve tan-
gent to it. The slope of the Foreign indifference curve at A* exceeds the slope of
the Home indifference curve at A. Because the slopes of the indifference curves
at the relative price of computers (the good on the horizontal axis), this proves that
the no-trade relative price of computers in Foreign exceeds the no-trade relative
price of computers at Home. With trade, Home will export computers (to obtain
the higher relative price in Foreign), and Foreign will export shoes (to obtain the
higher relative price at Home). Because Foreign is labor-abundant, this trade pat-
tern is in accordance with the Heckscher-Ohlin theorem.
Note: This question has redone the proof of the Heckscher-Ohlin theorem from the begin-
ning of Chapter 4. Because we now have used the Rybczynski theorem in part (a), the
comparison of the Home and Foreign PPFs is more precise than we achieved at the be-
ginning of Chapter 4 (where we relied on an intuitive comparison of the two countries’
PPFs).
Solutions ■ Chapter 5 Movement of Labor and Capital between Countries S-45
Output of
shoes, Q S
Output of
computers, Q C
A
A*
B
8. Continuing from problem 7, we now use the Factor Price Insensitivity result to com-
pare factor prices across countries in the Heckscher-Ohlin model.
a. Illustrate the international trade equilibrium on the Home and Foreign produc-
tion possibility frontiers. Hint: You can refer back to Figure 4-3 to see the inter-
national trade equilibrium.
Answer: The international trade equilibrium is as shown in Figures 4-3 and
4-4, with Home exporting computers and Foreign exporting shoes. Both coun-
tries face the same world relative price of computers (or shoes).
b. Suppose that the only difference between Foreign and Home is that Foreign has
more labor. Otherwise, the technologies used to produce each good are the same
across the countries. Then according to the Factor Price Insensitivity result, how
will the wage and rental compare in the two countries?
Answer: This is just like problem 7, where Foreign has more labor than Home
but is otherwise identical. In particular, they face the same world relative price.
So according to the Factor Price Insensitivity result, the inflow of labor (into
Foreign) has no effect on the wage or rental (as compared with those earned at
Home). In other words, the wage and rental in the two countries are the same!
This result is called the “factor price equalization” theorem and applies to coun-
tries trading in the Heckscher-Ohlin model, where technologies are the same
across countries.
c. Call the result in part (b) “factor price equalization. ” Is this a realistic result?
Hint: You can refer back to Figure 4-9 to see wages across countries.
Answer: The “factor price equalization” theorem is a logical result in the
Heckscher-Ohlin model, but it is not a very realistic result. In Figure 4-11 we
showed that wage differs a great deal across countries, whereas the “factor price
equalization” theorem would predict that wages are the same.
d. Based on our extension of the Heckscher-Ohlin model at the end of Chapter 4,
what is one reason why the “factor price equalization” result does not hold in
reality?
Answer: The reason that the “factor price equalization” theorem does not hold
in practice is that technologies differ quite a bit across countries, as we discussed
at the end of Chapter 4. Just like we need to take into account the differences
in technologies to obtain more realistic predictions about trade from the
Heckscher-Ohlin model, so too we need to recognize that the differences in
technologies will mean that factor prices differ across countries, even when they
are engaged in free trade and the relative prices of goods are the same.
9. Recall the formula R
P  P
P
K
(i  d) from the application, “The Effect of FDI on
Rentals and Wages in Singapore. ” Give an intuitive explanation for this formula for
the rental rate. Hint: Describe one side of the equation as a marginal benefit and the
other as a marginal cost.
Answer: The equation above is one way to calculate the real returns to (rental of )
capital, R/P. An intuitive way to think about this is to imagine that you are the owner
of a unit of capital and you are considering whether to rent it out at the prevailing
nominal rental rate, R, or to sell it and invest the proceeds. On one hand, you could
sell each unit of capital for a price of PK and receive interest income on the proceeds
of PKi. On the other hand, you could rent out the capital for a nominal payment of
R and incur the direct depreciation cost of the asset of PKd. Thus, the nominal pay-
ment you would require (R, the marginal benefit of rental) to make you indifferent
between the two options would be P Ki  P Kd, the sum of direct costs of renting out
and the opportunity cost of a sale (together, the marginal cost of rental). Dividing
S-46 Solutions ■ Chapter 5 Movement of Labor and Capital between Countries
both sides by the price level, P, puts the equation into real terms and yields the de-
sired equation.
10. 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?
Answer: 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. 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 5-2. How do your answers now compare with the pro-
ductivity growth shown in the last column?
Answer: 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).
11. 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.
Answer: Gains from trade in the following graph are analogous to consumer and
producer surplus in the conventional supply and demand setting. In this case,
Home employers are willing to pay up to W for the marginal product of labor
Solutions ■ Chapter 5 Movement of Labor and Capital between Countries S-47
(3) (4)
Productivity Productivity (5)
Using Capital Using Capital Productivity
(1) (2) Share of 0.5  Share of 0.33  from
Rental Wages (1)  0.5  (2)  0.5 (1)  0.33  (2)  0.67 Table 5-2
5.0 2.6 1.2 0.1 1.5
1.9 0.5 0.7 0.3 0.7
3.4 1.6 0.9 0.1 1.1
1.6 2.7 2.2 2.3 2.2
0.2 3.2 1.5 2.1 1.5
0.5 3.6 1.6 2.2 1.6
that they obtain for W ; thus the gains to the Home country are illustrated by the
horizontally striped triangle. Similarly, the immigrating Foreign workers are
willing to supply their marginal product for a lower wage in the Foreign coun-
try (W*) but receive a higher wage in the Home country (W**).
b. Are there gains that accrue to the Foreign country? If so, again show the magni-
tude of these gains in the diagram and show the world gains.
Answer: Gains to Foreign (including foreign emigrants) are represented by the
vertically striped triangle. Given positive gains to both countries, total gains from
immigration are also positive in this model.
12. 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 annu-
ally 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.
Answer: Assuming that housekeeping is a perfectly competitive industry, house-
keepers’ wages are equal to their marginal product of labor. Because wages are
higher in Singapore, housekeepers there are more productive.
b. What is the total gain to the housekeeper from migrating?
Answer: 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. Is there a corresponding gain for the employer in Singapore? Explain.
Answer: The gains to the employer in Singapore depend on whether the wage
is driven down by the migration, as shown in problem 11.
S-48 Solutions ■ Chapter 5 Movement of Labor and Capital between Countries
Wage, W Foreign
wage
Home
wage
O
A
LL
L
A*
W
W 
W 
W **
O *
L*
W *