14.

581 MIT International Trade

Lecture 1: Gains from Trade and
the Law of Comparative Advantage (Theory)
Dave Donaldson

Spring 2011

Todays Plan

Course logistics

A Brief History of the Field

Neoclassical Trade: Standard Assumptions

Neoclassical Trade: General Results

1

Gains from Trade

Law of Comparative Advantage

Todays Plan

Course logistics

A Brief History of the Field

Neoclassical Trade: Standard Assumptions

Neoclassical Trade: General Results

1

Gains from Trade

Law of Comparative Advantage

Course Logistics

Lecture: Monday, Wednesday 2:30PM-4:00PM, E52-398

Instructor: Dave Donaldson
O ce: E52-243g
Email: ddonald@mit.edu
O ce hours: by appointment

TA: Sahar Parsa

O ce: E51-090
Email: sparsa@mit.edu
O ce hours: by appointment

Course Logistics

Recitations: TBA
No required textbooks, but we will frequently use:
Avinash Dixit and Victor Norman, (DN)
Robert Feenstra, Advanced International Trade: Theory and Evidence
(F)
Elhanan Helpman and Paul Krugman, Market Structure and Foreign
Trade (HKa)

Relevant chapters of all textbooks will be available on Stellar

Course Logistics

Course requirements:
Four problem sets: 50% of the course grade
One referee report: 15% of the course grade
One research proposal: 35% of the course grade

Course Logistics
Course outline:
1

Neoclassical Trade (4 weeks)

1
2

New trade (4 weeks)

1
2
3

General Model
Special Cases: Ricardo, Ricardo-Viner, Heckscher-Ohlin

Increasing Returns and Monopolistic Competition

Monopolistic Competition with Firm Heterogeneity
Gravity models and gravity equations.

Topics:
1
2
3

Trade and Growth (1 week)

Trade and Labor Markets (1 week)
International Organization of Production (outsourcing, fragmentation
of production, multinational rms) (2 weeks)
Trade Policy (political economy, WTO) (1 week)

Under every topic we will have one lecture on the theory and then one
on the empirics; the goal is to learn as much as possible about each,
and about their interaction.

Todays Plan

Course logistics

A Brief History of the Field

Neoclassical Trade: Standard Assumptions

Neoclassical Trade: General Results

1

Gains from Trade

Law of Comparative Advantage

A Brief History of the Field

Two hundred years of theory

1830-1980: Neoclassical trade theory

) Ricardo
) Heckscher-Ohlin-Samuelson
) Dixit-Norman
1980-1990: New trade theory
) Krugman-Helpman
) Brander-Krugman
) Grossman-Helpman

A Brief History of the Field

The discovery of trade data; tighter integration of theory and empirics

1990-2000: Empirical trade

) Leamer, Treer, Davis-Weinstein
) Bernard, Tybout

2000-2010: Firm-level heterogeneity

) Melitz
) Eaton-Kortum
Where are we now?

Todays Plan

Course logistics

A Brief History of the Field

Neoclassical Trade: Standard Assumptions

Neoclassical Trade: General Results

1

Gains from Trade

Law of Comparative Advantage

International Trade: Standard Assumptions

What distinguishes trade theory from abstract general-equilibrium
analysis is the existence of a hierarchical market structure:
1
2

International good markets

Domestic factor markets

Typical asymmetry between goods and factors:

Goods enter consumersutility functions directly, are elastically
supplied and demanded, and can be freely traded internationally.
Factors only aect utility through the income they generate, they are in
xed supply domestically, and they cannot be traded at all.

Central Issues:
How does the integration of good markets aect good prices?
How do changes in good prices, in turn, aect factor prices, factor
allocation, production, and welfare?

International Trade: Standard Assumptions (Cont.)

While these assumptions are less fundamental, we will also often
assume that:
Consumers have identical homothetic preferences in each country
(representative agent).
Model is static (long-run view).

Many of these assumptions look very strong, but they can be dealt
with by clever reinterpretations of the model:
Transport costs could be handled by interpreting one of the good as
transportation services.
Factor mobility could be dealt with by dening as a good anything that
can be traded.
Goods and factors can be distinguished by locations, time, and states
of nature.

Neoclassical Trade: Standard Assumptions

Neoclassic trade models characterized by three key assumptions:

1
2
3

Perfect competition
Constant returns to scale (CRS)
No distortions

Comments:
We could allow for decreasing returns to scale (DRS) by introducing
hidden factors in xed supply.
Increasing returns to scale (IRS) are a much more severe issue, which
was (partially) addressed by New trade theory.

