Chapter 6
The Standard
Trade Model
Introduction
•  To understand the effects of international trade we must first
understand the causes.
•  One of the main cause of international trade is that countries
differ in their abilities to produce certain goods:
–  Technologies
–  Factor endowments
–  Market characteristics
–  Government policies
•  We develop the tools of production theory and producer
equilibrium.
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General Equilibrium Models
Road Map
•  Supply: Firm technology and profit maximization (or cost
minimization)
•  Demand: Consumer preferences and utility maximization
•  Equilibrium: Closed and Open economy
•  Gains from trade
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Production Possibility Frontier
•  The production possibility frontier describes the production
possibilities available to the economy given the technologies and
input constraints.
–  Suppose the economy produces two goods: X and Y.
–  How much Y can the economy produce if it produces a given
amount of good X, say X ?
•  Production Possibility Frontier Notes
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Profit Maximization
•  The economy’s problem is to maximize profits by choosing the
amount of each goods to produce conditional on the available
technologies and input constraints.
•  Assumptions
–  Perfect competition in all markets (exogenous prices)
–  Labor is perfectly mobile (WX = WY = W)
•  Profit Maximization Notes
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Utility Maximization
•  Consumers preferences over certain quantities of goods (X,Y) are
summarized by the utility function:
U = U ( X, Y )
• 
Consumers maximizes their utility by choosing how much X
and Y to consume conditional on their budget constraint
• 
Utility Maximization Notes
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How an Increase in the Relative Price of
Cloth Affects Relative Supply
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How an Increase in the Relative Price of
Cloth Affects Relative Demand
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Closed Economy Equilibrium
•  The closed economy equilibrium is defined by 3 conditions:
Producer Optimization :
Consumer Optimization :
PX MPL Y
=
= MRT
PY MPL X
PX Uʹ′X
=
= MRS
PY Uʹ′Y
Market Clearing : Demand = Supply (for X and Y)
•  Consumers and producers interact to determine the (unique)
equilibrium relative price such that these 3 conditions hold.
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Closed Economy Equilibrium
Y
•  The equilibrium is at point A:
–  MRT = MRS = PX PY
–  Demand equal supply in all
markets (X, Y and L)
A
−
PX
PY
•  At point A there is no reason for
any economic agents (producers,
consumers or workers) to change
their behavior.
X
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Open Economy Equilibrium
•  In an open economy firms can engage in international trade.
Therefore supply does not have to be equal to demand within
countries.
•  Trade balance condition: The value of a country’s export must
be equal to the value of its import:
PXT ( XC − X P ) + PYT (YC −YP ) = 0
where ( XC − X P ) and (YC −YP ) are respectively the excess
T
T
P
,
and
P
demands for goods X and Y and X
Y are the equilibrium
prices in the open economy.
•  Open economy equilibrium notes
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Gains from Trade
•  We can now address one of the most fundamental issues in
international trade: Under what circumstances is the country’s
overall welfare improved by international trade?
The ability of a country to trade at any price ratio
other then its autarky prices makes the country better off.
•  The country gains by exporting what is relatively more valuable
on world markets than at home and by importing from the rest of
the world what is relatively more costly to produce at home than
abroad.
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Gains from Trade
•  The direction of trade has no
importance.
•  The country can export or
import X and reach the same
utility level.
•  Gains from Trade Notes
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Gains from Trade
•  The gains from trade can be decomposed into two distinct
sources:
1.  Exchange: The gains from exchange refer to the fact that if
countries are endowed with different (amounts of) goods
they can gain by exchanging with each other.
2.  Specialization: The gains from specialization arise when the
country increase its output of the good it produce more
efficiently.
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Gains from Trade
§  The two sources of gains can
be illustrated in a graph
§  Autarky equilibrium occurs at
point A (Ua)
§  Gains from exchange: Suppose
the country can trade at free
trade prices but produce the
same output as in the closed
economy (Ue)
§  Gains from specialization:
Allows the country to adjust
production in respond to
changes in prices (Uf)
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Empirical Evidence
•  Some complications
–  Our theories make predictions based on differences between
autarky prices across countries. Autarky prices are generally
not observable, so we often rely on indirect tests.
–  The models make numerous simplifying assumptions. If the
tests reject the model it is difficult to know exactly why. We
can only ask: How close do we get?
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Empirical Evidence
1. Revealed preferences
•  It is difficult to test for the existence of Gains from Trade because
of the absence of autarky data.
•  Revealed preferences: consumer preferences are revealed by their
consumption patterns
•  Countries must consider themselves better off under trade than
autarky since they are engaged in international trade.
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Empirical Evidence
2. A natural experiment: Japan
•  Bernhofen and Brown (AER, 2005): What is the magnitude of the
gains from international trade?
–  In the late 1850s Japan reopened to world commerce after
over 200 years of self-imposed isolation.
–  By how much would real income have had to increase during
the autarky years to afford the trade consumption bundle?
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Empirical Evidence
•  Using the usual notation: ΔI = P A ⋅ C T − P A ⋅ C A
where A denotes autarky and T trade values.
•  Recall that market clearing implies:
PA ⋅ C A = PA ⋅ QA
•  We can therefore write:
ΔI = P A ⋅ C T − P A ⋅ C A + ( P A ⋅ C A − P A ⋅ Q A ) + ( P A ⋅ QT − P A ⋅ QT )


 


=0
=0
= P A ⋅ C T − P A ⋅ C A + P A ⋅ C A − P A ⋅ Q A + P A ⋅ QT − P A ⋅ QT
= P A ( C T − Q A + Q T − Q T ) = P A ( C T − Q T ) − P A (Q A − Q T )
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Empirical Evidence
ΔI = P A (C T − QT ) − P A (Q A − QT ) = P A ⋅ T − P A (Q A − QT )
≤ PA ⋅T
•  The inequality follows from the fact that QA is the profit
maximizing production bundle under autarky prices PA:
P A ⋅ Q A > P A ⋅ QT
•  Therefore, we can compute an upper bound for the change in
income is
ΔI P A ⋅ T
≤
I
I
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Empirical Evidence
•  To obtain an estimate for the gains from trade we need:
–  Autarky income (I)
–  Autarky prices (PA)
–  Trade (T)
•  There are measurement issues.
•  Depending on assumptions:
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ΔI
5.4% <
< 9.1%
I
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Conclusions
•  Differences in relative prices lead to gains from trade
–  export what is relatively more valuable on world markets
–  import from the rest of the world what is relatively more
costly to produce at home than abroad.
•  Those gains can be decomposed into exchange and specialization
gains
•  Why are relative prices different?
–  Technology (Ricardo)
–  Factor endowments (Heckscher-Ohlin)
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