Transcript K,L - WebCampus

Heckscher-Ohlin
Model
“Predicts trade across dissimilar countries and in
dissimilar goods: it says that labour abundant developing
countries will export labour-intensive products such as
food and clothing, whereas capital abundant developed
countries will export capital-intensive products such as
machinery and computers”. (Debraj Ray)
Heckscher-Ohlin Model
Outline
1. Two goods model
1.1 Assumptions
1.2 Production Possibilities : Combination of Factors
1.3. Production possibilities : Combination of Goods
1.4. Efficient production and consumption in autarky
1.5. What happens to consumption when both countries open to trade?
1.6. Integrated economy equilibrium: division of production
1.7. Integrated equilibrium consumption and trade
1.8. Production and factor price equalization
1.9. Factor prices and redistribution of income inside a country
1.10. Endowment changes (at given factor prices)
[ Nice « General Equilibrium » model :
goods and factor quantities and (relative) prices ]
[Gains 18]
[H-O trade 29]
[FPE 38]
[Stolper-S. 41]
[Rybcynski 44]
= 5 theorems
2
1. Two goods model
1.1 Assumptions
• 2 countries i : North (1) and South (2).
• 2 goods j = X and Y.
• 2 factors: capital (K) and labour (L).
• Factors mobility across industries but not across countries in the
medium term.
• Perfect competition and price flexibility in goods and factors markets.
Prices will be noted by: p ij .
• Identical production and utility function in both countries. Both
countries share the same knowledge.
• Constant returns to scale and decreasing returns of individual factors.
3
1.2. Production Possibilities :
Combination of factors
• Production function is given by: Q j  f j K , L for each good j.
As countries have identical knowledge, even when they do not produce the
same goods, this production function will be the same for all countries.
The constant returns to scale of the production function can be expressed
by:
f aK , aL   af K , L 
And the decreasing returns of individual factors implies that:
f aK , L  af K , L
The marginal productivity of individual factors is decreasing.
4
• Isoquants: give the combinations of labour and capital needed to produce
a certain amount Q of good j=X,Y, for a given production technology.
K
K
QX
A
QX
KA
LAX
< LAY
QY
L
QY
L
At A, the same reduction of K, requires a lower
increase of L to maintain the production of Y constant
than to maintain the production of X constant.
Labor is more efficient in Y than in X :
Y is “labor intensive” (Y “prefers” L).
The form of the isoquants shows that the factor intensity needed to produce
each good is different. While the good X is capital intensive good, the good
Y is labour intensive.
5
Combination of factors:
How to determine the required labour and capital for 1 (monetary cost)
unit of each good?
Maximize profits.
Prices of X and Y are given.
Under perfect competition
Factors prices, wages w and rental
rate (interest rate) r, are given .
For the given prices the producer will chose the quantity of labour and capital
that minimize the costs : wL  rK
Isocost
K 
w
L
r
Then, the slope of the isocost is  w/ r .
6
Cost minimization : tangency isoquant and isocost
For a given output of X (isoquant QX,A), and a given relative factor
price w/r, A is the cost-minimizing combination of factors K & L (with
cost CX,A= wLA+rKA).
K
QX,A
A
B
QY
-w/r
L
For a given and equal factor cost, in the graph, A represents the
optimum production level of good X, and B represent the optimum level
of production of good Y.
7
Expansion of production:
maintained proportions of factors for given w/r
How can we see the relative use of factors for each goods production?
In the expansion line: formed by the tangency points between the
isocost (for given w/r) and each isoquant.
KX/LX
KX
K
 Y
LX
LY
K
QX
KY/LY
Good X is more capital
intensive than good Y.
QY
L
8
Relative factor price changes (w/r )
What happens to the capital intensive good if wages go down?
As w goes down the isocost becomes less steep. On a new expansion line
we can see that the production process uses labour in a more intensive way
than before. however capital intensive good remains as such.
K
KX/LX
(KX/LX)'
Factor
space
w/r
w'/r
L
Note : The capital intensive good remains capital intensive relative to the other good which remains
labor intensive.
9
1.3. Production possibilities :
Combination of Goods
• Efficiency curve:
Using the isoquants in a factor endowment space (K,L)
- efficient allocations of factors in the production of both goods in one country.
