EC931 – International Trade (MSc option)
Winter 2022
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Trade in the neoclassical model
– Trade and comparative advantage in a pure exchange economy – Production and trade
– The neoclassical model: predictions vs. stylized facts
Trade policy instruments in the neoclassical model
– Small open economy case – Large economy case
– Tariff retaliation
Trade with scale economies and imperfect competition
– Imperfect competition
– Internal economies of scale
– Imperfect competition and scale economies – predictions and evidence – External economies of scale
– Trade policies under imperfect competition and scale economies
Trade and income distribution
– Winners and losers
– The political economy of trade policy formation
International economic integration
– Preferential liberalization – Multilateral liberalization
Trade and economic globalization trends
Source: IMF
Table 1). of intra-European trade. The sha s 1
Trade and economic globalization trends
Globalization waves Table 1 in the 19th and 20th centuries
Globalization waves in the 19th and 20th century
(Percentage change unless indicated otherwise)
European trade in world trade ro cent in 1953 to 31.2 per cent in regional trade expanded somewha
(% changes unless indicated otherwise)
Population growth GDP growth (real)
Per capita
Trade growth (real) Migration (net) Million
US, Canada, Australia, NZ (cumulative)
US, Canada, Australia, NZ (annual) Industrial countries (less Japan) (cumulative)
FDI as % of GDP (world)
0.8 a 1.7 1.9 2.1 a 3.8 5.1 1.3 a 2.0 3.1
17.9 a 0.42 a
50.1 12.7 0.90 0.55
… … … 5.2
Global FDI outward stock, year
a Refers to period 1870-1913.
Source: Maddison (2001), Lewis (1981), UNCTAD (2007), WTO (2007a).
Trade in the neoclassical model
– Trade and comparative advantage in a pure exchange economy – Production and trade
– The neoclassical model: predictions vs. stylized facts
Trade policy instruments in the neoclassical model
– Small open economy case – Large economy case
– Tariff retaliation
Trade with scale economies and imperfect competition
– Imperfect competition
– Internal economies of scale
– Imperfect competition and scale economies – predictions and evidence – External economies of scale
– Trade policies under imperfect competition and scale economies
Trade and income distribution
– Winners and losers
– The political economy of trade policy formation
International economic integration
– Preferential liberalization – Multilateral liberalization
The positive theory of international trade
Questions:
1) What are the causes of trade?
2) How are the patterns of trade determined?
3) Are there “gains” from trade?
4) What are the implications of trade for the organization and
location of production?
5) What are the implications of trade for income distribution?
We focus on 1-3 first, leaving 4 and 5 aside for the time being (we’ll address 4 and 5 later – 4 when discussing “new” trade theories, 5 when discussing the political economy of trade policy formation)
Trade in the neoclassical model
– Trade and comparative advantage in a pure exchange economy
– Production and trade
– The neoclassical model: predictions vs. stylized facts
Trade policy instruments in the neoclassical model
– Small open economy case – Large economy case
– Tariff retaliation
Trade with scale economies and imperfect competition
– Imperfect competition
– Internal economies of scale
– Imperfect competition and scale economies – predictions and evidence – External economies of scale
– Trade policies under imperfect competition and scale economies
Trade and income distribution
– Winners and losers
– The political economy of trade policy formation
International economic integration
– Preferential liberalization – Multilateral liberalization
Pure exchange economy: two countries and two goods
Two individuals/countries: A and B (one individual per country)
Two goods: 1 and 2
Consumption allocation: xA = (xA1 , xA2 ), xB = (xB1 , xB2 )
Well-behaved preferences (continuous, monotonic, convex) represented by utility functions Uj(xj), j = A,B
Initial endowments: yA = (yA1 , yA2 ), yB = (yB1 , yB2 )
x A = y A
x B = y B
(‘” refers to autarky)
Utility maximization subject to budget constraint, p j (x j − y j ) ≤ 0, requires
∂ U ( x ) / ∂ x 1 j j
j ≡MRS12(x)=
∂ U j ( x j ) / ∂ x 2 Autarky prices?
