The Specific Factors model
Maarten Bosker
Outline
• Introduction
• The Specific Factors Model
• International Trade in the Specific Factors Model
• Income Distribution and the Gains from Trade
• Political Economy of Trade: a first look
- Extension: International Labor Mobility
Introduction
• If trade is so good for the economy (see Ricardian model),
why is there sometimes such opposition?
• Two main reasons why international trade has strong
effects on the distribution of income within a country:
• Resources cannot move immediately or costlessly from one
industry to another
• Industries differ in the factors of production they demand
• The Ricardian model assumes these two away:
• Labor can costlessly move between industries
• Labor only factor of production in all industries
Introduction
• The Specific Factors model relaxes these two assumptions of
the Ricardian model
• As we will see, this has important consequences:
Countries as a whole still benefit from trade, but it may hurt
significant groups within the country
• e.g. workers with specific skills may lose their job and have a
difficult time finding a new job in a different industry
The Specific Factors model
The Specific Factors Model
The Specific Factors model
Assumptions of the model:
•
•
•
•
•
•
•
Two goods (say cars and food)
Three factors of production: labor (L), capital (K) and land (T)
Cars produced using labor and capital
Food produced using labor and land
Perfect competition & free/entry exit in both markets
All production factors internationally immobile
Labor is a perfectly mobile factor: it can costlessly move
between sectors
• Land and capital are specific factors: they can only be used
in the production of food and cars respectively
Specific Factors model
• As in Ricardian model, we first focus on what each economy
can produce
• Subsequently we can ask what will happen if a country opens
up to trade
• We start by asking: how much of the two goods can a
country produce?
• This depends on their production technologies
• They can be summarized by a production function
Specific Factors model
• The production function for cars gives the quantity of cars
that can be produced given any input of capital and labor:
QC = QC (K, LC)
• Similarly, the production function for food gives the quantity
of food that can be produced given any input of land and
labor:
QF = QF (T, LF)
• Where:
• QC and QF are the output of cars and food resp.
• K is the capital stock
• T is the amount of land available
• LC and LF is the amount of labor employed in
cars and food resp.
Production possibilities
• For example, the production function for cars:
(similar for food – except that food uses land (T) not capital (K)…)
e.g. a Cobb Douglas
production function:
QC = KαL1-α, 0 < α < 1
Production possibilities
• Why does it look like this?
• The shape of the production function reflects diminishing
marginal returns to labor
• 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 adds less output than
before
• In other words: the marginal product of labor, which is the
increase in output that corresponds to an extra unit of labor,
decreases with the number of people already employed
=> In a graph
Production possibilities
• The marginal product of labor in cars production (again
similar in food production)
Note: this is the derivative of the production function w.r.t. labor (L) !
Production possibilities
• Note, that also:
Output (QC ) = the area under the marginal product curve
dQc ≈ MPLc dLc
Production possibilities
• For the economy as a whole, the total labor employed in car
and food production must equal the total labor supply (people can
only work in one of the two sectors at the same time):
LC + LF = L
• How does the economy’s output mix change as labor is
shifted from one sector to the other?
• When labor moves from food to cars, food production falls
while output of cars rises
… but by how much?
• Using the production functions in cars and food, plus the
labor market equilibrium, we can derive the production
possibilities frontier of the economy
The production possibilities frontier
QF (increasing )
Food production function
Production possibility frontier(PP)
Q2
QF =QF(T, LF)
1'
2'
F
3'
LF
(increasing)
Q2C
L2F
L2C
1
2
Labor allocation(AA)
PP
QC
(increasing )
3
AA
LC (increasing )
cars
production function
QC =QC(K, LC)
Opportunity costs in the Specific Factors Model
• The slope of the PPF measures the opportunity costs of
cars in terms of food: how much food could be produced using
the resources now used to produce one unit of cars
• To produce one extra unit of cars, we need 1/MPLC units of labor
(remember: dQC = MPLC dLC)
• These units of labor could have instead been employed in food
production, producing MPLF / MPLC units of food (remember:
dQF = MPLF dLF)
• Opportunity cost of producing one extra unit of cars is
-(MPLF / MPLC) units of food
Opportunity costs in the Specific Factors Model
• This is not constant! (as in the Ricardian model, where unit labor requirements
did not depend on the amount already produced)
• It depends on how much food and cars are already produced
• The opportunity costs of producing a good rises with the amount of
the good already produced
• Why? Because of diminishing returns to labor in each sector:
We need more and more labor to produce one additional unit of a
good. Instead we can use this labor also to produce the other good.
Since, producing one less good frees up more and more labor, we
could have produced more and more of the other good
Opportunity costs in the Specific Factors model
Q3 F
Q2F
Q 3 C Q2 C
cars
Prices, wages and labor allocation
• How much will each sector produce?
