Course Logistics
Lecture: Mondays, Wednesdays 09:00AM-10:30AM, E51-057
Instructor: Arnaud Costinot
Office: E52-534
Email: [email protected]
Office hours: by appointment
Instructor: Dave Donaldson
Office: E52-554
Email: [email protected]
Office hours: by appointment
14.581 (Week 1) CA and GT Fall 2017 3 / 31
Course Logistics
TA: Yuhei Miyauchi
Email: [email protected]
Office hours: by appointment
Recitations: TBD
No required textbooks, but we will frequently use:
Dixit and Norman, Theory of International Trade (DN)
Feenstra, Advanced International Trade: Theory and Evidence (F)
Helpman and Krugman, Market Structure and Foreign Trade (HKa)
Relevant chapters of all textbooks will be available on Stellar
Relevant papers can be downloaded on Dropbox (link in the syllabus)
14.581 (Week 1) CA and GT Fall 2017 4 / 31
Course Logistics
Course requirements:
Four problem sets: 40% of the course grade
One referee report: 15% of the course grade
One presentation: 15% of the course grade (second week of December)
One research proposal: 30% of the course grade (due during IAP)
There will be no lecture on Wednesday Nov. 22 (Thanksgiving)
14.581 (Week 1) CA and GT Fall 2017 5 / 31
Course Logistics
Course outline:
1
Law of CA (1 week)
2
Ricardian Model (2.5 weeks)
3
Factor Proportion Theory, Factor Content of Trade, and Inequality (2.5
weeks)
4
Gravity Models and Trade Costs (1.5 week)
5
Fragmentation, Input-Output Linkages, and Aggregate Fluctuations
(1.5 week)
6
Growth, Development, and Market Integration (1.5 week)
7
Trade Policy (2 weeks)
14.581 (Week 1) CA and GT Fall 2017 6 / 31
International Trade: Standard Assumptions
What distinguishes trade theory from abstract general-equilibrium
analysis is the existence of a hierarchical market structure:
1
“International” good markets
2
“Domestic” factor markets
Typical asymmetry between “goods” and “factors”:
Goods enter consumers’ utility functions directly, are elastically
supplied and demanded, and can be freely traded internationally
Factors only affect utility through the income they generate, they are in
fixed supply domestically, and they cannot be traded at all
Central Issues:
How does the integration of good markets affect good prices?
How do changes in good prices, in turn, affect factor prices, factor
allocation, production, and welfare?
14.581 (Week 1) CA and GT Fall 2017 9 / 31
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:
Goods can be distinguished by locations, time, and states of nature
So even if trade is “free”, goods that are sold abroad may be subject to
transportation costs, whereas goods that are sold locally are not
In an Arrow-Debreu sense, goods sold in different locations are just
different goods that require different “production” costs
Factor mobility could be dealt with by defining as a good anything that
can be traded etc.
14.581 (Week 1) CA and GT Fall 2017 10 / 31
Neoclassical Trade: Standard Assumptions
“Neoclassic trade models” characterized by three key assumptions:
1
Perfect competition
2
Constant returns to scale (CRS)
3
No distortions
Comments:
We can always allow for decreasing returns to scale (DRS) by
introducing extra factors in fixed supply
Increasing returns to scale (IRS) are a much more severe issue
addressed by “New” trade theory
14.581 (Week 1) CA and GT Fall 2017 11 / 31
Neoclassical Trade: General Results
Not surprisingly, there are few results that can be derived using only
Assumptions 1-3
In future lectures, we will derive sharp predictions for special cases:
Ricardo, Assignment, Ricardo-Viner, and Heckscher-Ohlin models
Today, we’ll 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)
2
Law of comparative advantage (Deardorff 1980)
14.581 (Week 1) CA and GT Fall 2017 12 / 31
Basic Environment
Consider a world economy with n = 1, ..., N countries, each populated
by h = 1, ..., H
n
households
There are g = 1, ..., G goods:
y
n
≡ (y
n
1
, ..., y
n
G
) ≡ Output vector in country n
c
nh
≡ (c
nh
1
, ..., c
nh
G
) ≡ Consumption vector of household h in country n
p
n
≡ (p
n
1
, ..., p
n
G
) ≡ Good price vector in country n
There are f = 1, ..., F factors:
v
n
≡ (v
n
1
, ..., v
n
F
) ≡ Endowment vector in country n
w
n
≡ (w
n
1
, ..., w
n
F
) ≡ Factor price vector in country n
14.581 (Week 1) CA and GT Fall 2017 13 / 31
Supply
The revenue function
We denote by Ω
n
the set of combinations (y , v ) feasible in country n
CRS ⇒ Ω
n
is a convex cone
Revenue function in country n is defined as
r
n
(p, v) ≡ max
y
{
py |(y, v) ∈ Ω
n
}
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)
14.581 (Week 1) CA and GT Fall 2017 14 / 31
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 defined as
e
nh
(p, u) = min
c
n
pc|u
nh
(
c
)
≥ u
o
Comments (see Dixit-Norman pp. 59-64 for details):
Here factor endowments are in fixed supply, but easy to generalize to
case where households choose factor supply optimally
Holding p fixed, e
nh
(p, u) is increasing in u
Household’s optimization implies
e
nh
(p
n
, u
nh
) = p
n
c
nh
, (2)
where c
nh
and u
nh
are the consumption and utility level of the
household in equilibrium, respectively
14.581 (Week 1) CA and GT Fall 2017 15 / 31
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 first 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
14.581 (Week 1) CA and GT Fall 2017 16 / 31
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 off.
