Gains and Losses from Trade in the Specific-Factors Model
3
1. Why is the specific-factors model referred to as a short-run model? Answer: It is a short-run model because land and capital are specific to a particular sector and only labor is mobile between the sectors. 2. Figure 3-7 presents wages in the manufacturing and services sectors for the period 1973 to 2009. Is the difference in wages across sectors consistent with either the Ricardian model studied in Chapter 2 or the specific-factors model? Explain why or why not. Answer: The difference in wages across the sectors implies that the theoretical assumption of equalized earnings between the different industries is a simplification of the Ricardian and specific-factors models. 3. In the gains from trade diagram (Figure 3-3), suppose that instead of having a rise in the relative price of manufactures, there is a fall in that relative price. a. Starting at the autarky point A in Figure 3-3, show what would happen to production and consumption. U2
Output of agriculture, QA
Answer:
B
A
C
U1
Output of manufacturing, QM
S-19
S-20
Solutions
■
Chapter 3
Gains and Losses from Trade in the Specific-Factors Model
As seen in the previous diagram, a fall in the relative price of manufactures is shown by the smaller slope (in absolute value) of the international price line. The country produces at point B, at which the international price line intersects its PPF. The higher relative price of agriculture attracts workers into that sector such that the output of agriculture increases and the output of manufactured goods decreases. Now the highest level of utility is achieved where the highest possible indifference curve intersects with the new price line (at C). The increase in utility signified by the higher indifference curve is a measure of gains from trade. b. Which good is exported and which is imported? Answer: The decrease in the relative price of manufactures in the trade equilibrium (compared with autarky) also means that the country is importing manufactured goods and exporting agricultural goods. c. Explain why the overall gains from trade are still positive. Answer: Overall gains from trade are still positive because the country is able to sell agriculture at a higher price and buy manufactured goods at a lower price than it could have in autarky. The fact that the relative price (of manufactured goods) fell with trade indicates that the foreign country’s autarky relative price was lower. That is, in this case the country has a comparative advantage in agriculture. In Figure 3-4, the case illustrated is one in which the country has a comparative advantage in manufacturing goods and thus their export leads to an increase in their relative price. 4. Starting from equilibrium in the specific-factors model, suppose the price of manufactured goods falls so that wages fall from W to W in Figure 3-5. a. Show that the percentage fall in wages is less than the percentage fall in the price of manufacturing, so that the real wage of labor in terms of manufactured goods goes up. Answer: Wage PM · MPLM
W
PM · MPLM
W PM · MPL
0M
LM
L
L
LA
0A
L
As seen in the diagram, both the price of manufactured goods and the wages decrease. The key to this exercise is to realize that the vertical distance of the decrease in wage is less than the vertical distance of PM MPLM. Therefore:
PM MPLM W
Solutions
■
Chapter 3
Gains and Losses from Trade in the Specific-Factors Model
where W represents the change in wage. Dividing both sides by the initial wage (W´ P´M MPLM):
PM / P´M W / W´ This is the desired result: the percentage fall in the wage is less than the percentage fall in the price of manufacturing, so that the real wage of labor in terms of manufactured goods goes up. b. What happens to the real wage of labor in terms of agriculture? Answer: Because the wage decreases and the price of agricultural goods remains the same, the amount of agricultural goods that can be bought by labor decreases. That is, real wage decreases in terms of agriculture. c. Are workers better off, worse off, or is the outcome ambiguous? Answer: Because the real wage increases with respect to manufactured goods and decreases with respect to agriculture, the outcome will be ambiguous for workers. For some, who prefer to purchase a lot of agriculture, the price change means an overall loss in terms of how much they can buy. Others, who prefer to buy mainly manufactured goods, gain in terms of how much they can buy. 5. Use the following information to answer the questions below:
Manufacturing:
Sales revenue PM QM 150 Payments to labor W LM 100 Payments to capital RK K 50
Agriculture:
Sales revenue PA QA 150 Payments to labor W LA 50 Payments to land RT T 100
Holding the price of manufacturing constant, suppose the increase in the price of agriculture is 10% and the increase in the wage is 5%. a. Determine the impact of the increase in the price of agriculture on the rental on land and the rental on capital. Answer: Rental on land can be calculated as follows:
(PA / PA) PA QA (W / W) W LA R T _ RT RT T 10% 150 5% 50% R T _ 12. 5% RT 100 Recalling that the price of manufacturing remained constant, we get the rental on capital as
0 QM W LM RK K – W W LM RK _ RK W RK K
冢
冣
RK 100 5% 10%. RK 50
冢 冣
S-21
Chapter 3
Gains and Losses from Trade in the Specific-Factors Model
b. Explain what has happened to the real rental on land and the real rental on capital. Answer: Because of the 10% increase in the price of agriculture, the real rental on land rose whereas the real rental on capital fell. Therefore, landowners are better off because the percentage increase in the rental on land is greater than the percentage increase in the price of agriculture, whereas the price of manufacture is constant. Capital owners are worse off in terms of their ability to purchase both manufacture and agriculture because the rental to capital has fallen.
