UCDavis, 160a, SSII 2010 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 P
M
MPL
M and ( P
A
MPL
A
)’, which corresponds to a higher wage W’ . In manufacturing, the amount of labor decreases from O
M
L to
O
M
L’ 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 O
A
L to O
A
’ L’ (note that ( L’L ) is necessarily less than
( O
A
‘ - 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 P
A and P
M remain unchanged; hence, the rental rate for capital, P
M
MPK, decreases and the rental rate for land, P
A
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. 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 computer industry.
Redraw this diagram, but instead, shift to the right the origin for shoes. That is, expand the labor axis by the amount

L, but shift it to the left rather than to the right. 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 R
K 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 endowments of capital or labor change. Shifting the origin for shoes to the right expands 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 respective origins to find a unique intersection. In this case, the only possible intersection involves lengthening the shoes arrow and contracting the computers arrow. This illustrates the
Rybczynski theorem: the output of the labor-intensive industry increases with additional labor in the economy (vice versa for the capital-intensive industry). The new equilibrium is identical to that in Figure 5-7, so it does not matter to which industry the extra labor is initially added.

4. In the specific factors model for manufacturing goods and agriculture, consider a decrease in the stock of land. For example, suppose natural disaster decreases the quantity of arable land for planting crops. a) Redraw Figure 5.11 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
W'
P
A

MPL
A
P
A
 MPL’
A
B
P
M

MPL
M
O
M
L L'
L
O
A b) With less land per laborer in the agriculture sector, MPL
A 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 O
M
L to O
M
L’ , and agriculture labor decreases from O
A
L to O
A
L’. c).
Wage, W
P
A

MPL
A
A C
P
A

MPL'
A
W
W’ B
P
M

MPL
M
O
M
L L’ L’’ O
A

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, P
M
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, P
A
MPT, increases from A to B.
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 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.
6. Now consider a long-run model for a country producing 2 products (digital cameras and baskets) using 2 factors (capital and labor). a.
Which good would you expect to be capital-intensive? Which good would you expect to be labor-intensive? Why? b.
Suppose that foreign owners of domestic capital decide to decrease their investment.
Illustrate the effects of this change in a box diagram. Does output in each industry increase, decrease or stay the same? Do wages increase, decrease, or stay the same in each industry?

Total amount of capital in the economy,
K
Answer:
The withdrawn
FDI
Labor allocated to digital camera
L
Capital allocated to basket

K
S
K
O b
L
S

L
Labor allocated to basket
A
B

L
C
O
C
K
K
C

Capital allocated to digital camera
Total amount of labor in the economy, L a) Digital camera industry is capital-intensive while basket industry is labor-intensive. The former utilizes much more complicated technology and therefore requires a much larger quantity of upfront investment in research & development. b) Check the box diagram below; note the blue lines illustrates the new allocation of labor and capital between the two industries after the decrease in FDI. That is: the capital-intensive industry --- digital capital industry --- is shrinking and uses less labor and capital. While on the other hand, the labor intensive industry --- basket --- is expanding and uses more labor and capital than before the withdraw of FDI. The new equilibrium point is at B instead of A. Wage rate will keep at the same level as before since the world prices of products haven’t changed.
7.
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 5-
2. 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).
8. 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. 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 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 country ( W* ) but receive a higher wage in the Home country ( W** ). b. 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.
9. 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, as shown in problem 8 . 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.
10. Figure 5.16 is a supply and demand diagram for the world labor market. Consider a situation where Foreign workers immigrate to the home country, causing the Home wage to decrease to
W
NEW
> W’, and where the Foreign wage begins at W* and increases to W
NEW
> W’. a) Is this a stable outcome in the long run? That is, would you expect this pattern of immigration to stay the same, to reverse, or to stop at the new Home and Foreign wages? b) Going from old wages to the new, are there gains that accrue to the Home country? Are there gains that accrue to the Foreign country? If so, redraw the graph and identify the magnitude of the gains for each country. If not, say why not.
Answer a). This is not a stable long-run outcome. Since the Home country still offers a higher wage than the Foreign country, the migration will not stop, instead, workers will continue to immigrate to the Home country.
Wage, W
W
W
New
W'
W
*
New
W*
A
D
Gains to
Home
B
Foreign
Wage
A*
Home
Wage
Gains to
Foreign
O L L' O*
L World Amount of Labor
 b). Yes, there are gains from immigration incurred to both Home country and Foreign country, which are illustrated in the above graph (the purple area is gains to the Home country, while the yellow area is gains to the Foreign country).