- tangency points of the isoquants,
- equal marginal rate of substitution of K and L for both goods
M
K
OY
N
O
P
QX
QY
OX
L
For any point that is not a tangency point of the isoquants there is a way to
increase production of one good without reducing production of the other good.
10
•Production possibility frontier: is an curve in the goods space X,Y, that
shows all the possible combinations of goods X and Y which use an efficient
distribution of factors. It represents the maximal production of one good for
a given quantity of the other. And it is formed by the points on the efficiency
curve in the factor space K,L (Edgeworth box).
QY
J
K
Goods
Space
A
L
M
QX
The slope of the tangent curve in A represents the quantity of Y that must be
given up (“paid”) in order to obtain an additional unit of X.
11
Why does the production possibilities frontier have this shape?
Because it is more costly to do only one good. As soon as goods have
different intensity in the use of factors, there will be a factor that will
not be used in all it’s potential when we produce only one good.
QY
A
QX
If you free some capital and labor from Y’s production, the production of
X will increase substantially using intensively the large amounts of
capital freed by labor intensive Y. However the rate of increase in X will
decrease as you free more capital from Y (because labor-intensive Y
doesn’t have large quantities of K anymore to free up).
12
1.4 Which is the efficient production and consumption in autarky?
Consumption of goods:
It will depend on consumers preferences. The optimal production choice
in autarky is given by the tangency point between the indifference curve
of consumers and the production possibilities frontier for a given relative
price level.
QY
YC
C
Consumers indifference curve.
Goods
Space
-pX/pY
XC
QX
13
In autarky point C represents production and consumption quantities of
goods X and Y.
This point given by the tangency between production possibility
frontier and indifference curve respects the budget constraint given by:
B  p X X C  pY YC
where: p X is the price of good X.
pY is the price of good Y.
The slope of the budget constraint is given by the relative prices:

pX
pY
14
Consumption of factors
Where can we see the factor consumption?
Factor space K,L and isoquants X,Yof goods
K
Factor
Space
LY
KX
OY
KY
C
XC
YC
-w/r
OX
LX
L
The production and consumption decisions in the goods space
correspond to tangent isoquants in the factor space (Edgeworth box).
For the chosen isoquants, the use of factors for the production of each
good X and Y appears reading from each one’s origin, OX and OY.
At the tangent isoquants, the relative price (-w/r) of factors (rate of
substitution for autarky) appears.
15
1.5 What happens to consumption when both countries open to trade?
Countries are not longer bounded by their autarkic production possibilities but
by their budget. The budget constraint will be now given by the international
prices of goods that are being traded. It takes the form:
B  pWX QX  pYW QY
The slope of the new budget constraint is:
W
p
 X
pYW
The new consumption point is given by the tangency between the new budget
constraint and consumers indifference curve. While production takes place in
the tangency of the new budget constraint and the production possibilities
frontier.
Under trade production takes place in P’ and consumption in C’, this is
possible because the country imports the quantity X’P- X’C and exports
Y’P-Y’C.
16
Labor-intensive country (East) :
C
QY
Establishing
Gains from Trade
in the Goods
space
C'
Production
of Y
Consumption
P'
Y'P
YC
Y’s exports
P
Y'C
of Y
Indifference curve
X’s imports
New budget
constraint with
W
slope:  pX W
pY
-pX/pY
X'P
Production of X
XC
X'C
QX
Consumption of X
17
Where are the gains from trade?
According to the new relative prices, consumption will take place on a
different indifference curve, that belongs to the same family than the initial
one, but corresponds to a higher utility level of consumers.
The world relative price will be in between the relative prices existing in
autarky:
X
p1X
pW
p2X


Y
p1Y
pW
p2Y
1 is West, 2 is East : see graph
18
How do endowment differences between countries appear ?
-Shape of the production possibility frontier and relative prices
Production possibility frontiers in the East and in the West.
