Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gains from Trade and the Ricardian Models of
int’l Trade
Giuseppe De Arcangelis
2016 Fall Term
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Plan of the lecture
I
Review: introduction to int’l trade models and gains from
trade
I
The gravity model of international trade
I
Review: simple Ricardian model (2 × 2, many countries and 2
goods, 2 countries and many goods)
I
Many goods and 2 countries with a continuum of goods
(Dornbusch, Fischer, & Samuelson, 1977)
I
Many goods and many countries with a continuum of goods
and stochastic technologies (Eaton & Kortum, 2002)
Recall: the main reason why countries trade and gain from trade is
because they have different technologies. S
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Characteristics of models in int’l trade
Main reference: General Equilibrium in microeconomics
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Characteristics of models in int’l trade
Main reference: General Equilibrium in microeconomics
I Technologies: constant returns to scale (CRS) or increasing
RS (IRS); same or different among countries;
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Characteristics of models in int’l trade
Main reference: General Equilibrium in microeconomics
I Technologies: constant returns to scale (CRS) or increasing
RS (IRS); same or different among countries;
I Number of countries: small-country case vs 2-country world
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Characteristics of models in int’l trade
Main reference: General Equilibrium in microeconomics
I Technologies: constant returns to scale (CRS) or increasing
RS (IRS); same or different among countries;
I Number of countries: small-country case vs 2-country world
I Market structure: perfect vs. imperfect competition;
price-taker vs. price-maker firms;
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Characteristics of models in int’l trade
Main reference: General Equilibrium in microeconomics
I Technologies: constant returns to scale (CRS) or increasing
RS (IRS); same or different among countries;
I Number of countries: small-country case vs 2-country world
I Market structure: perfect vs. imperfect competition;
price-taker vs. price-maker firms; homogeneous vs.
heterogeneous firms;
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Characteristics of models in int’l trade
Main reference: General Equilibrium in microeconomics
I Technologies: constant returns to scale (CRS) or increasing
RS (IRS); same or different among countries;
I Number of countries: small-country case vs 2-country world
I Market structure: perfect vs. imperfect competition;
price-taker vs. price-maker firms; homogeneous vs.
heterogeneous firms; mono- vs. multiproduct firms
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Characteristics of models in int’l trade
Main reference: General Equilibrium in microeconomics
I Technologies: constant returns to scale (CRS) or increasing
RS (IRS); same or different among countries;
I Number of countries: small-country case vs 2-country world
I Market structure: perfect vs. imperfect competition;
price-taker vs. price-maker firms; homogeneous vs.
heterogeneous firms; mono- vs. multiproduct firms
I Preferences: collective indifference curves;
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Characteristics of models in int’l trade
Main reference: General Equilibrium in microeconomics
I Technologies: constant returns to scale (CRS) or increasing
RS (IRS); same or different among countries;
I Number of countries: small-country case vs 2-country world
I Market structure: perfect vs. imperfect competition;
price-taker vs. price-maker firms; homogeneous vs.
heterogeneous firms; mono- vs. multiproduct firms
I Preferences: collective indifference curves; conditions to avoid
problems with the distribution of income and heterogeneous
preferences:
I
I
homothetic preferences for all individuals (i.e. income
expansion curve is a straight line)
same preferences for all individuals
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Characteristics of models in int’l trade
Main reference: General Equilibrium in microeconomics
I Technologies: constant returns to scale (CRS) or increasing
RS (IRS); same or different among countries;
I Number of countries: small-country case vs 2-country world
I Market structure: perfect vs. imperfect competition;
price-taker vs. price-maker firms; homogeneous vs.
heterogeneous firms; mono- vs. multiproduct firms
I Preferences: collective indifference curves; conditions to avoid
problems with the distribution of income and heterogeneous
preferences:
I
I
homothetic preferences for all individuals (i.e. income
expansion curve is a straight line)
same preferences for all individuals
Then, when income and welfare increases, it is always possible
to find a distribution of income such that everybody is better
off.