Foreign Outsourcingof Goods and Services
1.
Consider an outsourcing model in which the labor hours of four activities in the United States and Mexico are as follows:
Note that labor hours in Mexico are four times those in the United States, reflecting Mexico’s lower productivity. Also note that the ratio of skilled to unskilled labor used in each activity increases as we move to the right, from 1/5 in assembly to 10/1 in R&D. Suppose that the wage of U.S. unskilled workers is $10 per hour and that of skilled workers is $25 per hour and that the wage of Mexican unskilled workers is $1 per hour and that of skilled workers is $5 per hour
(these values are made up to be convenient, not realistic). Also suppose that the trade costs are
25%, 30%, or 50%, which means that an additional 25%, 30%, or 50% is added to the costs of outsourcing to Mexico. a.
Fill in the blank cells in the following table by computing the costs of production of each activity in each country (two cells are filled in for you). b.
With trade costs of 50%, where is the value chain sliced? That is, which activities are cheaper to import from Mexico and which are cheaper to produce in the United States? c.
With trade costs of 30%, and then 25%, where is the value chain sliced?
Answer: a.
In italics in the following table: b.
With trade costs of 50%, assembly and component production are done in Mexico because the gross costs of importing these activities are lower than their respective costs in the United States. On the other hand, office services and R&D activities are done in the
United States. With trade costs of 30%, and then 25%, where is the value chain sliced?

c.
With trade costs of 25%, all activities are outsourced to Mexico, whereas with trade costs of 30%, assembly, component production, and office services are done in Mexico (R&D is still done in the United States).
2.
Consider an outsourcing model in which Home’s skilled labor has a higher relative wage than
Foreign’s skilled labor and in which the costs of capital and trade are uniform across production activities. a.
Will Home’s outsourced production activities be high or low on the value chain for a given product? That is, will Home outsource activities that are skilled-labor intensive or unskilled-labor-intensive? Explain. b.
Suppose that Home uniformly increases its tariff level, effectively increasing the cost of importing all goods and services from abroad. How does this affect the slicing of the value chain?
c.
Draw relative labor supply and demand diagrams for Home and Foreign showing the effect of this change. What happens to the relative wage in each country?
Answer: a. The high relative wage of Home skilled labor makes skilled-labor intensive activities more expensive at Home relative to Foreign. Equivalently, the low relative wage of unskilled labor makes unskilled-labor-intensive activities less expensive at Home relative to Foreign. As a result,
Home will undertake production activities lower on the value chain while outsourcing higher value activities to Foreign. b. A uniform increase in the tariff level causes fewer activities to be outsourced. The slicing of the value chain reflects this increased cost as a rightward shift; Home expands the set of activities that it does at Home to include incrementally higher value activities, whereas the set of high value outsourced activities shrinks. c. An expansion in the set of production activities done at Home (to include higher value ones) increases the average skill intensity of Home production. This increases the relative demand for skilled labor at Home. Similarly, because Foreign ceases to do its least skill-intensive activities, the average
3.
Consider a U.S. firm’s production of automobiles, including R&D and component production. a.
Starting from a no-trade equilibrium in a PPF diagram, illustrate the gains from outsourcing if the United States has comparative advantage in component production. b.
Now suppose that advances in engineering abroad decrease the relative price of research and development. Illustrate this change on your diagram and state the implications for production in the United States.