– In A: pA = (pA1 ,pA2 ) s.t. – In B: pB = (pB1,pB2) s.t.
p 1 p 2
p1 = MRSA12(yA)
p1 = MRSB12(yB) p2
Free trade
– Common prices (world prices): p = (p1, p2)
Terms of trade: p1/p2 External trade for A:
mA =xA−yA =(xA1 −yA1, xA2 −yA2)=(mA1,mA2) External trade for B:
mB = xB −yB = (xB1 −yB1, xB2 −yB2) = (mB1,mB2)
– Budget constraint for A:
p1xA1 +p2xA2 =p1yA1 +p2yA2 In vector notation:
pxA =pyA or
p mA = 0 (trade balance)
– Trade balance (budget constraint) for B: pmB =0
Trade equilibrium
– Trade equilibrium (in vector notation):
xA + xB = yA + yB or
mA + mB = 0 ⇒mA =−mB
– In equilibrium:
p1 = MRSA12(xA) = MRSB12(xB) p2
x1B OB x2B
= − m 2B y = xˆ
OA x1A
−mA =mB 11
Are there gains from trade?
xj, j = A,B, always attainable (pxj = pyj for any p); choice of xj over xj when both are feasible reveals that xj ≻ xj, i.e. trade is mutually beneficial (“principle of voluntary exchange”)
Trade patterns and autarky prices
– Revealedpreferenceimpliespj(xj−yj)=pjmj >0, j=A,B
(or else x j ≻ x j would be chosen in autarky) ⇒
pA1 mA1 +pA2 mA2 > 0 and pB1mB1 +pB2mB2 > 0 ⇒ pB1mA1 +pB2mA2 < 0
(sincemAi =−mBi,i=1,2)
– Dividing through by pjmA gives
p A1 m A2 m A2 p B1 m A2 m A2 A A>− A= Aand B<− A= A ifm1>0
p 2 m 1 m 1 p 2 m 1 m 1 p A m A m A p B m A m A
or A<− A= Aand B>− A= A ifm1<0
m 1 p 2 m 1 m 1 ⇔ mA1 >0, mA2 <0 and
i.e. under free trade each country imports the good that has a
comparatively higher autarky price and exports the good that has a comparatively lower autarky price
p 2 m 1 A B
p2 A p2 B
⇔ mA1 <0, mA2 >0
Trade prices
–Suppose > A> ⇒ m1 >0, m2 <0
A A B
p1 m2 p1 A A
p 2 m 1 p 2 A12
p m A Trade balance implies pm = 0 ⇒ p = mA
A hence p1
B >p1> p1
– Same conclusion with inequality signs reversed if A B
p1 <p1 p2 p2
– Free-trade prices lie “between” the two countries’ autarky prices
Determinants of trade
– Suppose A and B have the same preferences, the same endowment point (centre point in Edgeworth Box), and that there are no trade subsidies
Then, for trade to occur, at least one of the following must apply: (i) tastes differ; (ii) endowments differ
– Neoclassical trade theorists have focused mainly on (ii), which leads to the idea of comparative advantage
Endowment differentials: absolute advantage
– Suppose A and B have identical, homothetic preferences (income elasticity of demand equal to unity for all goods), implying that the contract curve coincides with the diagonal of the Edgeworth Box
– Also suppose that the two countries have the same level of endowment of good 1 but B has more of good 2 than A does, i.e. B has an absolute advantage with respect to good 2
– Then the endowment point is below the diagonal B A
and so B will end up exporting good 2 (the good in which it has an absolute advantage)
Contract curve
(iden5cal homothe5c preferences)
Equal endowments
pˆA BA y1 =y1
Endowment differentials: comparative advantage
– What if B has less of both goods than A does but it has comparatively more of good 2 than A does? I.e.
y B2 > y A2
In this case we say that B has a comparative advantage with respect
– Then, also in this case, the endowment point is below the diagonal
B A ⇒p1 >p1
and so B will end up exporting good 2 (the good in which it has a comparative advantage)
• (Can you find a counterexample for a scenario with identical non-homothetic preferences?)
