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Comparative Advantage

The Ricardian model and more

Luca De Benedictis

1

1University of Macerata - debene@unimc.it

Lecture 2

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The Ricardian model

Main characteristics and insights:

I

Countries are different because of technology [tastes and endowments are identical across nations]

I

Technology is linear [one factor of production, L, marginal productivity is constant]

I

Markets are perfectly competitive

I

Under autarky

ppxAA

y

=

aax·wx

y·wy

=

aax

y

I

Absolute advantage (a.a.) a

x

< a

x

Country H has an a.a. in the production of good x

I

Comparative advantage (c.a.)

ax

ay

<

aax y

Country H has an c.a. in the production of good x

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The Ricardian model (cont.)

Comparative advantage and trade flows prediction Country H exports good x if

aax

y

<

aax y

Proof If

aax

y

<

aax

y

⇐⇒

ppxAA

y

<

ppx∗A∗A y

.

This implies that M

x

< 0 and M

y

> 0. Country H exports good x

and imports good y . Country F does the opposite.

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The Ricardian model with a continuum of goods

I Ricardo’s insight can be extended to a world with many goods.

Dornbusch, Fischer and Samuelson, (AER, 1977) provide a tractable version (let’s call it the DFS model).

I Environment and Endowments: There are two countries (H and F , the latter indicated with a ∗) and n goods (j ∈ [1, n]) produced with labor.

Denote the endowments of labor by L and L. All markets are perfectly competitive.

I Technology: Unit labor requirements for good j in country H are given by ajLXj

j, while in country F , ajL

j

Xj. Without loss of generality we can index goods such that

a1

a1 > · · · > a

j

aj > · · · > aan

n. I Preferences: Preferences are Cobb-Douglas (Pn

j =1bj = 1) and identical in both countries, with a share bj= bj of income going to good j . I Continuum of goods: Goods are described in a continuum (move from a

discrete space to a continuous space): j ∈ [1, n] ⇒ z ∈ [0, 1].

A(z) ≡aa(z)(z). Where A0(z) < 0: is a decreasing function of z.

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The Ricardian model with a continuum of goods (2)

I The cost of producing good z in country H is given by w · a(z). Perfect competition ensures that good z is produced in H if and only if

a(z) · w ≤ a(z) · w, or if and only if z < ˜z , where ˜z is such that ω = w

w ∗= A(z). (1)

I Let’s use the balanced trade equation. Since there are no profits in equilibrium, defining θ(˜z) =R˜z

0 b(z)dz > 0 the fraction of world income spent in goods produced in country H, and 1 − θ(˜z) =R1

˜

z b(z)dz > 0 the fraction of world income spent in goods produced in country F.

0 < θ(˜z) < 1.

I H GDP is (income=value of production)

w · L = θ(˜z)(w · L + w· L) dividing by w· L, we obtain

ω = ww = θ(˜z)(ω +LL) −→ ω(1 − θ(˜z)) = θ(˜z) · LL I so, finally we obtain the balanced trade schedule

ω = w

w ∗= θ(˜z) 1 − θ(˜z)·L

L = D(˜z,L

L). (2)

I (1) and (2) define a system of two equations in two unknowns, ˜z and ω.

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The Ricardian model with a continuum of goods (3)

I The figure below illustrates the equilibrium. Remember that the curve A(z) is monotonically decreasing in z. On the other hand, D(˜z,LL)> 0 is monotonically increasing in z. But note also that D(0) = 0 and

limz→1= +∞. Hence, an equilibrium exists and is unique.

z w

A(z) D(z)

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DFS Model: comparative statics

I Suppose that population in F increases. From the point of view of H, you can interpret this as trade integration with a larger country.

I As illustrated in the Figure above, this leads to a fall in the set of goods produced in H (H loses industries), but to an increase in the relative wage in H.

I It is easy to see that H is better off. Real income in terms of goods produced in H before and after the rise in Lis unaffected, while it rises for all other goods.

I Workers in F lose, because their real wage in terms of goods produced in F before and after trade does not change, but it declines in terms of all other goods.

I Note that with technology being fixed, there is a one-to-one mapping between changes in the terms-of-trade and changes in welfare.

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DFS Model: comparative statics

I Suppose that technology in F increases.

I This leads to a fall in the set of goods produced in H (H loses industries), and to a decrease in the relative wage in H.

I It is easy to see that H is worst off. Real income in terms of goods produced in H before and after the rise in Lis reduced.

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DFS Model: comparative statics

I Let’s now introduce trade costs.

I If melting iceberg transport costs are present. In this event the specialization pattern is as follows:

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DFS Model and the gravity equation

I The trade volume is

2wLθ(˜z) = (2wL)(wL)

(wL) + (wL)= 2YY

YW , (3)

where Y denotes GDP.

I Hence, the DFS model predicts a simplified version (with no trade frictions) of the so-called gravity equation.

I It can easily be shown that any model with complete specialization, homothetic preferences, and no trade barriers delivers this prediction.

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The Ricardian model: rejuvenation

I How comparative advantages get measured?

I Indices of Reveal Comparative Advantages (De Benedictis, 2005) I New estimates of what causes Comparative Advantages

I we will see this next week

I The Ricardian model give uncertain predictions when we have more than two countries (Helpman, 2011).

I Eaton and Kortum (2003) extend the DFS model introducing two modern features: geography and a stochastic element associated to labor productivity

I we will see after Easter.

I The Ricardian model give poor predictions in terms of change in the structure of comparative advantages.

I A second classical model: Heckscher-Ohlin.

I we will talk about a little bit without doing any models.

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