• It is always optimal to use all available land for food
production, and all available capital for cars production.
But… how much labor will each sector employ?
• This depends on labor demand and labor supply (together
they determine wages)
• Labor supply is easy: L
• Labor demand:
• In each sector, employers will demand the number of
workers that maximizes their profit:
Prices, wages and labor allocation
Prices, wages and labor allocation
We can plot both sectors’ labor demand curves in one Figure
Note: we obtain the cars
curve by multiplying earlier
figure for MPLc by Pc
cars)
cars
Prices, wages and labor allocation
• Where the labor demand curves intersect, we find the
equilibrium wage and allocation of labor between the two
sectors
Why?
• The two sectors must pay the same wage because labor can
move between sectors
• If wages were higher in the cars sector, workers would
move from making food to making cars until wages are
equal
• Or, if wages were higher in the food sector, workers would
move in the other direction
Prices, wages and labor allocation
• This wage equality between sectors also gives us a
relationship between relative prices and opportunity costs:
• wF = wC <=> MPLF PF = MPLC PC
<=>
-(MPLF/MPLC) = -(PC/PF)
• At the production point the PPF is tangent to a line with slope
given by the relative price of cars in terms of food (with a
minus sign)
• This pinpoints the amount produced of both goods
=>
Production in the Specific Factors model
cars
What happens when prices change?
• How do the allocation of labor and the distribution of income
(among workers, capital owners and land owners) change
when the prices of food and cars change?
• Two cases:
1. A proportional change in prices (prices of both
goods increase with the same %)
2. A change in relative prices (prices of both goods
change, but each with a different %)
Hint: opening up to trade tends to change prices….!
A proportional increased in prices
PC 2 X MPLC
W
PC 1 X MPLC
PC increases
by 10%
2
PF increases
by 10%
W2
PF 1 X MPLF
Increase by
10% in the
salary
W1
Labor in
the cars sector LC
PF 2 X MPLF
W
1
Labor in the
food sector, LF
A proportional change in prices
• Relative prices unchanged: output remains the same
• Wages rise in the same proportion: no reallocation of workers
• Real wages (the ratio of wages to the prices of goods) do not
change:
• Workers earn 10% more, but each extra € also buys them
10% less of each good (both prices have increase by 10%)
• Also, owners of land and capital can ask 10% more for their
output, but also have to pay 10% more to their workers
• No real changes!
A change in relative prices
•
Things do change when relative prices change!
•
Suppose that the price of cars rises, whereas the price of
food remains the same

Relative price of cars goes up
•
Now what happens?
1. Allocation of labor between sectors changes
2. Welfare of workers, land owners and capital owners
changes
=>
A change in relative prices
cars
cars
A change in relative price - wages
• Increase in price of cars, will result in an increase in wages
paid in the cars sector
• This attracts people from the food sector who start working in
the cars sector
• In the end… wages will not rise as much as prices. Why not?
• MPLc drops because more people now work in the cars sector;
and remember that wc = MPLc Pc !
• Intuition: higher wages attract more workers, but because more
people want to work in the car sector now, employers can
reduce wages a bit and still get enough people to do the job
A change in relative prices - output
• Of course, all this also means that car output will rise
cars
A change in relative prices
Summing up:
If relative price of cars goes up,
•
Wages go up, but less than prices
•
Some people move from the food to the cars sector
•
Output of cars rises
=> Does everybody gain from this, or not?!
Income distribution and a change in relative prices
• What does this mean for the welfare of workers, land owners
and capital owners?
• Capital owners are better off
1. They earn more: output goes up, and the price of cars rises by
7% whereas wages only rise by less than 7%
2. Also: they can buy more food for a given amount of cars they
produce (relative price of cars has risen)
• Land owners are worse off
1. They earn less: output goes down, and wages rise whereas the
price of food remains unchanged
2. Also: they can buy less cars for a given amount of food they
produce (relative price of cars has risen)
Income distribution and a change in relative prices
•
Finally, workers
1. Wages go up, but
2. Price of cars has gone up even more, so that they can buy less
cars: relative wage in terms of cars falls
3. But, since price of food remains unchanged, they can buy
more food: relative wage in terms of food rises
Ambiguous whether they are better off or not, it depends on
their preferences for food and cars
•
•
If they really like food, so that food is a very large part of their
consumption, they will be better off
If they really like cars, they will be worse off
So, keep in mind when we start talking
about effects of trade =>
Income distribution and a change in relative prices
In the Specific Factors model, a change in relative prices will
• Benefit the owners of the factor specific to the sector whose
relative price increases
• Hurt the owners of the factor specific to the sector whose
relative price decreases
• And, the effect on the mobile factor is ambiguous
The Specific Factors model
Trade in the Specific Factors Model
Trade in the Specific Factors model
• Suppose a country opens up to trade, when will it actually
start trading?