QY
Establishing
Comparative
Advantage in the
Goods Space
Identical preferences
pX/pY West < pX/pY East
PPF-East
pX/pY East
PPF-West
QX
-Size of the factor space (Edgeworth box) (see sub 6)
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Conclusion of graphs:




Heckscher & Ohlin Theorem:
“A country exports the good which uses intensively its abundant factor,
and it imports the good which uses intensively the other factor”
N.B. Specialisation in “trade” not in “production”
Proof: world prices “between” domestic prices, which were
determined by endowments : see previous 2 graphs.
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1.6. Integrated economy equilibrium and division of production
When studying the integrated economy it is necessary to consider the
world factor endowment as a starting point to determine where
production is going to take place and which consumption level of each
good is going to be chosen by each country.
To see the world factor endowment we can build an Edgeworth box
where both countries factor endowments are represented starting from O1
and O2 for the North and the South respectively.
At equilibrium point E, the endowments of the North are represented by
O1-L1 and O1-K1 for labour and capital respectively. For the South the
endowments are given by O2-L2 and O2-K2.
21
World factor endowment = Sum of countries’ endowments
L2
O2
EAST
K
K1
O1
E
K2
WEST
L1
L
West = “capital abundant” ; East = “labour abundant”.
How do endowment differences between countries appear ?
-Shape of the production possibility frontier (as seen above 1.5.)
-Size of the factor space (Edgeworth box)
22
The efficiency curves and expansion lines of both countries can also
be represented in the world endowment box:
L2
O2Y
A
B
O1Y
K1
O2X
C
K2
D
O1X
L1
A and B are the expansion lines of goods Y and X, respectively, in the East.
C and D are the expansion lines of goods Y and X, respectively, in the West.
From an integrated world consumption view, the countries
efficiency curves are inefficient in terms of consumption …
23
The worldwide economy: if the world was a single country and all people
had the same preferences, the consumption would not longer be constrained
by each countries endowment (E) but by global factor endowment and it
could reach Q’:
L2
OY
Q’
K1
OX
E
K2
L1
However, a point like Q’ can not be reached by separated endowments. The best
option is to choose a production division between two countries under which all
factors are fully used, i.e. at point E, but consumers are satisfied better (i.e.
obtain quantities Q’).
24
The quantity of factor used ensures the full employment of factors.
The division of production replicates the integrated economy:
-thanks to constant returns to scale
-thanks to an endowment point E within the integrated expansion paths
L2
K
O2
Q’
K1
E
K1X
Y1
K1Y
O1
K2
X1
L1X
L1Y
L1
L
25
1.7. Consumption by country at integrated equilibrium and trade
Assumptions:
• Identical and homothetic preferences.
• Goods prices are equal between countries as trade takes place.
Consumption will take place according to preferences and budget. Both countries
consume both goods in the same proportion (identical preferences), then
consumption will take place over the diagonal of the Edgeworth box.
The budget constraint is given by the factors income: wLi +rKi of each country i.
Under factor equalization prices the budget constraint has equal slope for both
countries.
Consumption takes place at the intersection of the budget constraint and the Edgeworth
box diagonal.
26
L2
K
O2
Q’
E
K1
K2
X1
K 1X
C1X
Import
C1Y
Y1
Y
1
K
O1
Gains from Trade in the
Factor Space :
Consumption outside of
Endowment
C
Export
wr
L1X
LY1
L1
Comparative advantage
in the Factor Space :
relative factor
L
endowment
The West produces O1-X1 and O1-Y1 of good X and Y respectively; while it
consumes O1-CX1 and O1-CY1 of the same goods. This implies that it is a net
importer of good Y and a net exporter of good X.
27
Consumption point C will be outside the endowment possibilities of each
country:
= gain from trade !
Preferences are satisfied better !
Comparative advantage Theorem (Hecksher-Ohlin):
(Export according to factor endowment)
“A country exports the good which uses intensively its abundant factor,
and it imports the good which uses intensively the other factor”
Proof : See graph.
Note:
Production level can be measured along the expansion lines. Then, production of good X in
the North is O1-X1and production of Y is O1-Y1. The use of factors can be read in the
projection along the axes:
O1-K1X and O1-L1X of capital and labour for the
production of good X in the West.
O1-K1Y and O1-L1Y of capital and labour for the production
of good Y in the West.