Equal endowments
yB < yA 22
yB /yB >yA /yA 2121
General two-country, N-goods case
– Expenditure functions (dual representation of preferences):
Ej(p,Uj) ≡ minpxj |Uj(xj) ≥ Uj, j = A,B xj
where Uj(xj) denotes a utility function (primal representation) – Shephard’s lemma:
∂Ej(p,Uj) = xij(p,Uj), ∀i ∂pi
In vector notation:
xj(p,Uj) = Epj(p,Uj)
(compensated demand)
Autarky equilibrium
– (‘” refers to autarky)
Epj (p j , U j ) = y j
Ej(pj,U j) = pj yj N + 1 equations
N+1 variables (pj,Uj)
(market clearing, N equations) (budget constraint, one equation)
– Homogeneity of degree zero in prices implies only N − 1 independent prices; Walras’ law implies only N − 1 independent market clearing conditions
Free-trade equilibrium
EAp (p, UA) + EBp (p, UB) = yA + yB
EA(p,UA) = pyA EB(p,UB) = pyB
(market clearing)
(budget constraint for A) (budget constraint for B)
Gains from trade
Ej(p,U j) ≤ pxj = pyj = Ej(p,Uj)
– The first inequality follows from the definition of Ej(p,Uj):
x j yields utility U j and is the least cost way of attaining U j at prices pj, but it is not the least cost way of attaining U j at prices p
– The following equality follows from the fact that x j = y j
– The last equality follows from the budget constraint
Since Ej(p,Uj) is increasing in Uj, we conclude that Uj ≥ U j
Welfare comparison across different trade equilibria
– Consider two alternative trade equilibria from the point of view of a certain country (country index omitted) – equilibrium 0 and equilibrium 1 – and suppose that
p1x1 >p1x0 (p1x1−p1x0 >0)
Then x1 is revealed preferred to x0 (x1 is chosen when x0 could be)
– We can write:
p1 x1 −p1 x0 = p1 y−p1 (y+m0)+p0 m0
(the term p1 y equals p1 x1 by the budget constraint; y + m0 equals x0; p0 m0 equals zero)
p1 x1 −p1 x0 = (p0 −p1)m0
If this is positive then x1 is preferred to x0
– Improvement in the terms of trade:
vector of old net trades is “cheaper” at new prices
(p0−p1)m0>0 ⇒ p1m0
i.e. the vectors p and mA form a 900 angle, the vectors pA and mA form a narrower angle, the vectors pB and mA form a wider angle
– Free-trade prices lie between autarky prices
mA, − mB 11
B’s offer curve
pˆ A m A > 0
pˆBmA =−pˆBmB <0
mA =−mB A’s offer curve
Trade patterns and autarky prices
– Since, by revealed preference,
pAmA >0 andpBmA <0 ⇒−pBmA >0
we can write
( p A − p B ) m A > 0
i.e. the vectors (pA −pB) and mA form an angle that is less than 900 (they “point in the same direction”)
– The trade vector is positively correlated with the vector of autarky price differentials
Trade in the neoclassical model
– Trade and comparative advantage in a pure exchange economy
– Production and trade
– The neoclassical model: predictions vs. stylized facts
Trade policy instruments in the neoclassical model
– Small open economy case – Large economy case
– Tariff retaliation
Trade with scale economies and imperfect competition
– Imperfect competition
– Internal economies of scale
– Imperfect competition and scale economies – predictions and evidence – External economies of scale
– Trade policies under imperfect competition and scale economies
Trade and income distribution
– Winners and losers
– The political economy of trade policy formation
International economic integration
– Preferential liberalization – Multilateral liberalization
Production possibilities
– Consider a scenario with two goods and two countries (as before) but where yj is not exogenously given but is endogenously selected from a set Yj
– Yj: production possibilities set
represented by Φj(yj) ≥ 0, yj ≥ 0 i.e. Yj = {yj |Φj(yj) ≥ 0}
– Set {yj | Φj(yj) = 0}: production possibilities frontier (PPF)
– The endogenously selected output mix, yj, maximizes revenue, pyj (and thus profits)
x A = y A
x B = y B
Utility maximization subject to budget constraint requires
∂ U ( x ) / ∂ x 1 j j
j ≡MRS12(x)=
p 1 p 2
, j=A,B Revenue maximization subject to Φj(yj) ≥ 0 requires
∂ U j ( x j ) / ∂ x 2 jjjj
∂ Φ ( y ) / ∂ y 1 j j
j ≡MRT12(y)=
p 1 p 2
∂ Φ j ( y j ) / ∂ y 2
Autarky prices and autarky output mix?