Proof:
e(p, u
a
) ≤ pc
a
, by definition of e
= py
a
by market clearing under autarky
≤ r
(
p, v
)
by definition of r
= e
(
p, u
)
by equations (1), (2), and trade balance
Since e(p, ·) increasing, we get u ≥ u
a
14.581 (Week 1) CA and GT Fall 2017 17 / 31
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
14.581 (Week 1) CA and GT Fall 2017 18 / 31
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 commodity taxes
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
τ
h
the lump-sum transfer from the government to household h (τ
h
≤ 0
⇔ lump-sum tax and τ
h
≥ 0 ⇔ lump-sum subsidy)
14.581 (Week 1) CA and GT Fall 2017 19 / 31
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 τ
h
such that
τ
h
=
(
p − p
a
)
c
ah
− (w − w
a
)v
h
Budget constraint under autarky implies p
a
c
ah
≤ w
a
v
h
. Therefore
pc
ah
≤ wv
h
+ τ
h
Thus c
ah
is still in the budget set of household h under free trade
14.581 (Week 1) CA and GT Fall 2017 20 / 31
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 definition, government’s revenue is given by
−
∑
τ
h
=
(
p
a
− p
)
∑
c
ah
− (w
a
− w)
∑
v
h
: definition of τ
h
=
(
p
a
− p
)
y
a
− (w
a
− w)v : mc autarky
= −py
a
+ wv : zp autarky
≥ −r
(
p, v
)
+ wv : definition r
(
p, v
)
= −
(
py − wv
)
= 0 : eq.
(
1
)
+ zp free trade
14.581 (Week 1) CA and GT Fall 2017 21 / 31
Gains from Trade
Multiple households per country (II): commodity taxes
With this last comment in mind, we now restrict the set of
instruments to commodity taxes/subsidies
More specifically, suppose that the government can affect the prices
faced by all households under free trade by setting τ
good
and τ
factor
p
household
= p + τ
good
w
household
= w + τ
factor
14.581 (Week 1) CA and GT Fall 2017 23 / 31
Gains from Trade
Multiple households per country (II): commodity taxes
Proposition 3 In a neoclassical trade model with multiple households
per country, there exist commodity taxes/subsidies such that free
trade is (weakly) Pareto superior to autarky in all countries
Proof: Consider the two following taxes:
τ
good
= p
a
− p
τ
factor
= w
a
− w
By construction, household is indifferent between autarky and free
trade. Now consider government’s revenues. By definition
−
∑
τ
h
= τ
good
∑
c
ah
− τ
factor
∑
v
h
=
(
p
a
− p
)
∑
c
ah
− (w
a
− w)
∑
v
h
≥ 0,
for the same reason as in the previous proof.
14.581 (Week 1) CA and GT Fall 2017 24 / 31
Gains from Trade
Multiple households per country (II): commodity taxes
Comments:
Proof only relies on the existence of production gains from trade
Closely related to Diamond and Mirrlees’ (1971) production efficiency
When only commodity taxes are available, DM show that production
should remain efficient at a social optimum
Thus, trade, which acts as an expansion of PPF, should remain free
(ignoring issues of market power)
If there is a kink in the PPF, there are no production gains...
Similar problem with “moving costs”. See Feenstra p.185
Factor taxation still informationally intensive: need to know
endowments in efficiency units, may lead to different business taxes
14.581 (Week 1) CA and GT Fall 2017 25 / 31
Law of Comparative Advantage
Basic Idea
The previous results have focused on normative predictions
We now demonstrate how the same revealed preference argument can
be used to make positive predictions about the pattern of trade
Principle of comparative advantage:
Comparative advantage—meaning differences 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
14.581 (Week 1) CA and GT Fall 2017 26 / 31
Law of Comparative Advantage
Dixit-Norman-Deardorff (1980)
Let t
n
≡
y
n
1
−
∑
c
nh
, ..., y
n
G
−
∑
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:
∑
p
g
=
∑
p
an
g
= 1,
Notations:
cor
(
x, y
)
=
cov
(
x, y
)
p
var
(
x
)
var
(
y
)
cov
(
x, y
)
=
∑
n
i=1
(
x
i
− x
) (
y
i
− y
)
x =
1
n
∑
n
i=1
x
i
14.581 (Week 1) CA and GT Fall 2017 27 / 31
Law of Comparative Advantage
Dixit-Norman-Deardorff (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
)
∈ Ω
n
, the definition of r implies
p
a
y
n
≤ r
(
p
a
, v
n
)
Since u
n
(
c
n
)
= u
n
, the definition of e implies
p
a
c
n
≥ e
(
p
a
, u
n
)
The two previous inequalities imply
p
a
t
n
≤ r
(
p
a
, v
n
)
− e
(
p
a
, u
n
)
(3)
Since u
n
≥ u
an
by Proposition 1, e
(
p
a
, ·
)
increasing implies
e(p
a
, u
n
) ≥ e(p
a
, u
na
) (4)
14.581 (Week 1) CA and GT Fall 2017 28 / 31
Law of Comparative Advantage
Dixit-Norman-Deardorff (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
p
a
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 − p
a
)
t
n
≥ 0
14.581 (Week 1) CA and GT Fall 2017 29 / 31
Law of Comparative Advantage
Dixit-Norman-Deardorff (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.): By definition,
cov
(
p − p
a
, t
n
)
=
∑
g
p
g
− p
a
g
− p + p
a
t
n
g
− t
n
,
which can be rearranged as
cov
(
p − p
a
, t
n
)
=
(
p − p
a
)
t
n
− G
(
p − p
a
)
t
n
Given our price normalization, we know that p = p
a
. Hence
cov
(
p − p
a
, t
n
)
=
(
p − p
a
)
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
)]
14.581 (Week 1) CA and GT Fall 2017 30 / 31
Law of Comparative Advantage
Dixit-Norman-Deardorff (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
14.581 (Week 1) CA and GT Fall 2017 31 / 31