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1.8. Production and factor price equalization
If factor’s prices are equal in both countries, for given price of goods, the
intensity in the use of factors are equal in both countries, and equal to the
integrated economy use of factors. We can see this in the Edgeworth box:
K
O2
Factor price equalization across countries depend
upon their endowments. We consider 2 cases:
A – E is within the expansion paths at w/r
B – E is outside these expansion paths
O1
L
Through trade, countries produce more of what they do best, i.e. of
the goods which use their abundant factor more intensively. This raises
the price of this relatively cheap factor and brings it closer to the price of
this factor in the country where it is scarce. This trade effect can be
strong enough to equalize factor prices. If not, then one country will be
unable to produce one of the goods and pressures for factor mobility will
remain to try to equalize factor prices and replicate the integrated
economy.
29
A. Endowment point E is inside the diversification cone (expansion paths):
The division of production can be organized between the countries
at identical factor prices, so that both countries keep producing both goods
(cfr slide 25, box with division of production).
Reminder: graphical presentation of
expansion paths for goods (X,Y) at given factor prices (w/r)
and factor abundance of countries (1,2) for endowments E1 and E2:
K
GOODS
KX/LX
K1/L1
Countries
E1
K1
K2/L2
E2
K2
KY/LY
-w/r
L1
L2
L
30
Production of both goods (rather than full specialization):
The West is relatively abundant in capital. If it uses all the endowment
for the production of good X (capital intensive good) at given w/r, there
will be some labour that will be underemployed (see graph). The country
needs to keep producing both goods to ensure the full employment of
factors. As the same can be shown for the East at the same relative factors
prices (w/r, see previous graph), then there is factor price equalization:
East and West can work at the same prices and fully use all their factors.
K
K1 L1
K X LX
E1
K X  K1
K Y LY
O1
L X L1
L
Labour underemployment when country 1 produces X only at given w/r.
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B) Endowment point is outside the diversification cone
If the North is too rich in capital the real constraint will be given by
the amount of labour available. It is only going to produce good X,
which consumes all the endowment of labour, and leaves K1X-K1
underemployed.
L2
O2
K
K1
Unemployed
capital in
West
(North) at
FPE
K2
E
K1X
O1
L1
L
32
The North is over-endowed in capital as to produce under the price of the
integrated economy. The price of capital will have to decrease in order for
this economy to use all its endowment.
r goes
down
w/r increases
As a consequence the North will keep producing good X, which now
becomes more capital intensive than before, but still not as much as if
FPE could occur (w/r will stay higher in the capital rich country than in
an integrated economy and than in the other country).
33
E1
Capital over-endowment in the North
K X' L'X
K
K1
K X LX
Production of X at w/r’ instead of w/r<w/r’
E1
and at K’/L’ > K/L
K FPE
No production of Y, given at w’/r’ :
less output at w’/r’ than at w/r.
K Y' L'Y
Equal cost
(K,L) point :
wL+rK =
w’L+r’K
K Y LY
O1
L1
w r'
w r
L
34
The same situation can be reproduced for the South if it’s endowment
point is outside the diversification point.
If the South is over-endowed in labour, it can’t produce at the price of the
integrated economy. Then, the price of labour will have to decrease in
order for this economy to use all it’s endowment.
w goes
down
w/r decreases
As a consequence the South will keep producing good Y, which now
becomes more labour intensive than before.
35
Labour over-endowment in the South
K X LX
K
K Y LY
K2
w' r
wr
O2
K ' 'Y L' 'Y
E2
L2
L
36
The situations discussed in point B will lead to countries specializing in the
production of one good only. The North will specialize in the production of
capital intensive good, X; and the South will specialize in the production of
labour intensive good, Y.
When full specialization in production takes place there is no reason for
factor prices to equalize across nations.
Full specialization happens in 1 country, but need not to happen in both
when FPE is not reached (see next slide).
Factor Price equalization theorem: If both countries
produce both goods, factor price equalization will take place
when there is international trade on a perfect competitive market
and countries have access to the same production functions.
This requires factor endowments that are similar enough
Note : Unequal factor prices indicate an inefficiency (See chap. 3).
Specialization is then inefficient from a world consumption point of view.