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gains from
Trade:
partial
equilibrium
The
Gains
from
Tradegraph
At lower world price,
consumer surplus increases
to a+b+d Æ an increase of
b+d from no-trade
Price
S
At lower world price,
producer surplus falls to c
Æ a decrease of b from
no-trade
a
PA
b
Gain in trade is triangle d
with area equal to
½(M1)(PA-PW)
d
PW
c
D
S1
D1
Quantity
Imports, M1
(from Feenstra-Taylor, chp. 7)
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
;@ Gains
3?<: *?.12
; 99B@A?.A6<;
from Trade:
general equilibrium graph
good 2
X
C
X A = CA
p1/p2
good 1
AD<4<<1 2E.:=92
(from Pol Antràs64B?2
MIT lectures)
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity Equation: Definition 1
The strength of “economic attraction” between country i
(exporter) and country n (importer), as measured by the bilateral
trade, depends positively on some measure of economic mass of
each partner and negatively on the economic separation between
the two partners – see Head and Mayer (2013).
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity Equation: Definition 1
The strength of “economic attraction” between country i
(exporter) and country n (importer), as measured by the bilateral
trade, depends positively on some measure of economic mass of
each partner and negatively on the economic separation between
the two partners – see Head and Mayer (2013).
Definition 1:
Xi,n = λ · Si · Mn · φi,n
where
I
Si penetration capabilities of the exporter
I
Mn absorption capabilities of the importer
I
φi,n bilateral resistance between the two partners
I
λ is a constant
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity Equation: Definition 2
Xi,n =
Yi Xn
φi,n
Ωi Φn
|{z} |{z}
Si
Mn
where:
I
Yi =
P
n
Xi,n i.e. production in the exporter i
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity Equation: Definition 2
Xi,n =
Yi Xn
φi,n
Ωi Φn
|{z} |{z}
Si
Mn
where:
I
I
P
Yi = n Xi,n i.e. production in the exporter i
P
Xn = i Xi,n i.e. expenditure of the importer n
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity Equation: Definition 2
Xi,n =
Yi Xn
φi,n
Ωi Φn
|{z} |{z}
Si
Mn
where:
I
I
I
P
Yi = n Xi,n i.e. production in the exporter i
P
Xn = i Xi,n i.e. expenditure of the importer n
P φ Xk
P φ Yk
Ωi = k k,i
and Φn = k k,n
adjust the role of
Φk
Ωk
domestic production of the exporter and domestic absorption
of the importer with respect to third countries; they are called
“multilateral resistance” terms
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity Equation: Definition 2
Xi,n =
Yi Xn
φi,n
Ωi Φn
|{z} |{z}
Si
Mn
where:
I
I
I
P
Yi = n Xi,n i.e. production in the exporter i
P
Xn = i Xi,n i.e. expenditure of the importer n
P φ Xk
P φ Yk
Ωi = k k,i
and Φn = k k,n
adjust the role of
Φk
Ωk
domestic production of the exporter and domestic absorption
of the importer with respect to third countries; they are called
“multilateral resistance” terms
Note: Yi should be gross production (including intermediate
goods) and Xn absorption (production - export + import), but
they are approximated by GDP
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity Equation: Definition 3
Xi,n = λYia Ynb φi,n
where a and b are usually equal to 1 (but left unconstrained in a
regression).
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity Equation: Definition 3
Xi,n = λYia Ynb φi,n
where a and b are usually equal to 1 (but left unconstrained in a
regression). Although very intuitive and very used, this version
does not consider third-country effects
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity Equation: Definition 3
Xi,n = λYia Ynb φi,n
where a and b are usually equal to 1 (but left unconstrained in a
regression). Although very intuitive and very used, this version
does not consider third-country effects In log terms:
ln Xi,n = ln λ + a ln GDPi + b ln GDPn − γ ln disti,n
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity equation: GDP
variation
Figure 1: Trade is proportional to size
(a) Japan’s exports to EU, 2006
(b) Japan’s imports from EU, 2006
DEU
GBR
NLD
ESP
FRA
ITA
SWE
HUN
CZE
GRC
IRLAUT
FIN
POL
SVK
PRT
DNK
slope = 1.001
fit = .85
CYP
EST
SVN
MLT
FRA
ITA
GBR
IRL
NLD
DNKSWE
ESP
BEL
FIN AUT
HUN
CZE
POL
SVK
MLT
PRT
slope = 1.03
fit = .75
GRC
EST
LVA
SVN
LTU
.5
.05
Japan's 2006 exports (GRC = 1)
.1
.5
1
5
BEL
Japan's 2006 imports (GRC = 1)
1
5 10
50 100
10
DEU
CYP
LVA
.05
.1
.5
1
GDP (GRC = 1)
5
10
.05
LTU
.1
.5
1
GDP (GRC = 1)
5
10
(from Head and Mayer (2013))
preferred for certain types of data or research questions but more often the methods should be used
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity equation:
the effect of distance
Figure 2: Trade is inversely proportional to distance
(b) France’s imports (2006)
Imports/Partner's GDP (%, log scale)
.05 .1
5 10
.5 1
slope = -.683
fit = .22
other
500
slope = -.894
fit = .2
EU25
Euro
Colony
Francophone
.005
EU25
Euro
Colony
Francophone
.05
Exports/Partner's GDP (%, log scale)
.1
1
.5
5
10
25
(a) France’s exports (2006)
1000
2000
5000
Distance in kms
10000
20000
other
500
1000
2000
5000
Distance in kms
10000
20000
.005
(from Head and Mayer (2013))
trade flow on log GDP. For Japan’s exports, the GDP elasticity is 1.00 and it is 1.03 for Japan’s
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity Equation: What for?