c.
Does the U.S. firm gain from advances in research and development abroad? Explain why or why not.
Answer: a.
See the following figure , where the outsourcing equilibrium is B and b.
See the following figure , where the new equilibrium is B
’ and
C
’
.

c.
Because the United States imports R&D and exports components, a decrease in the relative price of R&D abroad represents an improvement in the U.S. terms of trade; as a result, U.S. output increases to Y2 so there are gains for the United States.
4. The diagram below shows what happened to the relative wage and relative demand for skilled labor in the U.S. manufacturing sector during the 1990s.These points are plotted using the data from Figures 7-6 and 7-7. a.
What must have happened to the demand and supply curves to explain this change in relative wage and relative employment? b.
Why do you think the demand and supply curves shifted this way? ( Hint: Think about where the workers who leave manufacturing might be going.)
Answer: a. The relative non-production wage increased significantly in U.S. manufacturing between 1990 and 2001 but the relative employment of non-production labor did not change much. This pattern is consistent with an outward shift in relative demand and an inward shift in relative supply for non-production workers. As such, relative demand for skilled labor has increased (shifted right) and the relative supply of skilled labor has decreased (shifted left). See the figure below. b. The increase in relative demand is a continuation of what we already saw in the 1980s, due to skilled-biased technologic change and outsourcing. The reduction in relative supply is new, however. One explanation for this is that skilled workers were pulled out of manufacturing and into services (because many skill-intensive service sectors have been expanding).

5. In Figure 7-12, we saw that a fall in the relative price of components leads to an increase in the amount of components imported, but that the amount of R&D exported from Home does not necessarily increase. To explore this further, complete the following: Let the relative price of components continue to fall in Figure 7-12, and show in a graph what happens to the equilibrium point on the isoquant for the final good.
Answer: As the relative price of components continues to fall, the use of components in the final good increases. Imports of components increase as the equilibrium production point moves out to the flatter portion of the final good isoquant, and the level of final good output increases (but at a diminishing rate due to diminishing returns in production). See the following figure .

6. Why is it relatively easier for an undeveloped country to export service activities through outsourcing than to participate in the global economy by producing manufacturing components?
Answer: Because outsourcing of manufactures involves the trade of intermediate inputs across several borders, there is an extra cost associated with transporting the goods. Therefore, a country must have good infrastructures such as developed roadways to participate in the global economy.
In India, for example, communications technology developed rapidly whereas transportation developed more slowly, which allowed the South Asian country to partake in service outsourcing.
7. It is widely noted that although China is the favored destination for manufacturing outsourcing, it is far behind India in the business of outsourced services. What are some differences between these two countries that may account for this causal observation?
Answer: Although wages are also low in India, due to its weak transportation infrastructure it is unable to successfully compete against China in manufacturing outsourcing. However, it has an advantage over China in service outsourcing because the country has developed an advanced communication infrastructure. Moreover, as a former British colony, India has a proficiency in the English language. The workforce in India is well educated and highly skilled in information technology. In addition, Tarun Khanna, a professor at the Harvard Business School, notes that
India has a thriving entrepreneurial effort unhampered by government bureaucracy, unlike China
( The McKinsey Quarterly, 2004). These include a low level of government intervention in the
Indian capital markets and no regulations in industries such as software.
8. Why is the outsourcing of white-collar or skill-intensive jobs a concern for many Americans?
Answer: Traditionally, white-collar workers have been relatively insulated from foreign competition in comparison with blue-collar workers. For decades the unemployment rate of skillintensive jobs, such as computer programming, was well below the national average. However, with the trend reversing between 2001 and 2002, the expected job security associated with advanced training and experience came into question. Although the loss of white-collar jobs was offset by the increase in service employment, many Americans fear that it is unclear how job opportunities will adjust to the new labor challenges.