RK / RK 0 W / W PA / PA RT / RT, for an increase in PA Real rental on capital falls
⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩
⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ Change in the real wage is ambiguous
Real rental on land rises
6. If, instead of the situation given in problem 5, the price of manufacturing was to fall by 10%, would landowners or capital owners be better off? Explain. How would the decrease in the price of manufacturing affect labor? Explain. Answer: Assuming that the decrease in the price of manufactures leads to a fall in wage by 5%, capital owners would be worse off because the rental on capital would decrease (20%) more than the drop in the price of manufacturing (10%). Landowners would be better off as the rental on land rises (10%). The effect on labor is ambiguous because although the percentage of wage decrease is less than the percentage fall in price of manufacturing, labor loses in terms of their availability to purchase agriculture. The rental on capital is found by calculating the following:
(PM / PM) PM QM (W / W ) W LM RK RK RK K 10% 150 5% 100 RK 20% RK 50 although the rental on land is
0 QA W LA RT — T RT W W LA RT W RT T
冢
冣
50 RT 5% 2. 5%. 100 RT
冢 冣
Putting it together we get
Real rental on capital falls
Change in the real wage is ambiguous
⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩
RK / RK PM / PM W / W 0 RT / RT, for a decrease in PM. ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩
■
⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩
Solutions
⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩
S-22
Real rental on land rises
Solutions
■
Chapter 3
Gains and Losses from Trade in the Specific-Factors Model
7. Read the article by Lori G. Kletzer and Robert E. Litan, “A Prescription to Relieve Worker Anxiety,” Policy Brief 01-2, Institute for International Economics, Washington, DC, http://www. iie. com/publications/pb/Pb01-2. htm, which refers to the U. S. recession of 2000–2001. Then answer the following questions. a. Under the most recent version of Trade Adjustment Assistance (TAA) in the United States that they refer to, how many extra weeks of unemployment insurance (UI) are workers eligible for? What two criteria must they meet to qualify for this extra unemployment insurance? Answer: “Under the most recent version of the Trade Adjustment Assistance (TAA) Act, qualified workers may gain an additional 52 weeks of UI payments, provided they are enrolled in an approved training program. A similar program, the North American Free Trade Agreement Transitional Adjustment Assistance (NAFTA-TAA) program, was created in 1993. For eligibility, workers must prove that they lost their job because of increased imports from, or a shift in production to, either Canada or Mexico. ” b. Consider the proposal for “wage insurance” that Kletzer and Litan make in their article. What criteria would a worker need to meet to qualify for this insurance? What amount of extra income would they receive from the insurance? Answer: “Wage insurance would work as follows: Eligible workers would receive some fraction of their wage loss, which could vary by age and tenure of the worker for up to 2 years following the initial date of job loss, but would begin to be paid only when workers found a new job. ” “To qualify for our proposed supplemental wage insurance benefit, workers need only document that they have been ‘displaced’ according to criteria similar to the operational definition of displacement used by the BLS in its Displaced Worker Surveys (plant or company closed or moved, elimination of position or shift, insufficient work); that they had served at their previous job for a minimum period of time: we suggest 2 years; and that they have suffered an earnings loss (from old job to new job) . . . ” c. If Kletzer and Litan’s new plan for “wage insurance” had been adopted by the United States, what would have been the budgetary cost in 1999 when unemployment was 4. 2%? How does this compare with the amount that is now spent on unemployment insurance? Answer: “Assuming a 50% replacement and subsidy rate, the table indicates that our wage insurance and health insurance program would have cost about $2. 9 billion in 1999, when the national unemployment rate averaged 4. 2%. “The total cost, less than $4 billion, might have been a major obstacle when federal deficits were high and growing but is not a problem now, and in any event would be small in relation to the more than $20 billion that is now spent on unemployment insurance . . . ” 8. In the specific-factors model, assume that the price of agricultural goods decreases whereas the price of manufactured goods is unchanged (PA / PA 0 and PM / PM 0). Arrange the following terms in ascending order:
RT / RT
RK / RK
PA / PA
PM / PM
W / W
Hint: Try starting with a diagram such as Figure 3-6 but change the price of agricultural goods instead. Answer: It helps to separate this exercise into two parts. The first part is to arrange the percentage changes in wages and goods prices. This part is similar to problem 4 except that now it is the price of agriculture that is decreasing. By similar logic, the
S-23
S-24
Solutions
■
Chapter 3
Gains and Losses from Trade in the Specific-Factors Model
percentage change in price of agricultural goods is larger than the percentage change in wage, which in turn is larger than the percentage change in the price of manufactured goods (zero). Thus,
0 PM / PM W / W PA / PA For the second part, adding the percentage changes in specific-factors rental rates, recall that in this model, although the real return to labor is ambiguous (which means that more agricultural products but fewer manufactured goods can be purchased by labor), the real return to capital and land can both be determined and move in opposite directions. The general rule for the specific-factors model is that a decrease in the relative price of an industry leads to a real loss of the factor specific in that industry, and a real return to the specific factor in the other industry. This means that the percentage change in losses to land is greater than both price changes and that the percentage change in returns to capital is greater than both price changes, which is equivalent to saying that fewer of both goods can be purchased by landowners although more of both goods can be purchased by capital owners, respectively.