I
Very good fit! A “fact of life” (Deardorff, 1998).
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity Equation: What for?
I
Very good fit! A “fact of life” (Deardorff, 1998). But what
theory?
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity Equation: What for?
I
Very good fit! A “fact of life” (Deardorff, 1998). But what
theory?
I
Empirical challenges: Many zeros
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity Equation: What for?
I
Very good fit! A “fact of life” (Deardorff, 1998). But what
theory?
I
Empirical challenges: Many zeros
Some striking results:
I
I
I
I
distance does not matter when considering provinces of the
same country (McCallum, 1995)
nonlinear effect (dummy for the border effect)
Main recent applications: a reference for potential trade
among partners
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Gravity Equation: literature
Relevant references:
I
Original paper by Tinbergen (1962)
I
“Gravity for Beginners”
I
Attempts of theoretical foundations: J. E. Anderson (1979),
Deardorff (1998), Eaton and Kortum (2002)
I
Importance of trade costs: J. Anderson and van Wincoop
(2003)
I
Useful reviews: J. E. Anderson and van Wincoop (2004), De
Benedictis and Taglioni (2011), J. E. Anderson (2011), Head
and Mayer (2013)
I
Extensions to trade in financial assets Portes and Rey (2005),
FDI and migration
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: Assumptions
I
Perfect competition
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: Assumptions
I
Perfect competition
I
Free trade
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: Assumptions
I
Perfect competition
I
Free trade
I
One factor of production, labor (L), perfectly mobile among
sectors of the economy, but internationally immobile
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: Assumptions
I
Perfect competition
I
Free trade
I
One factor of production, labor (L), perfectly mobile among
sectors of the economy, but internationally immobile
I
Technologies with fixed coefficients: aik = labor requirement
for good i in country k
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: Assumptions
I
Perfect competition
I
Free trade
I
One factor of production, labor (L), perfectly mobile among
sectors of the economy, but internationally immobile
I
Technologies with fixed coefficients: aik = labor requirement
for good i in country k
I
Let us start with two goods X and Y
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: Assumptions
I
Perfect competition
I
Free trade
I
One factor of production, labor (L), perfectly mobile among
sectors of the economy, but internationally immobile
I
Technologies with fixed coefficients: aik = labor requirement
for good i in country k
I
Let us start with two goods X and Y
I
and two countries, A and B, with labor endowments, LA and
LB .
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade (2 × 2): PPF
Production possibility frontier (PPF):
axk X k + ayk Y k = Lk
This is a straight line with slope
Giuseppe De Arcangelis
axk
ayk
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade (2 × 2): PPF
Production possibility frontier (PPF):
axk X k + ayk Y k = Lk
k
This is a straight line with slope aaxk
y
By dividing by the labor endowment, we obtain the PPF per unit
of labor:
axk x k + ayk y k = 1
where x k ≡
Xk
Lk
and y k ≡
Yk
.
Lk
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade (2 × 2): PPF
Production possibility frontier (PPF):
axk X k + ayk Y k = Lk
k
This is a straight line with slope aaxk
y
By dividing by the labor endowment, we obtain the PPF per unit
of labor:
axk x k + ayk y k = 1
k
k
where x k ≡ XLk and y k ≡ YLk .
This shows graphically comparative and absolute advantages.