Todays Plan

Course logistics

A Brief History of the Field

Neoclassical Trade: Standard Assumptions

Neoclassical Trade: General Results

1

Gains from Trade

Law of Comparative Advantage

Neoclassical Trade: General Results

Not surprisingly, there are few results that can be derived using only
Assumptions 1-3.
In the next three classes, we will derive sharp predictions for special
cases of the neoclassical trade: Ricardo, Ricardo-Viner, and
Heckscher-Ohlin.
Today, well stick to the general case and show how simple revealed
preference arguments can be used to establish two important results:
1

Gains from trade (Samuelson 1939)

Law of comparative advantage (Deardor 1980)

Basic Environment

Consider a world economy with n = 1, ..., N countries, each populated

by h = 1, ..., Hn households.
There are g = 1, ..., G goods:
yn
c nh
pn

(y1n , ..., yGn ) Output vector in country n

(c1nh , ..., cGnh ) Consumption vector of household h in country n
(p1n , ..., pGn ) Good price vector in country n

There are f = 1, ..., F factors:

vn
wn

(v1n , ..., vFn ) Endowment vector in country n

(w1n , ..., wFn ) Factor price vector in country n

Supply
The revenue function

We denote by n the set of combinations (y , v ) feasible in country n.

CRS ) n is a convex cone

Revenue function in country n is dened as

r n (p, v )

max fpy j(y , v ) 2 n g

y

Comments (see Dixit-Norman pp. 31-36 for details):

Revenue function summarizes all relevant properties of technology.
Under perfect competition, y n maximizes the value of output in
country n:
r n (p n , v n ) = p n y n

(1)

Demand
The expenditure function

We denote by u nh the utility function of household h in country n.

Expenditure function for household h in country n is dened as
n
o
e nh (p, u ) = min pc ju nh (c ) u
c

Comments (see Dixit-Norman pp. 59-64 for details):

Here factor endowments are in xed supply, but easy to generalize to

case where households choose factor supply optimally.
Holding p xed, e nh (p, u ) is increasing in u.
Households optimization implies
e nh (p n , u nh ) = p n c nh ,
where c nh and u nh are the consumption and utility level of the
household in equilibrium, respectively.

(2)

Gains from Trade

One household per country

In the next propositions, when we say in a neoclassical trade model,

we mean in a model where equations (1) and (2) hold in any
equilibrium.
Consider rst the case where there is just one household per country.
Without risk of confusion, we drop h and n from all variables.
Instead we denote by:
(y a , c a , p a ) the vector of output, consumption, and good prices under
autarky.
(y , c, p ) the vector of output, consumption, and good prices under free
trade.
u a and u the utility levels under autarky and free trade.

Gains from Trade

One household per country

Proposition 1 In a neoclassical trade model with one household per

country, free trade makes all households (weakly) better o.
Proof:
e (p, u a )

pc a ,
= py a
r (p, v )
= e (p, u )

by
by
by
by

denition of e
market clearing under autarky
denition of r
equations (1), (2), and trade balance

Since e (p, ) increasing, we get u

ua

Gains from Trade

One household per country

Comments:
Two inequalities in the previous proof correspond to consumption and
production gains from trade.
Previous inequalities are weak. Equality if kinks in IC or PPF.
Previous proposition only establishes that households always prefer
free trade to autarky. It does not say anything about the
comparisons of trade equilibria.

Gains from Trade

Multiple households per country (I): domestic lump-sum transfers

With multiple-households, moving away from autarky is likely to

create winners and losers.
How does that relate to the previous comment?

In order to establish the Pareto-superiority of trade, we will therefore

need to allow for policy instruments. We start with domestic
lump-sum transfers and then consider more general policies.
We now reintroduce the index h explicitly and denote by:
c ah and c h the vector of consumption of household h under autarky
and free trade.
v ah and v h the vector of endowments of household h under autarky
and free trade.
u ah and u h the utility levels of household h under autarky and free
trade.
h the lump-sum transfer from the government to household h ( h 0
, lump-sum tax and h 0 , lump-sum subsidy).

Gains from Trade

Multiple households per country (I): domestic lump-sum transfers

Proposition 2 In a neoclassical trade model with multiple households

per country, there exist domestic lump-sum transfers such that free
trade is (weakly) Pareto superior to autarky in all countries.
Proof: We proceed in two steps.
Step 1: For any h, set the lump-sum transfer h such that
h = (p

p a ) c ah

(w

w a )v h .

Budget constraint under autarky implies p a c ah

pc ah

w a v h . Therefore

wv h + h .

Thus c ah is still in the budget set of household h under free trade.

Gains from Trade

Multiple households per country (I): domestic lump-sum transfers

Proposition 2 In a neoclassical trade model with multiple households

per country, there exist domestic lump-sum transfers such that free
trade is (weakly) Pareto superior to autarky in all countries.
Proof (Cont.):
Step 2: By denition, governments revenue is given by
h = (p a p ) c ah (w a w ) v h
= (p a p ) y a (w a w )v
= py a + wv
r (p, v ) + wv
= (py wv ) = 0

: denition of h
: mc autarky
: zp autarky
: denition r (p, v )
: eq. (1) + zp free trade

Gains from Trade

Multiple households per country (I): domestic lump-sum transfers

Comments:
Good to know we dont need international lump-sum transfers.
Domestic lump-sum transfers remain informationally intensive (where
to nd data on c ah ?)