RT / RT PA / PA W / W PM / PM RK / RK 9. Suppose two countries, Canada and Mexico, produce two goods, timber and televisions. Assume that land is specific to timber, capital is specific to televisions, and labor is free to move between the two industries. When Canada and Mexico engage in free trade, the relative price of televisions falls in Canada and the relative price of timber falls in Mexico. a. In a graph similar to Figure 3-5, show how the wage changes in Canada because of a fall in the price of televisions, holding constant the price of timber. Can we predict that change in the real wage? Answer: As shown by the following figure, real wage falls but by less than the percentage decrease in the price of televisions. Vertical distance PTV · (MPLTV )
Wage
PTIM · MPLTIM
A W PTV · MPLTV W B
PTV · MPLTV
W 0TV
LTV
L
L
LTIM
0TIM
L
Labor
Solutions
■
Chapter 3
Gains and Losses from Trade in the Specific-Factors Model
b. What is the impact of opening trade on the rentals on capital and land in Canada? Can we predict that change in the real rentals on capital and land? Answer: Because capital is specific to the television sector, the drop in the relative price of televisions will lead to a fall in the rental on capital. With Canada exporting timber, rental on land will rise because land is specific to the timber industry. c. What is the impact of opening trade on the rentals on capital and land in Mexico? Can we predict that change in the real rentals on capital and land? Answer: Through the exports of televisions, the relative price of televisions will rise in Mexico, which will lead to an increase in the rental on capital. By contrast, the rental on land will fall. d. In each country, has the specific factor in the export industry gained or lost, and has the specific factor in the import industry gained or lost? Answer: In both cases, the specific factor in the export industry (i. e. , land in Canada and capital in Mexico) gained whereas the factor specified to the import industry (i. e. , capital in Canada and land in Mexico) loses when the two countries engage in trade. 10. Home produces two goods, computers and wheat, where capital is specific to computers, land is specific to wheat, and labor is mobile between the two industries. Home has 100 workers and 100 units of capital, but only 10 units of land. a. Draw a graph similar to Figure 3-1, with the output of wheat on the vertical axis and the labor in wheat on the horizontal axis. What is the relationship between the output of wheat and the marginal product of labor in the wheat industry as more labor is used? Answer: See the following graph. Wheat output, QW
MPLW 1
Labor in wheat, LW
As more labor is added to the production of wheat, the marginal product of labor declines so that although the output of wheat continues to increase, the output is increasing at a decreasing rate.
