Lezione 2 bis
Differences in technology
1
The causes of international trade
• Now we start to consider the causes of international trade. We will
investigate the economic characteristics underlying the pattern of
comparative advantage.
• A convenient method to investigate the cause of international trade
is to imagine a world in which there is no trade. In terms of our
simple model this circumstance occurs when all autarky price ratios
are identical and there are no scale economies
2
The causes of international trade
• In particular, five conditions guarantee the no-trade situation:
1) identical production functions among coutries
2) the same relative endowments in all countries
3) constant returns to scale
4) identical and homogeneous tastes in all countries
5) the absence of distortions (taxes, subsidies, imperfect
competition)
• If any one of these five conditions is relaxed, then international trade
will occur. Therefore, in a reverse way, the five conditions underlying
the no-trade situation can be thought of as the principal
determinants of international trade.
• From a methodological point of view, it is useful to analyse each
determinant in isolation through specific models. Now we will focus
on differences in technology between countries (differences in
production functions)
3
A simple model of production function
differences
• We consider the Ricardian model, a one-factor model in which
differences in technology are expressed in terms of differences in
labour productivity across countries: the amount of output that can
be obtained from one unit of labour differs across countries.
• Constant return to scale are assumed. Given that this is a one-factor
model, this hypothesis implies a linear production possibility frontier.
• The other implication associated with the hyphotesis of a single
factor is that the second condition of the five illustrated previously is
not relaxed (the same relative endowments in all countries)
• We also impose the remaining conditions: no distortions and tastes
are identical
4
Absolute and comparative advantage
• In the model, labour is the only constraint on the production. If the
economy produces good X and good Y, we can write the production
functions and the labour constraint as:
X  Fx ( Lx )
Y  Fy ( Ly )
L  Lx  L y
• Under the hypothesis of constant returns to scale, we can express
production functions as:
X  L x
Y  L y
5
Absolute and comparative advantage
 are positive constants and represent the
• where  and
marginal products of labour in industries X and Y respectively
• The Ricardian approach based on the concept of comparative
advantage is illustrated in the following tables.
• In table 1, country H has an absolute advantage in the production of
Y:  h   f . Country F an absolute advantage in the production of
X:  h   f
• Table 2 shows the possibility of increasing world production of both
commodities through specialization
6
2. Changes in outputs due to
1. Marginal products of labor
Home
reallocation of one worker from X
to Y in Country H and one worker
from Y to X in Country F
Foreign
Home
Foreign
Total
X
 h  20
 f  30
X
–20
+30
+10
Y
 h  20
 f  10
Y
+20
–10
+10
3. Marginal products of labor
Home
4. Changes in outputs due to
reallocation of four workers from X
to Y in Country H and one worker
from Y to X in Country F
Foreign
Home
Foreign
Total
X
h  5
 f  30
X
–20
+30
+10
Y
h  5
 f  10
Y
+20
–10
+10
7
Absolute and comparative advantage
• Table 3 shows a different situation. Now Country F is more efficient
in the production of both goods. Is trade still possible in this new
situation?
• Yes, because H has a comparative advantage in the production of
good Y:  h /  h   f /  f (or, equivalently, we can say that H has a
relative lower opportunity cost of Y in terms of X)
• Table 4 illustrates the existence of gains from specialization and
trade also in the case in which a country (in this case, Country F)
has an absolute advantage in both productions
8
The production possibility frontier
• The following figure illustrates the production frontier for country H
and F based on the pattern of comparative advantage as reported in
the previous table 1
• we denote L h and L f
the labour endowments in the two
countries H and F, respectively. The production frontier for Country
H (HH’) has a maximum X output of  h L h and a maximum Y
output of  h L h . The production frontier for Country F (FF’) has a
maximum X output of  f L f and a maximum Y output of  f L f
• The slope of a country’s production frontier is:  Y / X   / 
9
Y
H
F
Ah
●
●
0
Af
H’
F’
X
Production frontier and autarky equilibrium
10
The production possibility frontier
• The country’s autharky price ratio is given by the slope of its
production frontier. But the slope reflects comparative advantage.
Therefore autarky prices reflect comparative advantage
• The following diagram shows what happens when countries open to
*
a
international trade. If p  ph for country H is indifferent to
producing at any point along the production frontier.
• At any price ratio p* that differs from the slope of the production
frontier, a country will specialize completely.
• If p *  pha H will specialize in X at point H’. The reason is that
p *x