– In A: pA, yA, – In B: pB, yB,
A s.t. p1
= MRSA12(yA) = MRTA12(yA) = MRSB12(yB) = MRTB12(yB)
s.t. p1 p2
M R S j ( xˆ j ) = M R T j ( yˆ j ) = pˆ 1
12 12 pˆ p
Trade equilibrium
– Trade equilibrium:
xA + xB = yA + yB or
mA + mB = 0 – In equilibrium:
p1 = MRSA12(xA) = MRTA12(yA) = MRSB12(xB) = MRTB12(yB) p2
AU: xˆj=yˆj FT: xˆj≠yˆj
m2A = − m 2B
B ’ s P P F
m1B = −m1A
A ’ s P P F
Are there gains from trade?
(i) Let xj be the utility maximizing bundle for prices p and for the
autarky output mix yj; since a choice of xj = yj would be
attainable, xj is revealed preferred to xj, i.e. xj ≻ xj
(ii) Also, yj is always attainable for producers, and so a choice of yj
over yj implies pyj ≥ pyj = pxj, i.e. xj is a feasible choice from yj; since xj is chosen over xj when both are feasible
(pxj = pyj), xj is revealed preferred to xj, i.e. xj ≻ xj
Putting it all together, we conclude that
xj ≻xj ≻xj
(i) can be thought of as reflecting re-optimization on the consumption side (consumption gains); (ii) can be thought of as reflecting re-optimization on the production side (production gains)
xˆ j = yˆ j
Determinants of trade
– Given equal tastes (and absent trade subsidies) differences in
production possibilities cause trade
– Where do production possibilities come from? Let v j, j = A, B, be a vector of factor endowments, and let Ωj(yj,vj) ≥ 0 represent technologies, i.e. yj is technologically feasible from vj if and only if Ωj(yj,vj) ≥ 0. In formal terms,
Φj(yj) ≥ 0 ⇔ Ωj(yj,vj) ≥ 0
– Thus, differences in production possibilities can arise because of
(i) Differences in technologies (different Ωj’s)
(ii) Differences in factor endowments (different vj’s)
Trade and technology differentials: the Ricardo model
– Two goods, 1 and 2
One production input (labour), nontraded, priced at w j, j = A, B
Technologies differ across countries
Single-output, constant-returns-to-scale production
⇒ marginal costs, c1j(wj), c2j(wj), independent of output levels and equal to unit costs:
c1j(wj) = α1jwj c2j(wj) = α2jwj
with αij > 0, i = 1, 2 (unit input requirements)
⇒ marginal product of labour equals 1/αij, i = 1, 2
– PPFs are linear and have constant slopes equal (in absolute value) to
MRTj = c1j(wj) = α1j 12 c2j (w j ) α2j
Trade in the Ricardo model
– In autarky, pj = cj(wj), pj = cj(wj) ⇒ p1 = α1 1122 j
⇒ autarky price differentials are solely determined by technology; i.e. comparative advantage is determined by comparative technology differentials (productivity ratios rather than levels)
– Under free trade, trade prices will lie between the two countries’ autarky prices
– For any prices other than autarky prices, the revenue maximizing output mix is at a corner: full specialization under free trade
– Each country will fully specialize in the production of the good for which it has a comparatively lower autarky price and export some of its production, and will import the good for which it has a comparatively higher autarky price
(If one country is much “smaller” than the other, then only the smaller country will fully specialize)
FULL SPECIALIZATION
FULL SPECIALIZATION