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade (2 × 2): Autarky
Autarky in country A:
A A
A
pf
x = ax w
Giuseppe De Arcangelis
A A
A
pf
y = ay w
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade (2 × 2): Autarky
Autarky in country A:
A A
A
pf
x = ax w
A A
A
pf
y = ay w
Since labor is perfectly mobile, the wage w A is equal in both
sectors of country A; hence the relative autarky price is:
A =
pf
^
pxA
axA
=
pyA
ayA
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade (2 × 2): Autarky
Autarky in country A:
A A
A
pf
x = ax w
A A
A
pf
y = ay w
Since labor is perfectly mobile, the wage w A is equal in both
sectors of country A; hence the relative autarky price is:
A =
pf
^
pxA
axA
=
pyA
ayA
Hence, in equilibrium the relative price is equal to the slope of the
linear PPF.
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade (2 × 2): Int’l Equilibrium
f
f
f
A <p
B and ∃p ∗ : p
A < p∗ < p
B ; hence:
Let us assume pf
axA
axB
∗
<
p
<
ayA
ayB
It follows that A (B) has a comparative advantage in good X (Y ),
hence A (B) exports goods X (Y ).
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade (2 × 2): Wages and
Specialization
A A
A
Let us recall for good X , in country A: pf
x = ax w , and in country
B B
B
B: pf
x = ax w .
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade (2 × 2): Wages and
Specialization
A A
A
Let us recall for good X , in country A: pf
x = ax w , and in country
B B
B
B: pf
x = ax w . So country A exports good X as long as
f
A
B
pf
x < px ; hence:
axA
wB
<
axB
wA
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade (2 × 2): Wages and
Specialization
A A
A
Let us recall for good X , in country A: pf
x = ax w , and in country
B B
B
B: pf
x = ax w . So country A exports good X as long as
f
A
B
pf
x < px ; hence:
axA
wB
<
axB
wA
f
B
A
Similarly for good Y if country B is the exporter: pf
y < py , or
ayA
wB
> A
B
ay
w
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade (2 × 2): Wages and
Specialization
A A
A
Let us recall for good X , in country A: pf
x = ax w , and in country
B B
B
B: pf
x = ax w . So country A exports good X as long as
f
A
B
pf
x < px ; hence:
axA
wB
<
axB
wA
f
B
A
Similarly for good Y if country B is the exporter: pf
y < py , or
ayA
wB
> A
B
ay
w
Interpretation: the wage of country A can be double of country’s
B wage, but A still exports those goods for which the productivity
is more than double.
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade (2 × 2): Equilibrium
Condition on Wages
Alternative condition for international exchange:
ayA
axA
wB
<
<
axB
wA
ayB
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Example: Equilibrium Condition on Wages in a Ricardian
World
Labor requirements in the table:
Cloth
Wine
ToT
I
UK
4
8
1/2
P
6
9
2/3
UK exports Cloth as long as: 4WUK < 6WP or
Giuseppe De Arcangelis
GT & Ricardian Models
WUK
WP
<
6
4
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Example: Equilibrium Condition on Wages in a Ricardian
World
Labor requirements in the table:
Cloth
Wine
ToT
UK
4
8
1/2
P
6
9
2/3
I
UK exports Cloth as long as: 4WUK < 6WP or
I
P exports Wine as long as: 8WUK > 9WP or
Giuseppe De Arcangelis
GT & Ricardian Models
WUK
WP
WUK
WP
>
<
9
8
6
4
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Example: Equilibrium Condition on Wages in a Ricardian
World
Labor requirements in the table:
Cloth
Wine
ToT
UK
4
8
1/2
P
6
9
2/3
I
UK exports Cloth as long as: 4WUK < 6WP or
I
P exports Wine as long as: 8WUK > 9WP or
I
Hence, for this trade pattern:
Giuseppe De Arcangelis
6
4
>
WUK
WP
>
9
8
GT & Ricardian Models
WUK
WP
WUK
WP
>
<
9
8
6
4
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
World PPF
I
Max producible quantity of Y in the world:
Giuseppe De Arcangelis
GT & Ricardian Models
LA
ayA
+
LB
;
ayB
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
World PPF
LA
ayA
Max producible quantity of Y in the world:
I
When decreasing the quantity produced of Y by 1 unit, ayk
units of labor are free and when employed in the other sector
it will produce
ayk
;
axk
Giuseppe De Arcangelis
GT & Ricardian Models
+
LB
;
ayB
I
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
World PPF
LA
ayA
Max producible quantity of Y in the world:
I
When decreasing the quantity produced of Y by 1 unit, ayk
units of labor are free and when employed in the other sector
it will produce
I
Since
ayA
axA
>
ayB
,
axB
+
LB
;
ayB
I
ayk
;
axk
we start producing X in country A;
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
World PPF
LA
ayA