*
*

MRT

MP
/
MP


p


p
LY
LX
x
y
*

py
11
Y
p1*  p ha
H
C2
● C
1
●
p2*  p ha
●
Ah
X
H’
Specialization at alternative world price ratios
12
The production possibility frontier
• Equilibrium with p *  pha is given by
p *x  w  p *y   X  X , Y=O
13
Excess demand and international
equilibrium
• Results previously illustrated are transferred to an excess demand
diagram.
• The “flat” section of Country H’s excess demand curve at its autarky
price ratio reflects the result discussed in the previous diagram: H
will consume at Ah but will be indifferent to producing at any point on
its production frontier
• At world price ratios greater than autarky price ratio H will wish to
export X. At world price ratios less than autarky price ratio H will
wish to import X
14
p
p = px / py
p ha
●
●
p1*
C1
p
p*
p
a
h
●
Eh
a
f
C2
p2*
-(Xc –Xp) H’
●
0
H
(Xc –Xp)
Country H‘s excess demand curve
Ef
-(Xc –
Xp)
Ef
0
Eh (X –X )
c
p
International equilibrium
15
Excess demand and international
equilibrium
• The right side diagram in the previous figure shows the excess
demand curve for both countries based on their production frontiers
• International equilibrium occurs at price ratio p* at which the import
demand of H matches the export supply of F.
• The equilibrium world price ratio falls between the autarky price
ratios of the two countries. In the case in which this circumstance
does not occur, both countries would wish to export the same good
• We know that when free trade price ratio is different from autarky
price ratio for both countries, they attain mutual gains from trade. In
the present model both countries must gain from trade although the
distribution of the gains from trade could be uneven (the country with
a larger distance between free trade price ratio and autarky price
ratio gains more)
16
The role of wages
• Until now, we have seen that in the Ricardian model comparative
advantage is determined simply by differences in technology across
countries. What is the role of wages in Ricardian model?
• International differences induce adjustment of wages in order to
reflect underlying real productivity differences. More productive
economies will have higher real wages in equilibrium. However all
workers gain real income in moving from autarky to free trade
• The discussion about the role of wages in the model can start from
the initial equilibrium in autarky. Because of perfect competition, we
have:
p ay  h  w h
p ax a h  w h
17
The role of wages
• From the previous profit maximization condition, it follows that the
relative price in autarky is independent of the wage rate:
pha   h /  h
• Given that the ratio between the marginal products in the two
industries is equivalent to the ratio between input coefficients in the
two industries, the previous expression reflects the Ricardian Labour
Theory of Value
• However, the wage rate is relevant for determining real wages of
workers:
w h / p ax   h
w h / p ay   h
• These “real wages” can be interpreted graphically as the end points
on the budget line of an individual worker who owns 1 unit of labour
18
Y
h
●
Slope p*
●
Uf
Ua
0
●
h
●
X
 h / p*
Budget line of an individual worker in Country H
19
The role of wages
• Now we consider the move from autarky to free trade. This
movement induces an adjustment of nominal wages in both
countries.
• To determine the impact on real wages, note that H Country exports
Y and F Country exports X. Therefore, in H country the real wage for
a home worker is constant in terms of good Y because the
competitive condition of production in industry Y requires that
w h / p*y   h
• Of course, the previous condition does not involve the good X
because this good is not produced at home. This means that the
real wage in terms of X changes because of the new price ratio
determined by trade.
20
The role of wages
• If H Country exports good Y, the international price ratio will be lower
than the autarky price ratio and now the home worker can buy X at a
lower price:
p*   h /  h
• Given that the price ratio p* is the vertical intercept (  h ) over the
horizontal intercept, this last one has to be  h / p * .
• So the new real wage in terms of good X (the new horizontal
intercept) increases in the presence of free trade:
w h / p *x   h / p *   h
21
The role of wages
• So trade does not change the domestic real wage in terms of the
good exported but alters the domestic real wage in terms of the
good imported. Note in the previous figure that with the new budget
line the utility of the domestic individual worker increases (same
argument applies to the worker of the foreign Country, whose
income is constant in terms of the good X but increases in terms of
the good Y).
• A final important point about the role of wages. It is probable that in
free trade real wages are higher in one country in comparison with
the other. Suppose that the home country has an absolute
advantage in both industries. In such situation, for the good X we
have  h   f