Trade and endowment differentials: the Heckscher-Ohlin model
– Two goods, 1 and 2
– Two production inputs, L and K (labour and capital), nontraded,
respectively priced at wLj , wKj , j = A, B
– Identical homothetic preferences in the two countries
– Single-output, constant-returns-to-scale technologies, different across sectors but identical across countries
⇒ marginal costs, c1(wLj , wKj ), c2(wLj , wKj ), independent of output levels and equal to unit costs
Different technologies across sectors implies that production possibilities are strictly convex
The Heckscher-Ohlin model (continued)
– Factor input ratios only depend on factor prices:
L i j y i j
j > j, j=A,B
i.e. sector 1 is labour intensive and sector 2 is capital intensive (comparatively speaking)
– Assumption. No factor intensity reversals:
∂ c 2 / ∂ w Lj L 2j j j
j = j, ∀(wL,wK)
∂c2 /∂wK K2
i.e. one sector (sector 1 in this case) is always labour intensive and the other sector is always capital intensive for all factor prices
j= j Ki yi
∂ c i / ∂ w Lj
∂ c i / ∂ w Lj
j, i=1,2,j=A,B
– Factor ratios are assumed to differ across sectors, e.g.:
∂ c 1 / ∂ w Lj L 1j
∂c1 /∂wK K1
Autarky prices in the Heckscher-Ohlin model
– Assume different factor endowments across countries, e.g. (bars
denote endowments):
i.e. A is comparatively labour rich and B is comparatively capital rich – Then the autarky price of the labour intensive good will be
comparatively lower in A than in B
Sketch of proof: (i) if 1 is comparatively labour intensive, then, for given prices p1/p2, the ratio y1/y2 will be higher in the country that is comparatively labour rich ( , next slide);
(ii) the absolute value of the slope of a concave PPF (which must equal p1/p2) is increasing in the ratio y1/y2; (iii) results (i) and (ii) together imply that if sector 1 is the labour intensive sector and country A is comparatively labour rich, then, for any given common ratio y1/y2, A’s PPF will be flatter than B’s PPF; (iv) given common homothetic preferences, (iii) implies that the autarky price ratio p1/p2 will be higher in B than in A
– If sector 1 is labour intensive, a higher L, for a given K, raises y1 and
⇒ a higher labour to capital endowment ratio translates into a higher y1/y2 output ratio
– One-to-one mapping between output price ratio
p1/p2 = c1(wL, wK)/c2(wL, wK) = c1(wL/wK, 1)/c2(wL/wK, 1)
and wL/wK: both the numerator and the denominator are concave in wL/wK but they have different slope and curvature, and so (assuming no factor intensity reversals) there is a unique level of wL/wK for which c1(wL/wK,1)/c2(wL/wK,1) equals a given p1/p2
– So, for a given p1/p2, the ratio wL/wK is given, and so are unit compensated demands ∂ci/∂wL ≡ αiL, ∂ci/∂wK ≡ αiK, i = 1, 2
– Solving the system of linear equations (factor markets clearing) y1α1L+y2α2L =L
y1α1K + y2α2K = K we obtain
y1 = K α1K
L/K−α2L/α2K α1L/α1K − α2L/α2K α1L/α1K−L/K α1L/α1K − α2L/α2K
Good 1 labour intensive Country A labour rich
B ’ s P P F
A ’ s P P F
Trade in the Heckscher-Ohlin model
– Heckscher- : A country
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