Max producible quantity of Y in the world:
I
When decreasing the quantity produced of Y by 1 unit, ayk
units of labor are free and when employed in the other sector
it will produce
ayA
axA
>
ayB
,
axB
+
LB
;
ayB
I
ayk
;
axk
we start producing X in country A;
I
Since
I
We switch to the technology of country B only when all
workers in A are employed in sector X ;
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
World PPF
LA
ayA
Max producible quantity of Y in the world:
I
When decreasing the quantity produced of Y by 1 unit, ayk
units of labor are free and when employed in the other sector
it will produce
ayA
axA
>
ayB
,
axB
+
LB
;
ayB
I
ayk
;
axk
we start producing X in country A;
I
Since
I
We switch to the technology of country B only when all
workers in A are employed in sector X ;
I
The world PPF has a kink when switching the technology.
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: main results
I
Under strictly convex preferences, we can prove gains from
trade for both countries.
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: main results
I
I
Under strictly convex preferences, we can prove gains from
trade for both countries.
Obtain the int’l terms of trade with the excess-demand curves
for both countries.
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: main results
I
I
I
Under strictly convex preferences, we can prove gains from
trade for both countries.
Obtain the int’l terms of trade with the excess-demand curves
for both countries.
Linear technologies imply full specialization: in each country
only the export sector exists and no import sector, so no
distributional issues arise (unless the int’l ToT equals one
domestic ToT)
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: main results
I
I
I
I
Under strictly convex preferences, we can prove gains from
trade for both countries.
Obtain the int’l terms of trade with the excess-demand curves
for both countries.
Linear technologies imply full specialization: in each country
only the export sector exists and no import sector, so no
distributional issues arise (unless the int’l ToT equals one
domestic ToT)
Absolute advantages for country k iff:
0
aik < aik ∀i and k 0 6= k.
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: main results
I
I
I
I
Under strictly convex preferences, we can prove gains from
trade for both countries.
Obtain the int’l terms of trade with the excess-demand curves
for both countries.
Linear technologies imply full specialization: in each country
only the export sector exists and no import sector, so no
distributional issues arise (unless the int’l ToT equals one
domestic ToT)
Absolute advantages for country k iff:
0
aik < aik ∀i and k 0 6= k. The model cannot assure factor
price equalization (since # goods/markets 6= # factors) and
country k has always the higher real wages, before and after
opening up to int’l trade.
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: main results
I
I
I
I
I
Under strictly convex preferences, we can prove gains from
trade for both countries.
Obtain the int’l terms of trade with the excess-demand curves
for both countries.
Linear technologies imply full specialization: in each country
only the export sector exists and no import sector, so no
distributional issues arise (unless the int’l ToT equals one
domestic ToT)
Absolute advantages for country k iff:
0
aik < aik ∀i and k 0 6= k. The model cannot assure factor
price equalization (since # goods/markets 6= # factors) and
country k has always the higher real wages, before and after
opening up to int’l trade.
Dimension of the country, income effect and substitution
effect.
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: 2 goods and many countries
To obtain the production and the trade patterns, use the
maximization principle for the world GDP (expressed in terms of
Y ):
max GDP = Y + p ∗ X
s.t. world PPF
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: 2 goods and many countries
World transformation curve as the simplex of the various
transformation curves.
Order the autarky relative prices:
pe1 < pe2 < · · · < pf
N
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: 2 goods and many countries
World transformation curve as the simplex of the various
transformation curves.
Order the autarky relative prices:
pe1 < pe2 < · · · < pf
N
Assume p ∗ the int’l terms of trade:
∗
0
pe1 < pe2 < · · · < pf
^
< · · · < pf
N
N0 < p < p
|
{z
}
| N +1 {z
}
Export X
Export Y
countries 1, . . . , N 0 (N 0 + 1, . . . , N) export X (Y ) and import Y
(X ).