When relative prices in the other country are different
from the prevailing relative prices in the country itself in
autarky
• Why?
If they are the same, the country is equally well off producing
all its goods itself
• No good from other countries is cheaper to import
• And, no other country will find one of the country’s goods
particularly attractive (no exports)
Trade in the Specific Factors model
• To see if relative prices change due to trade, we first need to
know the prevailing relative prices when a country does not
trade (relative prices in autarky)
• (as always) these prices are determined by relative demand
(RD) and relative supply (RS)
• Relative demand (RD): if relative price of a good goes up,
relative demand of that good goes down
• Relative supply (RS): if relative price of a good goes up,
relative supply goes up
=> together RS and RD determine prices =>
Relative prices in autarky
cars
Note: you can derive the RS
curve using a country’s PPF
cars
cars
Relative prices with Trade
•
When a country opens up to trade, prices change because
1. Relative demand changes: people in other countries have
different preferences than those in your own country (e.g. at
the same relative prices they are willing to buy more cars
and less food)
2. Relative supply changes: firms in other countries can
produce goods at higher or lower cost than firms in your own
country
• different technologies (Ricardian model)
• different resources (amount of land, labor or capital)
How does trade change relative prices?
• For simplicity: assume preferences are the same all over the world,
so that relative demand does not change
• Suppose that for a given relative price of cars in terms of food, the
foreign country is willing to produce relatively less cars, because it
for example:
• is less productive in cars production (less skills / technology)
• is more productive in food production (more skills / technology)
• has less capital per worker (more workers/machine = less efficient)
• has more land per worker (fewer workers/acre = more efficient)
• In this case the world’s RS curve lies to the left of the country’s own
RS curve, and opening up to trade changes relative prices =>
How does trade affect relative prices?
• The relative price of cars in the country goes up!
cars
cars
How does trade affect relative prices?
• Why?
• The country can produce cars relatively cheaply, because it
for example:
• is more productive in cars production than the rest of the world
• has more capital / workers available to produce cars
• As a result, prices for cars in the country are relatively low
compared to the rest of the world
• When it opens to trade: other countries start to buy cars in
the country selling food in return, this increased demand/
supply raises the relative price of cars
Gains from Trade
The
Specific
Factors
model
in the Specific Factors Model ?!?
Home
Foreign
+
Free Trade
?
=
Gains from trade?
• Without trade the country’s production of cars and food (QC
and QF) necessarily equals its consumption (say DC and DF):
• QF = DF and QC = DC
• With trade it becomes possible to produce more/less than
consumed and import/export the rest
• In particular, in our example, the country starts to produce
more cars and less food (relative price of cars goes up)
• It can consume all this, but it can also start to export cars
(selling it at PC) and import food (buying it at PF)
• Is it better of when doing this?
Gains from trade?
• Well, first of all it cannot spend more than it earns:
PC x DC + PF x DF = PC x QC +PF x QF
• Rewriting this budget constraint gives a relationship between
a country’s imports and exports:
(DF - QF) = (PC / PF) x (QC – DC )
• This tells us how much a country needs to export in order to
finance its imports
• if it sells one more unit of cars on world markets it gets PC for it,
with this money it can buy (PC / PF) units of food in return
Gains from trade!
•
In Autarky it produces and
consumes QAF and QAC
•
With trade it produces
Q1F and Q1C
Q AF
It can always trade these goods at
the prevailing world prices
and consume any bundle of
goods along the budget constraint
•
slope = -PAc/PAF
So also those in the blue area,
where both the amount of cars
and food consumed are larger
than in autarky !
QAC
cars
cars
Country as a whole always gains from trade!
Gains from trade!... but not for all?
• Trade always benefits a country as a whole (i.e. it expands
consumption possibilities). Unfortunately, this does not mean
that everybody gains from trade
• Trade has strong effects on the income distribution within a
country
• Why? Remember that trade changes relative prices!
• Benefit the owners of the factor specific to the sector whose
relative price increases: the exporting sector
• Hurt the owners of the factor specific to the sector whose
relative price decreases: the sector that faces toughest
competition from imports
• Effect on mobile factors is ambiguous
Income (re)distribution and the Gains from Trade
• However, trade benefits a country as a whole by expanding
choices
• Possible to redistribute income so that everyone gains from
trade!
• Those who gain from trade could compensate those who
lose and still be better off themselves.
• That everyone could gain from trade does not mean that they
actually do – redistribution usually hard to implement
Trade and Income redistribution
• Trade creates winners and losers in the Specific Factors
model
• In the real world this effect of trade may actually be smaller or
larger
• Why smaller?
• The specific factors cannot move to the other sector
(completely immobile)
• In the real world this is usually not the case:
people can acquire new skills, machines can be changed,
land can be replanted or used to build a factory on
=> Heckscher-Ohlin model
Trade and unemployment
Losses can also be (even) larger?
