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Lecture 4
The Specific-Factors Model:
Trade and Income Distribution
Overview
The specific factor (SF) model was developed and formalized mathematically by
Ronald Jones (1971) and Michael Mussa (1974). Jones referred to it as the 2 good-3
factor model. Mussa developed a simple graphical depiction of the equilibrium which can
be used to portray some of the model results. It is this view that is presented in most
textbooks.
The model's name refers to its distinguishing feature; that one factor of production is
assumed to be "specific" to a particular industry. A specific factor is one which is stuck in
an industry or is immobile between industries in response to changes in market
conditions. A factor may be immobile between industries for a number of reasons. Some
factors may be specifically designed (in the case of capital) or specifically trained (in the
case of labor) for use in a particular production process. In these cases it may be
impossible, or at least difficult or costly, to move these factors across industries.
The specific factor model is designed to demonstrate the effects of trade in an economy
in which one factor of production is specific to an industry. The most interesting results
pertain to the changes in the distribution of income that would arise as a country moves to
free trade.
The model shows that opening a country to trade generates winners and losers.
Winners: factors sector to export sector
Losers: factors specific to import competing sectors.
We can think of Specific-Factors models as a short or medium run version of HO model
in which some factors of production are specific to some sectors and can not move to
other sectors in the short run.
Assumptions of the Model
 Two goods: An economy can produce two goods,
Manufactures QM and Food, QF

Two Countries: Home and Foreign

Three Factors of Production:
• Production of Manufacturing requires Labor L and Capital K
QM = QM (K, LM)
(1)
•
Production of Food requires Labor L and Land T
QF = QF (T, LF)
(2)
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•
Labor is perfectly mobile between the two sectors.
LM + LF = L
(3) (full employment condition)
•
•
Capital and Land and immobile between the sectors –are sector specific
Supply of the Three inputs are given and fixed
Technology
• Constant Returns to Scale (CRS) production functions:
Perfect competition prevails in all markets.
The two countries differ only in their factor endowments (same tastes, same tech)
Production Possibilities Frontier
Use equations 1-3 to derive the PPF of the economy.
• To analyze the economy’s production possibilities, we need only to ask how the
economy’s mix of output changes as labor is shifted from one sector to the other.
The Specific Factors Model
Figure 3-1: The Production Function for Manufactures
Output, QM
QM = QM (K, LM)
Labor input, LM
Copyright © 2003 Pearson Education, Inc.
•
•
•
•
Slide 3-9
The shape of the production function reflects the law of diminishing marginal
returns.
Adding one worker to the production process (without increasing the amount of
capital) means that each worker has less capital to work with.
Therefore, each additional unit of labor will add less to the production of output
than the last.
Figure 3-2 shows the marginal product of labor, which is the increase in output
that corresponds to an extra unit of labor.
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The Specific Factors Model
Figure 3-2: The Marginal Product of Labor
Marginal product
of labor, MPLM
MPLM
Labor input, LM
Copyright © 2003 Pearson Education, Inc.
Slide 3-11
Derivation of PPF from MP curves and total labor endowment
The Specific Factors Model
Figure 3-3: The Production Possibility Frontier in the Specific Factors Model
Output of food,
QF (increasing )
Production function
for food
Q2F
QF =QF(K, LF)
Economy’s production
possibility frontier (PP)
1'
2'
3'
Labor input in
food, LF
(increasing )
L
Q2M
L2F
L2M
1
2
Economy’s allocation
of labor (AA)
Copyright © 2003 Pearson Education, Inc.
Prices, Wages, and Labor Allocation
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AA
L
Labor input
in manufactures,
LM (increasing )
PP
Output of
manufactures, QM
(increasing )
Production function
for manufactures
QM =QM(K, LM)
Slide 3-12
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
How much labor will be employed in each sector?
• To answer the above question we need to look at supply and demand in
the labor market.
•
Demand for labor:
• In each sector, profit-maximizing employers will demand labor up to the
point where the value produced by an additional person-hour equals the
cost of employing that hour.
The demand curve for labor in the manufacturing sector can be written:
•
MPLM x PM = W
•
(4)
The demand curve for labor in the food sector can be written:
MPLF x PF = W
(5)

The wage rate must be the same in both sectors, because of the assumption that labor
is freely mobile between sectors.

The wage rate is determined by the requirement that total labor demand equal total
labor supply:
LM + LF = L
(6)
The Specific Factors Model
Figure 3-4: The Allocation of Labor
Wage rate, W
Wage rate, W
1
PF X MPLF
(Demand curve
for labor in food)
W1
PM X MPLM
(Demand curve for labor in
manufacturing)
Labor used in
manufactures, LM
L1M
Labor used
in food, LF
L1F
Total labor supply, L
Copyright © 2003 Pearson Education, Inc.

