Gains and Losses from Trade in the Specific-Factors Model

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 particularsector and only labor is mobile between the sectors.

2. Figure 3-7 presents wages in the manufacturing and services sectors for the period1973 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 orwhy not.

Answer: The difference in wages across the sectors implies that the theoretical as-sumption of equalized earnings between the different industries is a simplification ofthe Ricardian and specific-factors models.

3. In the gains from trade diagram (Figure 3-3), suppose that instead of having a rise inthe 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 pro-duction and consumption.

Answer:

S-19

3

U1

U2

A

B

C

Output of manufacturing, QM

Ou

tpu

t o

f ag

ricu

ltu

re, Q

A

As seen in the previous diagram, a fall in the relative price of manufactures isshown by the smaller slope (in absolute value) of the international price line. Thecountry produces at point B, at which the international price line intersects itsPPF. The higher relative price of agriculture attracts workers into that sectorsuch that the output of agriculture increases and the output of manufacturedgoods decreases. Now the highest level of utility is achieved where the highestpossible indifference curve intersects with the new price line (at C). The increasein utility signified by the higher indifference curve is a measure of gains fromtrade.

b. Which good is exported and which is imported?

Answer: The decrease in the relative price of manufactures in the trade equilib-rium (compared with autarky) also means that the country is importing manu-factured 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 tosell agriculture at a higher price and buy manufactured goods at a lower pricethan it could have in autarky. The fact that the relative price (of manufacturedgoods) fell with trade indicates that the foreign country’s autarky relative pricewas lower. That is, in this case the country has a comparative advantage in agri-culture. In Figure 3-4, the case illustrated is one in which the country has a com-parative advantage in manufacturing goods and thus their export leads to an in-crease in their relative price.

4. Starting from equilibrium in the specific-factors model, suppose the price of manu-factured 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 priceof manufacturing, so that the real wage of labor in terms of manufactured goodsgoes up.

Answer:

As seen in the diagram, both the price of manufactured goods and the wages de-crease. The key to this exercise is to realize that the vertical distance of the de-crease in wage is less than the vertical distance of �PM � MPLM. Therefore:

�PM � MPLM � �W

S-20 Solutions ■ Chapter 3 Gains and Losses from Trade in the Specific-Factors Model

Wage

W

W �

�PM · MPLM

PM� · MPLM

PM · MPL

0M LM 0ALAL L�

L �

where �W represents the change in wage. Dividing both sides by the initialwage (W´ � P M � MPLM):

�PM / P M � �W / W´

This is the desired result: the percentage fall in the wage is less than the percent-age fall in the price of manufacturing, so that the real wage of labor in terms ofmanufactured 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 remainsthe same, the amount of agricultural goods that can be bought by labor de-creases. 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 goodsand decreases with respect to agriculture, the outcome will be ambiguous forworkers. For some, who prefer to purchase a lot of agriculture, the price changemeans an overall loss in terms of how much they can buy. Others, who preferto 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 ofagriculture 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 onland and the rental on capital.

Answer: Rental on land can be calculated as follows:

��

RR_

T

T� �

��

RR_

T

T� � � 12. 5%

Recalling that the price of manufacturing remained constant, we get the rentalon capital as

�RK � �0 � QM �

K�W � LM�

��

RR

K

K� �

_–��

WW���WRK

�

�

LKM

����

RR

K

K� � �5% � ��

15000

�� � �10%.

(�PA / PA) � PA � QA � (�W / W) � W � LA�����

RT � T

10% � 150 � 5% � 50%���

100

Solutions ■ Chapter 3 Gains and Losses from Trade in the Specific-Factors Model S-21

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 rentalon land rose whereas the real rental on capital fell. Therefore, landowners are bet-ter off because the percentage increase in the rental on land is greater than thepercentage increase in the price of agriculture, whereas the price of manufactureis constant. Capital owners are worse off in terms of their ability to purchaseboth manufacture and agriculture because the rental to capital has fallen.

�RK / RK 0 �W / W �PA / PA �RT / RT, for an increase in PA

6. If, instead of the situation given in problem 5, the price of manufacturing was to fallby 10%, would landowners or capital owners be better off? Explain. How would thedecrease in the price of manufacturing affect labor? Explain.

Answer: Assuming that the decrease in the price of manufactures leads to a fall inwage by 5%, capital owners would be worse off because the rental on capital woulddecrease (20%) more than the drop in the price of manufacturing (10%). Landown-ers would be better off as the rental on land rises (10%). The effect on labor is am-biguous because although the percentage of wage decrease is less than the percentagefall in price of manufacturing, labor loses in terms of their availability to purchaseagriculture.

The rental on capital is found by calculating the following:

��

RR

K

K� �

��

RR

K

K� � � �20%

although the rental on land is

�RT � �0 � QA �

T—

�W � LA�

��

RR

T

T� � �

�

WW���WRT

�

�

LT

A��

��

RR

T

T� � 5% � ��

15000

�� � 2. 5%.