• Opening to trade shifts jobs from import-competing to
exporting sectors
• In the Specific Factors model, workers move costlessly
between sectors
• However, in the real world this may not happen
instantaneously
• Finding new jobs in the exporting sector may not be easy
• Opening to trade may lead to an increase in (short-run)
unemployment
Trade and unemployment – some evidence
In the US at least, this effect appears to be relatively small:
• From 1996 to 2008, only about 2.5% of involuntary displacements
stemmed from import competition or plants moved overseas
• Also there is little correlation between import penetration and
unemployment:
Trade and unemployment – recent evidence
But, a (much) more careful look reveals a (much) gloomier picture:
Source: American Economic Review, 2013, 103(6), 2121-2168
The Political Economy of Trade (see Ch.9-12)
• Trade creates winners and losers, but it increases welfare in a
country as a whole =>
• Role for the government to provide a safety net for groups losing a
lot from trade (e.g. low-skilled workers in the EU)?!
• This is not easy:
• Identifying losers and winners is not easy
• Optimal trade policy must weigh one group’s gain against
another’s loss
• Actual trade policy often dominated by small interest groups
(farmers in the EU), whereas those that gain from trade
(typically all consumers!) are much less informed and organized
to counterlobby
(see the striking `sugar example’ on p.100 of the book, or…)
Summary: Trade & the Specific Factors model
1 International trade often has strong effects on the distribution of
income within countries -- produces losers as well as winners
2 Income distribution effects arise for two reasons:
• Factors of production cannot move costlessly and quickly from
one industry to another
• Changes in an economy’s output mix have differential effects
on the demand for different factors of production
3 International trade affects the distribution of income 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
Summary: Trade & the Specific Factors model
4 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
5 Most economists would prefer to address the problem of
income distribution directly, rather than by restricting trade
6 Those hurt by trade are often better organized than those
who gain, causing trade restrictions to be adopted that are
far from “optimal”
The Specific Factors model
Adapting the Specific Factors model:
International Labor Mobility
International Labor Mobility
• So far, labor can move freely between sectors within a
country, but not between countries
• Not such a bad assumption, as in the real world restrictions
on international labor mobility are very severe
(it is much easier to move goods, capital or money across borders)
• However, if workers were allowed to migrate, what would
happen to income in the two countries. Who benefits, and
who loses?
• The Specific Factors model can be adapted to analyze these
questions:
International Labor Mobility
• Suppose two countries each produce the same good (food)
using land and labor (with diminishing returns to labor)
• NOTE: no trade because both countries produce the same
good
• But, workers may want to move to the other country (trade in
factors of production instead of in goods)
• Why? They might be able to earn higher real wages in one
country compared to the other
• Technology differences
• Different land to labor ratios
International labor mobility
• People move across borders until real wages are equal in the two
countries: you can buy the same things for your wages in both
countries (= equal purchasing power of wages)
• Suppose technologies are the same, but initially more people live
and work in Home than in Foreign: OL1 in Home > L1O* in Foreign
• In each country real wages are determined by the MPLF
(remember that wF = PF MPLF <=> (wF / PF) = MPLF)
• The MPL depends on the technology of each of the two countries,
and, because of diminishing returns, it falls the more people are
already working in the food sector
(so real wages in Home are lower than in Foreign)
International labor mobility – real wages
•
Without labor mobility:
real wage in Home lower than in
Foreign (C < B)
•
If people can migrate, what
happens?
•
They move from Home to Foreign!
•
When does this stop?
•
When real wages in the two
countries are equal (A)
•
What happens? Who gains and who
loses?
International labor mobility – winners and losers
•
•
•
•
•
•
•
Workers initially in Home gain (also
those who moved to Foreign): their
real wage rises
Workers initially in Foreign lose:
their real wage falls
Output in Foreign rises (+dQF)
Output in Home falls (-dQH)
But, overall world output rises
(red triangle): labor moves to
places where it is more productive!
Landowners in Foreign gain, their
output rises + they pay lower wages
Landowners in Home lose, their
output falls + they pay higher wages
+dQF
-dQH
International labor mobility – some evidence
• Does migration lead to the wage changes predicted?
• Over the 1870 – 1913 period, migration did move the world toward
more equalized real wages
International labor mobility – some evidence
• Immigration in the US has come and gone and come again
• Immigrants as % of total US population in the 20th century:
Immigration in the US economy
• Recent migration, mostly concerns workers with the lowest
skill levels: increase in the supply of low-skilled workers
• If anything, what did this do?
• reduced real wages for low-skilled US workers (increased
competition with immigrants), while raising real wages for
the more educated (goods/services produced by lowskilled workers become cheaper)
• widening income gap between high and low skilled
workers