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: many goods and 2 countries
Let us measure wages in country Home (H) and Foreign (F ) in the
same currency and respectively as: w and w ∗ .
Then H exports good j iff : pej < pej∗ . Or, given perfect competition:
aj w < aj∗ w ∗
Giuseppe De Arcangelis
⇒
aj∗
w
<
w∗
aj
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: many goods and 2 countries
Let us measure wages in country Home (H) and Foreign (F ) in the
same currency and respectively as: w and w ∗ .
Then H exports good j iff : pej < pej∗ . Or, given perfect competition:
aj w < aj∗ w ∗
⇒
aj∗
w
<
w∗
aj
f∗
Similarly, F exports good j 0 iff : pf
j 0 > pj 0 . Or:
a w>
j0
aj∗0 w ∗
Giuseppe De Arcangelis
⇒
aj∗0
w
>
w∗
aj 0
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: many goods and 2 countries
We can order the M goods according to their comparative costs.
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: many goods and 2 countries
We can order the M goods according to their comparative costs.
Then we can easily determine the pattern of trade:
aj∗0
aj∗
a∗
a1∗
w
< ··· < M
< ··· <
< ∗ <
a1
aj 0
w
aj
aM
{z
}
|
|
{z
}
Exports of H
Exports of F
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: many goods and 2 countries
We can order the M goods according to their comparative costs.
Then we can easily determine the pattern of trade:
aj∗0
aj∗
a∗
a1∗
w
< ··· < M
< ··· <
< ∗ <
a1
aj 0
w
aj
aM
{z
}
|
|
{z
}
Exports of H
Exports of F
How to determine
w
w∗ ?
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
Ricardian model of Int’l trade: many goods and 2 countries
We can order the M goods according to their comparative costs.
Then we can easily determine the pattern of trade:
aj∗0
aj∗
a∗
a1∗
w
< ··· < M
< ··· <
< ∗ <
a1
aj 0
w
aj
aM
{z
}
|
|
{z
}
Exports of H
Exports of F
How to determine ww∗ ? We need to model preferences (just like we
need to specify the demand side to determine the terms of trade).
We use Dornbusch et al. (1977).
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
References I
Anderson, J., & van Wincoop, E. (2003). Gravity with gravitas: A
solution to the border puzzle. American Economic Review,
93(1), 170-192.
Anderson, J. E. (1979, March). A theoretical foundation for the
gravity equation. American Economic Review, 69(1), 106-16.
Anderson, J. E. (2011). The Gravity Model. Annual Review of
Economics, 3(1), 133-160.
Anderson, J. E., & van Wincoop, E. (2004, September). Trade
costs. Journal of Economic Literature, 42(3), 691-751.
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
References II
De Benedictis, L., & Taglioni, D. (2011). The Gravity Model of
International Trade. In L. De Benedictis & L. Salvatici
(Eds.), The Trade Impact of European Union Preferential
policies: An Analysisthrough Gravity Models (chap. 4).
Springer. (forthcoming)
Deardorff, A. (1998, October). Determinants of bilateral trade:
Does gravity work in a neoclassical world? In The
regionalization of the world economy (p. 7-32). National
Bureau of Economic Research, Inc.
Dornbusch, R., Fischer, S., & Samuelson, P. A. (1977, December).
Comparative advantage, trade, and payments in a ricardian
model with a continuum of goods. American Economic
Review, 67(5), 823-39.
Giuseppe De Arcangelis
GT & Ricardian Models
Introduction
The gravity model of international trade
The basics of the Ricardian model
References
References III
Eaton, J., & Kortum, S. (2002, September). Technology,
geography, and trade. Econometrica, 70(5), 1741-1779.
Head, K., & Mayer, T. (2013, January). Gravity equations:
Workhorse, toolkit, and cookbook (CEPR Discussion Papers
No. 9322). C.E.P.R. Discussion Papers.
McCallum, J. (1995, June). National borders matter: Canada-u.s.
regional trade patterns. American Economic Review, 85(3),
615-23.
Portes, R., & Rey, H. (2005, March). The determinants of
cross-border equity flows. Journal of International
Economics, 65(2), 269-296.
Tinbergen, J. (1962). Shaping the world economy: Suggestions for
an international economic policy. New York: The Twentieth
Century Fund.
Giuseppe De Arcangelis
GT & Ricardian Models