Lectures, 1
COMPARATIVE–ADVANTAGE TRADE
WHY TRADE?
Economists recognize three basic reasons. i Comparative advantage — trade to exploit differences
between countries; ii Increasing returns to scale — trade to concentrate on fewer things and to do them
better; iii Imperfect competition — trade to expose firms to more competition to force them to behave
mere efficiently.
In a comparative-advantage world countries trade to exploit their differences: technology; factor
endowments; tastes; and also man-made differences such as those due to government policies.
Key assumptions: (i) perfect competition in all markets; (ii) no externalities of production or of
consumption. This rules out economies of scale and imperfect competition. (Worry about this later).
Engaging in trade is costly, so it makes sense only if it confers gains. So let's start by looking at the
nature of possible gains from trade.
I THE GAINS FROM
TRADE
Argument is obvious for a
single individual:
Distinguish production gain
and consumption gain from
trade.
Figure 1-1
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General Case
Will compare an autarky equilibrium with a free-trade one.
NOTATION
Autarky
Trade
xA
x
production bundle
dA
d
consumption bundle
vA
v
factors used
pA
p
commodity price vector
wA
w
factor reward vector
(1) xA = dA
(autarky)
(2) px = pd
(balanced trade)
(3) pxA - wvA # px - wv
[=0]
(profit maximization)
Expression (3) depends on perfect competition (which gives an analogous expression for each firm in the
economy) and on no externalities in production (which allows us to add up over all firms). Substituting
(1) and (2) into (3) gives:
(I)
pdA - wvA < pd - wv
The algebraic counterpart to the above diagrams. With a single individual we can apply WARP directly.
What about a collection of individuals? If (I) held for each individual, the assumption of no externalities
in consumption would again allow us to employ the WARP for each. But no reason to expect this. Note
that (1)–(3) hold for every autarky equilibrium (obtainable for any lump–sum redistributions of
endowments or of goods) and for every free–trade equilibrium. Thus:
There is no system of autarky lump–sum redistributions that would leave everyone better off
than in any free–trade equilibrium—otherwise the analog of (I) would be violated for each
individual and therefore in the aggregate as well.
W ilfred J. Ethier
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(N.B.: These are transfers within a country, not between countries). Or to phrase it somewhat differently:
The Basic GAINS FROM TRADE
In any trading equilibrium, gainers must gain at least as much as losers lose,
relative to autarky.
This is the basic gains-from-trade argument. Note the three basic qualifications:
i
There may be losers as well as gainers.
ii
The gainers may or may not outnumber the losers.
iii The comparison is between free trade (or at least some trade) and autarky, not between free
trade and restricted trade.
From this we might conjecture:
GAINS FROM TRADE II
For each situation obtainable under autarky, there exists some system of lump-sum
taxes and subsidies that makes everyone at least as well off with free trade.
[Briefly discuss formal issues involved here (e. g., Grandmont and McFadden, "A Technical Note on
Classical Gains from Trade," JOURNAL OF INTERNATIONAL ECONOMICS , May 1972, pp 109-26; paper
by Otani in same issue; Kemp and Wan, INTERNATIONAL ECONOMIC REVIEW , 1972). The basic issue
is the existence of the desired free-trade equilibrium with transfers. We cannot simply appeal to the
Second Theorem of Welfare Economics because we need to rule out international transfers. Note that the
italicized statement—what was actually demonstrated—is a statement about nonexistence, whereas the
assertion in the box is about existence.
Will not discuss these issues.]
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II THE PRINCIPLE OF COMPARATIVE ADVANTAGE
We are now ready to turn to comparative advantage. For simplicity, we suppose factors are inelastically
supplied, i.e., v is fixed.
Principle of Comparative Advantage
Suppose two goods (A and B) and two countries (home, H, and foreign, F). If in the absence of free trade,
PB /PA is less in H than in F, we say: “H has a comparative advantage over F in B relative to A.” In this
case, with free trade:
1
Neither country will reduce production of the good in which it has a comparative advantage
nor produce more of the other good.
2
Neither country will import the good in which it has a comparative advantage.
3
All exchanges will take place at terms between the relative autarky prices in H and F
inclusively.