Putting it together we get

�RK / RK �PM / PM �W / W 0 �RT / RT, for a decrease in PM.

(�PM / PM) � PM � QM � (�W / W ) � W � LM�����

RK � K

�10% � 150 5% � 100���

50

S-22 Solutions ■ Chapter 3 Gains and Losses from Trade in the Specific-Factors Model

Real rental on capital falls

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩

Change in the realwage is ambiguous

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩

Real rental on land rises

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩

Real rental on capital falls

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩

Change in the realwage is ambiguous

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩

Real rental on land rises

⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩

7. Read the article by Lori G. Kletzer and Robert E. Litan, “A Prescription to RelieveWorker Anxiety,” Policy Brief 01-2, Institute for International Economics, Washing-ton, DC, http://www. iie. com/publications/pb/Pb01-2. htm, which refers to theU.S. recession of 2000–2001. Then answer the following questions.

a. Under the most recent version of Trade Adjustment Assistance (TAA) in theUnited States that they refer to, how many extra weeks of unemployment insur-ance (UI) are workers eligible for? What two criteria must they meet to qualifyfor 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 mustprove that they lost their job because of increased imports from, or a shift in pro-duction to, either Canada or Mexico. ”

b. Consider the proposal for “wage insurance” that Kletzer and Litan make in theirarticle. 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 re-ceive some fraction of their wage loss, which could vary by age and tenure of theworker for up to 2 years following the initial date of job loss, but would beginto be paid only when workers found a new job. ”

“To qualify for our proposed supplemental wage insurance benefit, workers needonly document that they have been ‘displaced’ according to criteria similar to theoperational definition of displacement used by the BLS in its Displaced WorkerSurveys (plant or company closed or moved, elimination of position or shift, in-sufficient work); that they had served at their previous job for a minimum periodof time: we suggest 2 years; and that they have suffered an earnings loss (from oldjob to new job) . . . ”

c. If Kletzer and Litan’s new plan for “wage insurance” had been adopted by theUnited States, what would have been the budgetary cost in 1999 when unem-ployment was 4. 2%? How does this compare with the amount that is now spenton unemployment insurance?

Answer: “Assuming a 50% replacement and subsidy rate, the table indicates thatour wage insurance and health insurance program would have cost about $2. 9billion in 1999, when the national unemployment rate averaged 4. 2%.

“The total cost, less than $4 billion, might have been a major obstacle when fed-eral deficits were high and growing but is not a problem now, and in any eventwould be small in relation to the more than $20 billion that is now spent on un-employment insurance . . . ”

8. In the specific-factors model, assume that the price of agricultural goods de-creases 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 agricul-tural goods instead.

Answer: It helps to separate this exercise into two parts. The first part is to arrangethe percentage changes in wages and goods prices. This part is similar to problem 4except that now it is the price of agriculture that is decreasing. By similar logic, the

Solutions ■ Chapter 3 Gains and Losses from Trade in the Specific-Factors Model S-23

percentage change in price of agricultural goods is larger than the percentage changein wage, which in turn is larger than the percentage change in the price of manufac-tured goods (zero). Thus,

0 � �PM / PM �W / W �PA / PA

For the second part, adding the percentage changes in specific-factors rental rates, re-call that in this model, although the real return to labor is ambiguous (which meansthat more agricultural products but fewer manufactured goods can be purchased bylabor), the real return to capital and land can both be determined and move in op-posite directions. The general rule for the specific-factors model is that a decrease inthe relative price of an industry leads to a real loss of the factor specific in that in-dustry, and a real return to the specific factor in the other industry. This means thatthe percentage change in losses to land is greater than both price changes and that thepercentage change in returns to capital is greater than both price changes, which isequivalent to saying that fewer of both goods can be purchased by landowners al-though 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 televi-sions. Assume that land is specific to timber, capital is specific to televisions, and la-bor is free to move between the two industries. When Canada and Mexico engagein free trade, the relative price of televisions falls in Canada and the relative price oftimber falls in Mexico.

a. In a graph similar to Figure 3-5, show how the wage changes in Canada becauseof a fall in the price of televisions, holding constant the price of timber. Can wepredict that change in the real wage?

Answer: As shown by the following figure, real wage falls but by less than thepercentage decrease in the price of televisions.

S-24 Solutions ■ Chapter 3 Gains and Losses from Trade in the Specific-Factors Model

Wage

Labor

W

B

A

W �

��PTV · (MPLTV )

PTV · MPLTV

PTIM · MPLTIM

0TV LTV 0TIMLTIML� L

L �

�W

Vertical distance

PTV � · MPLTV

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 rela-tive price of televisions will lead to a fall in the rental on capital. With Canadaexporting timber, rental on land will rise because land is specific to the timberindustry.