37
Demonstration of FPE and specialization distribution
using isoquants and isocosts
K
Same total production of X,
Different factor intensities,
same total cost at w/r and w’/r
Not same production of Y
Equal cost
(K,L) point :
wL+rK =
w’L+r’K
Qx
at same total cost of X and
different w/r and w’/r [QED]
(Y can only be sold by low w/r
country)
Qy
-w’/r
Q’y
-w/r
To produce and trade both goods at same price (and cost) than other country, same factor prices
required in both countries. Otherwise only one good can be produced at same cost by both.
L
38
1.9. Factor prices and redistribution of income inside a country
What happens to production and to factor prices when goods price change ?
(due to trade opportunities or to change in worldwide preferences)
How does production react to the output price shock?
Try to increase the production of the good whose price goes up.
E.g. when opening up to trade, countries will increase the production of
goods that can be exported and reduce the production of those that will
be imported.
How are resources freed for this production?
By freeing capital and labor from the other sector.
Suppose, the price of the labor-intensive good goes up.
The capital intensive good will free factors, but it will tend to free more
capital than labor (because it has more) in such a way that the laborintensive good will use capital in a more intensive way.
39
What happens to the relative price of the factors?
The rising price of labor whose demand has increased (to produce more
of a labor-intensive good by assumption) will lead to factor mobility
and to economizing on this (now relatively scarce) factor in both
sectors.
Illustration: the giants and the dwarfs
Imagine people ranked by their height, and divided in two groups at
some cut-off point : the tall ones (the giants) and the lower ones (the
dwarfs).
Now assume the cut-off point is changed, so that the tallest of the dwarfs
moves to the group of the giants.
The effect is that the average height in both groups has fallen !
Similarly, the shifting “the most labor one can” from a “capitalintensive” sector to a labor intensive one, leads to a reduction in the
labor-intensity of both sectors!
40
Effect on the purchasing power of each factor ?
Use perfect competition P=Cost,
Assume PY + 10% , PX unchanged,
We know W up:
How much ? At least 10% allowed by PY + 10% ,
Must R go down?
Yes if W up and PX unchanged,
Then W up by more than all prices, R down compared to all prices.
Stolper-Samuelson theorem: (relative price theorem) : a relative increase
in a good’s price leads to an increase of the income and purchasing power of the
factor that is used intensively in it’s production and to a fall in the income of the
other factor.
This applies, whatever the source of the price change.
In North-South trade opening, the scarce factor loses in each country, the
abundant one gains (they are the opposite ones in each country).
41
Graphical illustration :
Goods factor intensity after reduction of capital intensive good price
K
K X
LX '
K X LX
KY
LY '
KY
w r 
'
w r 
LY 
L
42
Decrease of capital intensive good price in the endowment box.
OY
K
X
Y
X’
Y’
wr
w r '
OX
General Equilibrium view :
L
All change in price (factor and goods) and quantity (factor and goods) are
visible and explained in 1 graph !
43
1.10. Endowment changes (at given factor prices)
What happens if factor endowments change?
In the case of small open economies it is common that the availability of
capital increases. If the goods and factors relative prices remains equal,
an increase in the capital endowment leads to an increase in the
production of the capital intensive good and reduction of the labour
intensive good.
Factor quantity theorem (Rybczynski): for given factor prices,
an increase in the available quantities of one factor leads to an increase
in the production of good that use it on an intensive way. The
production of the other good is reduced.
Note : Capital is a factor that can be accumulated through savings !
44
OY
K
A
B
OX
OX'
L
Initial production levels: OX-A of good X and OY-A of good Y.
Final production levels: O’x-B of good X and OY-B of good Y.
45
5 key results of 2x2x2 model


Gains from trade
Comparative advantage in good that uses intensively
the locally abundant factor (general effect of indirectly exporting
the abundant factor through the goods exported) (Heckscher-Ohlin-Vanek)




Factor price equalization if both countries produce both
goods (Heckscher-Ohlin)
Price change in goods benefits to factor intensively
used in higher priced goods, and hurts other factor but
gains > losses (Stolper-Samuelson)
Increase in one factor increases production of good
using it intensively and decreases production of other
good (Rybczynski)
! Model is static, reality is dynamic : capital and technical
progress accumulation…
46