Slide 3-16
At the production point the production possibility frontier must be tangent to a
line whose slope is minus the price of manufactures divided by that of food.
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Opportunity Cost and Prices: As in the Ricardian model, the slope of the
PPF, which is the opportunity cost of manufacturing, also equals the relative price
of manufacturing.
The Specific Factors Model
Figure 3-5: Production in the Specific Factors Model
Output of food, QF
Slope = -(PM /PF)1
1
Q1F
PP
Q1
Output of manufactures, QM
M
Copyright © 2003 Pearson Education, Inc.

Slide 3-18
Relationship between relative prices and output:
-MPLF/MPLM = -PM/PF
(7)
International Trade in the Specific Factors Model
Let’s assume Home is capital abundant and Foreign is land abundant. They have an equal
amount of labor endowment.
 Trade, Relative Prices and Patterns of Trade
• Since compared to Foreign, Home is capital abundant the pre-trade relative price
of manufactures in Home is lower than the pre-trade relative price in Foreign.
• International trade leads to a convergence of relative prices.
• Foreign will export Food and Home will export manufacturing
QF
C
U2
A
U1
B
Slope=-PM/PF
QM
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Gains from Trade
• In absence of international trade, the economy produces and consumes at point A.
With trade the economy produces at point B and consumes at point C. The rice of
utility from U1 to U2 is a measure of the gains from trade for the economy.
The Effect of Trade on Factor prices
a) Wage rate and Labor allocation
• What happens to the allocation of labor and the distribution of income when the
prices of food and manufactures change?
• Consider an increase manufacturing prices increase in Home.
• When only PM rises, labor shifts from the food sector to the manufacturing sector
and the output of manufactures rises while that of food falls.
• The wage rate (W) does not rise as much as PM since manufacturing
employment increases and thus the marginal product of labor in that sector
falls.
• Suppose that PM increases by 10%. Then, we can show that the wage rate increase
by a lesser percentage say by 7%.
Wage
Wage
∆PM.MPLM =10%
W2
B
7%
P2M.MPLM
W1
A
P1M.MPLM
P F.MPLF
OM
L1
L2
OF
Are workers better off as a result of intentional trade?
Let’s look at the change in real wage rates: (W/ PM) & (W/ PF)
(W/ PM) ↓ because %∆PM > %∆W
(W/ PF) ↑ because %∆W > 0 = %∆PF
We cannot say whether workers are better or worse off; this depends on the relative
importance of manufactures and food in workers’ consumption.
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a) Price change and Change of return on Specific Factors
• What is the economic effect of PM ↑ on owners of specific factors.
• when PM ↑ =>
LM ↑ = (K/L) ↓ => MPK↑ = RK/PM ↑ and
LF ↓ = (T/L) ↑ => MPT↓ = RT/PF ↓
• for RK/PM ↑ it must be that: %∆RK> %∆PM >0 e.g., 12% > 10% > 0
• and for RT/PF ↓ it must be that: %∆RT< %∆PM =0 e.g., -8% < 0
In general:
If %∆PF > 0 and %∆PM = 0 then: %∆RK < 0 < %∆W < %∆PF < %∆RT
If
%∆PM >0 and %∆PM = 0 then: %∆RT < 0 < %∆W < %∆PM < %∆RK
Income Distribution and the Gains from Trade

To assess the effects of trade on particular groups, the key point is that
international trade shifts the relative price of manufactures and food.

Trade benefits the factor that is specific to the export sector of each country, but
hurts the factor that is specific to the import-competing sectors.
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Trade has ambiguous effects on mobile factors.
Could those who gain from trade compensate those who lose, and still be better
off themselves?
• If so, then trade is potentially a source of gain to everyone.

The fundamental reason why trade potentially benefits a country is that it expands
the economy’s choices.
• This expansion of choice means that it is always possible to redistribute
income in such a way that everyone gains from trade.
CASE STUDY
Manufacturing and Services