and therefore: w h / p*x   h   f  w f / p*x .
• (same dimonstration applies to good Y).
22
The distribution of gains from trade: big
versus small countries
• One of the most important determinant of the distribution of the
gains from trade among countries is the size of economies,
measured in terms of either their factor endowments or their
productivity levels
• Suppose to make Country F bigger by shifting its production frontier
farther out in a parallel way. This can be achieved either by
increasing factor endowment L f or by increasing  and 
• The following figure shows the expansion of production frontier from
'
'
• F0 F0 to F1 F1
23
Y
p0*
p0*
C1
F1
C0
F0
0
'
0
F
'
1
X
F
Growth in Country F
24
The distribution of gains from trade: big
versus small countries
• The expansion of the production frontier will lead Country F to wish
to trade more at any international price ratio.
• In the next figure, we can observe the effect of the growth of the
Country F in terms of the excess demand curve. The horizontal
segment (equivalent to the distance OF1' ) expands indicating that
the Country F now wishes to trade more at any price ratio.
• But the equilibrium price ratio also changes and p0* can no longer
be an equilibrium price ratio: there is an excess supply of X, so the
world price ratio must fall
25
Eh
Ef
E
●
'
f
●
p ha
● *●
p0
*
1
p
●
●
●
●
●
●●
Eh
p af
E 'f
Ef
-(Xc –
Xp)
0
(Xc –Xp)
Expansion in Country F’s excess demand
26
The distribution of gains from trade: big
versus small countries
• The change of international price ratio has important implications in
terms of the distribution of the gain from trade.
• Country F gains less by growth than in the case of equilibrium at the
*
initial world price ratio p0 . In particular, F’s terms of trade have
deteriorated, while H’s terms of trade have improved
• The positive impact of F’s growth
on H’s
welfare due to a decline of
*
*
international price ratio from p0 to p1
is shown in the following
figure.
27
Y
H
C
● 1
● C0
p1*
p0*
0
H’
X
Effect of growth in country F on country H
28
The distribution of gains from trade: big
versus small countries
• The following figure shows an extreme case of uneven distribution of
the gains from trade. Now Country F is so large in comparison with
Country H that the equilibrium is reached at the autarky price ratio of
Country F. In this case, all gains from trade are captured by Country
H and Country F is indifferent to trade.
• The discussion on the trade effects associated with the growth of
country size leads to observe that smaller economies are the more
probable gainer from free trade
• Another point to remark is that the productivity growth of a country
may be beneficial for the other (in the cases illustrated previously, H
benefits from productivity growth of F in terms of a lower price of its
import good)
29
p
Eh
Ef
p ha
●
●
●
● ●
p
a
f
Eh
-(Xc –
Xp)
Ef
0
Eh
Ef
(Xc –Xp)
Equilibrium world price equal to Country F’s autarky price
30
Concluding remarks: key points
• The slope of of a country’s production frontier reflects its relative
abilities to produce X and Y. When the slope of production frontier
differs between two countries a pattern of comparative advantage
emerges. Actually, differences in the slope of PPF imply differences
in the autarky price ratio and this creates the potential for gains from
trade also in the case a country has an absolute advantage in both
industries
• Even if potential for gains from trade exists, it is not sure that these
gains are captured in free trade. Another condition is required: the
equilibrium free trade price ratio must lie between the autarky price
ratios for the two countries. If this condition is satisfied, each country
specializes according to its comparative advantage and gains from
trade
31
Concluding remarks: key points
• Individual workers in each country gains from trade in terms of an
improvement of their living standards relative to autarky.
However, real wages can be different in the two countries and the
country with an absolute advantage necessarily has the higher real
wages. So absolute advantage (in terms of productivity) is an
important element of evaluation in international real wage
comparison but is not relevant in terms of the direction of trade
• The economic size is an important factor affecting the distribution of
gains from trade. The economic size can be measured as the
distance of PPF from the origin. When a country becomes bigger, its
terms of trade tend to deteriorate and the equilibrium world price
ratio tend to converge to the country’s autarky price ratio. This
implies a transfer of gains from trade to the other country (because
the distance between the word price ratio and the autarky price ratio
of this country becomes maximum)
32
Concluding remarks: key points
• Therefore small country are likely to be the major gainers from free
trade. That countries benefit from productivity growth in trading
partners through the decline in prices of import goods
33