In addition, we have the welfare implications:
4
In each country gainers gain at least as much as losers lose, relative to autarky.
5
The free-trade equilibrium is globally constrained-Pareto-efficient (the constraint being that
factors are internationally immobile).
Usual textbook explanation of comparative advantage
General Principle of Comparative Advantage.
Suppose there are two countries (H and F), no externalities, and unique, competitive autarky equilibria in
each country. If they move to a competitive free-trade equilibrium where, for some social welfare index
consistent with autarky and free-trade consumption, u(d) $ u(dA ) in each country:
W ilfred J. Ethier
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1.
In each country,
2.
If M denotes the home net import vector,
3.
The trade and autarky price vectors satisfy
4.
World output will be constrained Pareto-efficient.
5.
In each country gainers gain at least as much as losers lose.
Proof of the Comparative Advantage Theorem
Assertion 4 follows from basic welfare economics, and 5 is the gains–from–trade theorem. Thus we need
prove 1, 2, and 3. We have
by profit maximization. Thus
so that
This gives the first assertion. Have, for the home country:
p a d $ p a d a = p a x a $ p a x.
Thus
Now
by balanced trade. Thus
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Similarly for the foreign country,
But M = -M* so (1) and (2) imply that
This proves the second assertion, and the third likewise follows.
III THE GENERAL EQUILIBRIUM OF INTERNATIONAL TRADE
a Walras' Law
where B, A denote demands and b, a supplies. There are no other sources of or ways to dispose of
income. Alternatively,
b International Equilibrium
c Elasticity
Have M(p) = B(p, e) - b(p), where e = A + pB. If y = a + pB, then e = y by the budget constraint. (We will
not be addressing issues concerned with internal distribution, so you may as well take u as a scalar, rather
than as a vector of utilities of individual households).
W ilfred J. Ethier
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Differentiate the definition of M(p):
Now, the Slutsky equation is:
Substituting:
or,
Discuss income and substitution effects. The substitution effects are unambiguously negative. Since
Me/Mp = B, My/Mp = b and M = B - b,
or
or
e = c + s + m = cE/(M/B) + sE/(X/a) + m
which are defined accordingly from the preceding expression (where cE and sE are conventional
elasticities).
Also s =(p/M)(db/dp) = -(da/db) (db/dp)(p/X) = -(p/X)(da/dp) = [(1/p)/X][da/d(1/p)].
e is the elasticity of the M(p) curve:
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Here, e = BC/AB at B.
Could as well define the elasticity of export supply:
^
^
^ ^
Now from Walras's Law, M
+ p^ = X,
or 1 + (M/p)
=
^ ^
X/p
Figure 1–10
Thus:
f = e-1.
So, f = c + s + (m-1), where m-1 can be interpreted as the marginal propensity to export.
Summary on elasticities:
e=c+s+m
(= (B/M)cE + (a/X)sE + m)
e / - (p/M)(dM/dp)
where
c / - (p/M)(MB/Mp#u)
(consumption substitution elasticity)
s / [(1/p)/X][da/d(1/p)]
(production substitution elasticity)
m / p(MB/ME)
(marginal propensity to import)
f = c + s + (m-1)
g = f/e = (e-1)/e
where f / [(1/p)/X][dX/d(1/p)] = e - 1
where g / [M/X][dX/dM]
d The Marshall-Lerner condition
Let á denote a shift parameter. Then the basic comparative statics of international equilibrium pM(p,á) =
M*(1/p) is given by:
W ilfred J. Ethier
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Thus low elasticities (i.e. values of e + e* not much above unity) imply that exogenous shocks induce
price volatility, and that the exercise of market power becomes more tempting (individual agents have no
market power, by assumption, but individual countries may: here the second distinguishing feature of
international trade theory—that there is more than one sovereign government—becomes important).
Discuss with respect to perceived problems of primary-good exporters. Discuss DC–DC trade vs.
DC–LDC trade, etc.
Circumstances tending toward satisfaction of the M-L condition, also written as:
So “optimism” is associated with:
(1)
(2)
(3)
(4)
(5)
high total elasticities
high substitution elasticities
low trade volumes
high marginal preferences for imported goods
small international differences in spending propensities.