Gains from Trade

Multiple households per country (II): commodity and factor taxation

With this last comment in mind, we now restrict the set of

instruments to commodity and factor taxes/subsidies.
More specically, suppose that the government can aect the prices
faced by all households under free trade by setting good and factor
according to:
p household = p + good
w household = w + factor

Gains from Trade

Multiple households per country (II): commodity and factor taxation

Proposition 3 In a neoclassical trade model with multiple households

per country, there exist commodity and factor taxes/subsidies such
that free trade is (weakly) Pareto superior to autarky in all countries.
Proof: Consider the two following taxes:
good = p a

factor

= w

p
w

By construction, household is indierent between autarky and free

trade. Now consider governments revenues. By denition
h

= good c ah factor v h
= (p a p ) c ah (w a w ) v h

for the same reason as in the previous proof.

0,

Gains from Trade

Multiple households per country (II): commodity and factor taxation

Comments:
Previous argument only relies on the existence of production gains from
trade.
If there is a kink in the PPF, we know that there arent any...
Similar problem with moving costs (see Feenstra p.185).
Factor taxation still informationally intensive: need to know
endowments per e ciency units, may lead to dierent business taxes.

Todays Plan

Course logistics

A Brief History of the Field

Neoclassical Trade: Standard Assumptions

Neoclassical Trade: General Results

1

Gains from Trade

Law of Comparative Advantage

Law of Comparative Advantage

Basic Idea

The previous results have focused on normative predictions.

We now demonstrate how the same revealed preference argument can
also be used to make positive predictions about the pattern of trade.
Principle of comparative advantage:
Comparative advantage meaning dierences in relative autarky
prices is the basis for trade.
Why? If two countries have the same autarky prices, then after
opening up to trade, the autarky prices remain equilibrium prices. So
there will be no trade....
The law of comparative advantage (in words):
Countries tend to export goods in which they have a CA, i.e. lower
relative autarky prices compared to other countries.

Law of Comparative Advantage

Dixit-Norman-Deardor (1980)

Let t n
y1n c nh , ..., yGn c nh denote net exports in country
n.
Let u an and u n denote the utility level of the representative household
in country n under autarky and free trade.
Let p an denote the vector of autarky prices in country n.
Without loss of generality, normalize prices such that:
pg = pgan = 1,
Notations:
cov (x, y )
var (x ) var (y )
n
cov (x, y ) = i =1 (xi x ) (yi
1 n
x =
xi
n i =1
cor (x, y ) =

y)

Law of Comparative Advantage

Dixit-Norman-Deardor (1980)

Proposition 4 In a neoclassical trade model, if there is a

representative household in country n, then cor (p p a , t n )

0.

Proof: Since (y n , v n ) 2 n , the denition of r implies

pa y n

r (p a , v n ) .

Since u n (c n ) = u n , the denition of e implies

pa c n

e (p a , u n ) .

The two previous inequalities imply

pa t n
Since u n

r (p a , v n )

e (p a , u n ) .

(3)

u an by Proposition 1, e (p a , ) increasing implies

e (p a , u n )

e (p a , u na )

(4)

Law of Comparative Advantage

Dixit-Norman-Deardor (1980)

Proposition 4 In a neoclassical trade model, if there is a

representative household in country n, then cor (p p a , t n )

0.

Proof (Cont.): Combining inequalities (3) and (4), we obtain

pa t n

r (p a , v n )

e (p a , u na ) = 0,

where the equality comes from market clearing under autarky.

Because of balanced trade, we know that
pt n = 0.
Hence

(p

pa ) t n

0.

Law of Comparative Advantage

Dixit-Norman-Deardor (1980)

Proposition 4 In a neoclassical trade model, if there is a

representative household in country n, then cor (p p a , t n )
Proof (Cont.): By denition,
p a , t n ) = g pg

cov (p

pga

p + pa

pa ) t n

G (p

tgn

tn ,

which can be rearranged as

cov (p

p a , t n ) = (p

pa ) t n .

Given our price normalization, we know that p = p a . Hence

cov (p

p a , t n ) = (p

pa ) t n

0.

Proposition 4 derives from this observation and the fact that

sign [cor (p

p a , t n )] = sign [cov (p

p a , t n )] .

Law of Comparative Advantage

Dixit-Norman-Deardor (1980)

Comments:
With 2 goods, each country exports the good in which it has a CA, but
with more goods, this is just a correlation.
Core of the proof is the observation that p a t n

0.

It directly derives from the fact that there are gains from trade. Since
free trade is better than autarky, the vector of consumptions must be
at most barely attainable under autarky (p a y n p a c n ).
For empirical purposes, problem is that we rarely observe autarky...
In future lectures we will look at models which relate p a to (observable)
primitives of the model: technology and factor endowments.