From 2005 to 2007, about 876 thousand workers were displaced in
manufacturing, and 2.3 million in services, as shown in Table 3.1.
 Of those laid off in manufacturing, 64% were re-employed by January 2008, but
nearly half of these (49%) earned less in their new job.
 For services, however, 68% were re-employed by January 2008, and more than
half of these (56%) earned the same or more in their new jobs!
 Four lessons:
1- Wages differ across different sectors in the economy, so our theoretical
assumption that wages are the same in both industries is a simplification.
2- Many workers are displaced each year and must find jobs elsewhere. Some of
these workers may be laid off due to competition from imports, but there are other
reasons, too: for instance, products that used to be purchased go out of fashion;
firms re-organize as computers and other technological advances become
available; and firms change locations.
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3- The majority of displaced workers find a new job within two years, but not
necessarily at the same wage. It is typically older workers (aged 45 to 64) who
experience earnings losses when shifting between jobs, whereas younger workers
(aged 25 to 24) are often able to find a new job with the same or higher wages.
4- The real wage for production workers fell in the United States between 1979 and
1995, and in later chapters we will examine the reasons for that fall.
Table 3.1 Job Losses in Manufacturing and Service Industries, 2005–2009
Unemployment:
 One realistic feature that we have ignored in the specific-factors model is
unemployment.
 One of the reasons we ignore unemployment in this model is that many
economists feel that unemployment is a macroeconomic phenomenon, caused by
business cycles, and it is hard to combine business cycle models with
international trade models.
 But the other, simpler reason is that even when people are laid off due to import
competition, many of them do find new jobs within a reasonable period of time,
and sometimes they find jobs at higher wages. Therefore, even if we take into
account spells of unemployment, once we recognize that workers can find new
jobs – possibly in industries that are expanding due to their exports – then we still
could not conclude that trade is necessarily good or bad for workers.
Trade Adjustment Assistance
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Should the government step in to compensate workers who are looking for jobs,
or who do not find them in a reasonable period of time?
The unemployment insurance program in the United States provides some
compensation, regardless of the reason for the layoff.
In addition there is a Trade Adjustment Assistance (TAA) program that offers
additional unemployment insurance payments (for up to one year) to workers who
are laid off due to import competition and who are enrolled in a retraining
program.
Since 1993, there has also been a special TAA program under the North American
Free Trade Agreement (NAFTA) for workers who are laid off due to import
competition from Mexico or Canada.
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Other countries, too, have programs like TAA to compensate those harmed by trade. A
particularly interesting example occurred with the unification of East and West
Germany on June 30, 1990. On that date, all barriers to trade between the countries were
removed, as well as all barriers to the movement of labor and capital between the two
regions. The pressure from labor unions to achieve wage parity (i.e. equality) between the
East and West, meant that companies in former East Germany were faced with wages
that were far above what they could afford to pay.
According to one estimate, only 8% of former East German companies would be
profitable at the same high wages paid in the West. In the absence of government
intervention, it could be expected that severe bankruptcy and unemployment would
result, leading to migration to the former West Germany.
Economists studying that situation proposed that deep wage subsidies – or “flexible
employment bonuses” – should be given in former East Germany, thereby allowing
factories to employ their workers while only paying a fraction of their wages.
Furthermore, it was argued that the wage subsidies would essentially pay for themselves,
because without them, the government would have to provide unemployment insurance
on a massive scale to the persons left without jobs. As it turns out, wage subsidies of this
type were not used, and unemployment in the East along with migration to the West
continues to be a policy issue.
Programs like TAA are intended to share the overall gains from trade with workers who
lose their jobs because of trade competition, but not all economists or policy makers
agree with these programs. Why should workers who are laid off because of import
competition be treated any differently from someone who is laid off for any other reason?
And would the compensation provided to workers just allow them to remain
unemployed? Regardless of whether you agree or disagree with the idea that workers laid
off due to import competition deserve special treatment, it is useful to think about the best
way to design a compensation program.
A Preliminary View of The Political Economy of Trade:
Trade often produces losers as well as winners.
 Optimal Trade Policy
• The government must somehow weigh one person’s gain against another
person’s loss.
– Some groups need special treatment because they are already relatively
poor (e.g., shoe and garment workers in the United States).
– Most economists remain strongly in favor of more or less free trade.
• Any realistic understanding of how trade policy must look at the actual
motivations of policy.
 Income Distribution and Trade Politics
• Those who gain from trade are a much less concentrated, informed, and
organized group than those who lose.
– Example: Consumers and producers in the U.S. sugar industry
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Summary

International trade often has strong effects on the distribution of income within
countries, so that it often produces losers as well as winners.

Income distribution effects arise for two reasons:
• Factors of production cannot move instantaneously and costlessly from
one industry to another.
• Changes in an economy’s output mix have differential effects on the
demand for different factors of production.
A useful model of income distribution effects of international trade is the specificfactors model.
• In this model, differences in resources can cause countries to have
different relative supply curves, and thus cause international trade.
• In the specific factors model, factors specific to export sectors in each
country gain from trade, while factors specific to import-competing
sectors lose.
• Mobile factors that can work in either sector may either gain or lose.
Trade nonetheless produces overall gains in the sense that those who gain could in
principle compensate those who lose while still remaining better off than before.
Economists do not normally count the costs of unemployment as a loss from
trade, because people are able to find jobs elsewhere. In the United States, for
example, about one-half of persons laid off from manufacturing find new jobs
within two years, though often at lower wages. For persons laid off from service
industries, about 70% find jobs within two years, and often at the same or higher
wages.
Trade Adjustment Assistance policies are intended to compensate those who are
harmed due to trade, by providing addition income during the period of
unemployment.
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