S-25
S-26
Solutions
■
Chapter 3
Gains and Losses from Trade in the Specific-Factors Model
b. Draw the production possibilities frontier (PPF) for Home with wheat on the horizontal axis and computers on the vertical axis. Answer: See the following graph. Computer output, QC Slope (MPLC / MPLW ) A MPLC
B MPLW
Production possibilities frontier, PPF
Wheat output, Q
W
c. Explain how the price of wheat relative to computers is determined in the absence of trade. Answer: In the absence of international trade, the relative price of wheat is the slope of the line tangent to the PPF and Home’s indifference curve. d. Reproduce Figure 3-5 with the amount of labor used in wheat measuring from left to right along the horizontal axis, and the amount of labor used in computers moving in the reverse direction. Answer: See graph below. Labor market equilibrium
Wage
Value of marginal product of computer PC · MPLC
Value of marginal product of wheat
A W
PW · MPLW
0W
LW
LC
L
0C
L
Wheat labor
Computer labor
Solutions
■
Chapter 3
Gains and Losses from Trade in the Specific-Factors Model
e. Assume that because of international trade, the price of wheat rises. Analyze the effect of the increase in the price of wheat on the allocation of labor between the two sectors. Answer:
Vertical distance PW · (MPLW )
Wage
B W W P´W · MPLW
W A
PW · MPLW
0W
LW
L
L
LC
0C
L
Wheat labor
Computer labor
The increase in the price of wheat shifts the PW MPLW curve upward to PW' MPLW so that the new equilibrium is at point B. The amount of labor used in wheat increases from 0WL to 0WL', although the amount of labor devoted to computers decreases from 0CL to 0CL'. Although the wage rises from W to W ', the increase is less than the vertical shift of the PW MPLW curve given as PW MPLW. 11. Similar to Home in problem 10, Foreign also produces computers and wheat using capital, which is specific to computers; land, which is specific to wheat; and labor, which is mobile between the two sectors. Foreign has 100 workers and 100 units of land, but only 10 units of capital. It has the same production functions as at Home. a. Will the no-trade relative price of wheat be higher in Home or in Foreign? Explain why you expect this outcome. Answer: The no-trade relative price of wheat will be higher in Home than Foreign because Foreign has more units of land relative to Home. In other words, with more capital available for labor than land, the marginal product of labor in wheat is lower than the marginal product of capital in computers at Home. Because wages are equalized across the sector, price must be higher in the wheat industry:
PW MPLW PC MPLC The situation would be opposite for the foreign country, which has more land than capital. In this case, the price of capital is higher relative to the price of wheat without trade.
S-27
S-28
Solutions
■
Chapter 3
Gains and Losses from Trade in the Specific-Factors Model
Computer output, Q *C
Slope ( MPL *C / MPL *W )
A MPL *C
B MPL*W Production possibilities frontier, PPF
Wheat output, Q *W
b. When trade is opened, what happens to the relative price of wheat in Foreign and to the relative price of wheat in Home? Answer: When the two countries engage in trade, Home will export computers so that the relative price of wheat decreases at Home, whereas Foreign will export wheat, which will increase the relative price of wheat in Foreign. c. Based on your answer to (b), predict the effect of opening trade on the rental on land in each country, which is specific to wheat. What about the rental on capital, which is specific to computers? Answer: With Home exporting computers, the rental on capital will increase while the rental on land will decrease. Because Foreign exports wheat, landowners will experience an increase in the rental on land, whereas capital owners will lose because of the decrease in the rental on capital. 12. In the text, we learned that workers displaced by import competition are eligible for compensation through the Trade Adjustment Assistance (TAA) program. In addition to workers, firms are also eligible for support through Trade Adjustment Assistance for Firms, a federal program that provides financial assistance to manufacturers affected by import competition. Go to www. taacenters. org to read about this program, and answer the following questions: a. What criteria does a firm have to satisfy to quality for benefits? Answer: According to the website, manufacturers are qualified to receive benefits from the TAA if imports have contributed to declines in their employment and sales or production. b. What amount of money is provided to firms and for what purpose? Answer: Under the “50/50 cost sharing” program, the TAA pays up to $75,000 for projects to improve a manufacturer’s competitiveness. The funds go toward the cost of hiring industry experts, including consultants, engineers, and designers for projects.
Solutions
■
Chapter 3
Gains and Losses from Trade in the Specific-Factors Model
c. Provide an argument for and an argument against the continued funding of this federal program. Answer: Opponents of TAA would argue that the program is costly. The following figure shows the total expenditures of the program from 1995 to 1999, where more than half of the cost is administrative and operations related. Proponents of TAA would draw on the positive effect the assistance program has on the manufacturing industry and local economy. Trade adjustment assistance centers’ total expenditures, cooperative agreement years 1995-99
$6,000,000
$5,000,000
$4,000,000
$3,000,000
$2,000,000
$1,000,000
Operations and administrative costs
Note: Operations and administrative costs include staff time spent assisting firms with the certification process and preparing adjustment plans, in addition to the cost of funding day-to-day operations. Source: GAO derived from TAA Centers’ data.
t hw es ut
te
rs
Consultant costs
So
W es
Je ew
rn
ey
ic nt tla N
-A id M
G
re
he ut So
at
as
La
te
ke s
rn
a ic er m
M
id
-A
th or N
M
ou
nt
w es
t
ai
t w es id
oc ky
M
ew N
R
N
ew
En
gl
Yo r
an
k
d
n
$0
S-29