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 willrise in Mexico, which will lead to an increase in the rental on capital. By con-trast, the rental on land will fall.

d. In each country, has the specific factor in the export industry gained or lost, andhas the specific factor in the import industry gained or lost?

Answer: In both cases, the specific factor in the export industry (i. e. , land inCanada and capital in Mexico) gained whereas the factor specified to the importindustry (i. e. , capital in Canada and land in Mexico) loses when the two coun-tries engage in trade.

10. Home produces two goods, computers and wheat, where capital is specific to com-puters, 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 axisand the labor in wheat on the horizontal axis. What is the relationship betweenthe output of wheat and the marginal product of labor in the wheat industry asmore labor is used?

Answer: See the following graph.

As more labor is added to the production of wheat, the marginal product of la-bor declines so that although the output of wheat continues to increase, the out-put is increasing at a decreasing rate.

Solutions ■ Chapter 3 Gains and Losses from Trade in the Specific-Factors Model S-25

Labor in wheat, LW

1

MPLW

Wheat output, QW

b. Draw the production possibilities frontier (PPF) for Home with wheat on thehorizontal axis and computers on the vertical axis.

Answer: See the following graph.

c. Explain how the price of wheat relative to computers is determined in the ab-sence of trade.

Answer: In the absence of international trade, the relative price of wheat is theslope 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 fromleft to right along the horizontal axis, and the amount of labor used in comput-ers moving in the reverse direction.

Answer: See graph below.

S-26 Solutions ■ Chapter 3 Gains and Losses from Trade in the Specific-Factors Model

A

B

Wheat output, QW

Computeroutput, QC

Slope � � (MPLC / MPLW )

MPLC

MPLW

Production possibilitiesfrontier, PPF

Wage

Computerlabor

Labormarketequilibrium

Value ofmarginal productof computer

Value ofmarginal productof wheat

Wheat labor

WA

PC · MPLC

PW · MPLW

0W LW 0CLCL

L

e. Assume that because of international trade, the price of wheat rises. Analyze theeffect of the increase in the price of wheat on the allocation of labor betweenthe two sectors.

Answer:

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 inwheat increases from 0WL to 0WL', although the amount of labor devoted tocomputers 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 usingcapital, 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 ofland, 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? Ex-plain why you expect this outcome.

Answer:The no-trade relative price of wheat will be higher in Home than For-eign 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 inwheat is lower than the marginal product of capital in computers at Home. Be-cause 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 landthan capital. In this case, the price of capital is higher relative to the price ofwheat without trade.

Solutions ■ Chapter 3 Gains and Losses from Trade in the Specific-Factors Model S-27

Wage

Computerlabor

Wheat labor

Verticaldistance

B

AW

W �

��PW · (MPLW )

P´W · MPLW

PW · MPLW

0W LW 0CLCL�L

L �

�W

b. When trade is opened, what happens to the relative price of wheat in Foreignand to the relative price of wheat in Home?

Answer: When the two countries engage in trade, Home will export comput-ers so that the relative price of wheat decreases at Home, whereas Foreign willexport 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 onland in each country, which is specific to wheat. What about the rental on cap-ital, which is specific to computers?

Answer: With Home exporting computers, the rental on capital will increasewhile the rental on land will decrease. Because Foreign exports wheat, landown-ers will experience an increase in the rental on land, whereas capital owners willlose because of the decrease in the rental on capital.

12. In the text, we learned that workers displaced by import competition are eligible forcompensation through the Trade Adjustment Assistance (TAA) program. In additionto workers, firms are also eligible for support through Trade Adjustment Assistance forFirms, a federal program that provides financial assistance to manufacturers affectedby import competition. Go to www. taacenters. org to read about this program, andanswer 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 bene-fits from the TAA if imports have contributed to declines in their employmentand 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 $75,000for projects to improve a manufacturer’s competitiveness. The funds go towardthe cost of hiring industry experts, including consultants, engineers, and design-ers for projects.

S-28 Solutions ■ Chapter 3 Gains and Losses from Trade in the Specific-Factors Model

A

B

Wheat output, Q*W

Computer output, Q*C

Slope � � ( MPL*C / MPL*W )

MPL*C

MPL*W

Production possibilitiesfrontier, PPF

c. Provide an argument for and an argument against the continued funding of thisfederal program.

Answer: Opponents of TAA would argue that the program is costly. The fol-lowing figure shows the total expenditures of the program from 1995 to 1999,where more than half of the cost is administrative and operations related. Pro-ponents of TAA would draw on the positive effect the assistance program has onthe manufacturing industry and local economy.

Solutions ■ Chapter 3 Gains and Losses from Trade in the Specific-Factors Model S-29

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

$0

New E

nglan

dNew

York

Midw

est

Rocky

Mou

ntain

North

west

Mid-

Amer

icaSou

thea

stern

Great

Lak

esM

id-Atla

ntic

New Je

rsey

Wes

tern

South

west

Operations and administrative costs Consultant 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.