Comparative Advantage, Trade And Payments In A Ricardian Model With A Continuum Of Goods
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R. Dornbusch
COMPARATIVE ADVANTAGE,
TRADE AND PAYMENTS IN A RICARDIAN
MODEL WITH A CONTINUUM OF GOODS
S. Fischer P. A. Samuelson
Number 178 April 1976
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COMPARATIVE ADVANTAGE,
TRADE AND PAYMENTS IN A RICARDIAN
MODEL WITH A CONTINUUM OF GOODS^
R. Dornbusch S. Fischer P. A. Samuelson
Number 178 April 1976
The views expressed in this paper are the authors' sole
responsibility and do not reflect those of the Department
of Economics, the Massachusetts Institute of Technology,
the Ford Foundation, or the National Science Foundation.
JUN 26 1976 I
Revised
April 1976
COMPARATIVE ADVANTAGE, TRADE AND PAYMENTS IN A RICARDIAN
MODEL WITH A CONTINUUM OF GOODS*
R. Dornbusch S. Fischer P. A. Samuelson
Massachusetts Institute of Technology
This paper discusses Ricardian trade and payments theory in the case
of a continuum of commodities. The analysis thus extends the development
of the many- commodity, two-country comparative advantage analysis as
presented, for example in Haberler (1937) and as historically reviewed
by Chipman (1965) . Perhaps surprisingly, the continuum assumption simplifies
the analysis in comparison with the discrete many-commodity case.
The distinguishing feature of the Ricardian approach emphasized in this
paper is the determination of the competitive margin in production between
imported and exported goods. The analysis advances the existing literature
by showing formally how tariffs and transport costs establish a range of
commodities that are not traded, and how the price-specie flow mechanism does
or does not give rise to movements in relative cost and price levels.
The formal real model is introduced in Part I. Its equilibrium
determines the relative wage and price structure and the efficient international
specialization pattern. Part II considers standard comparative
static questions of growth, demand shifts, technological change, and
transfers. Extensions of the model to nontraded goods, tariffs and
R. Dornbusch acknowledges gratefully a Ford Foundation Grant; S. Fischer,
NSF GS-41428; and P. Samuelson, NSF 75-04053.
0727632
- 2
transport costs are then studied in Part III. Monetary considerations
are introduced in Part IV, which examines the price-specie mechanism under
stable parities, floating exchange rate regimes, and also questions of
unemployment under sticky money wages.
- 3 -
I. THE REAL MODEL
In this part we develop the basic real model and determine the
equilibrium relative wage and price structure along with the efficient
geographic pattern of specialization. Assumptions about technology are
specified in Section A. Section B deals with demand. In Section C the
equilibrium is constructed and some of its properties are explored.
Throughout this section we assume zero transport costs and no other impediments
to trade.
A. Technology and Efficient Geographic Specialization
The many-commodity Ricardian model assumes constant unit labor
requirements (aI,,...n, a ) and (a,I,..n.,a ) for the n commodities that can
be produced in the home and foreign countries, respectively. The commodities
are conveniently indexed so that relative unit labor requirements
are ranked in order of diminishing home-country comparative advantage,
* * *
a,1/a1, > ... > a.1/a1. > ... > a /a n n
where an asterisk denotes the foreign country.
In working with a continuum of goods, we similarly index commodities
on an interval, say[o,l], in accordance with diminishing home-country comparative
advantage. a commodity, z, is associated with each point on
the interval, and for each commodity there are unit labor requirements in
*
the two countries, a(z) and a (z) , with relative unit labor requirement
given by
*
(1) A(z) = 2_i£L . A . (z) < . a(z)
For a review of the Ricardian model, see Chipman (1965)
- 4
The relative unit labor requirement function in (1) is by assumption
continuous and by construction (ranking or indexing of goods) nonincreasing
in z. We make the stronger assumption that A(z) is in fact
decreasing in z. The function A(z) is shown in Figure 1 as the downward
sloping schedule.
Consider now the range of commodities produced domestically and
those produced abroad, as well as the relative price structure associated
*
with given wages. For that purpose we define as w and w the domestic
and foreign wages measured in any (common!) unit. The home country will
efficiently produce all those commodities for which domestic unit labor
costs are less than or equal to foreign unit labor costs. Accordingly,
any commodity z will be produced at home if
* *
(2) a (z) w < a (z) w
or
(2') oj < A(z)
where
*
(3) co = w/w
is the ratio of our real wage to theirs (our "double-factorial terms of
trade"). It follows that for a given relative wage co the home country
will efficiently produce the range of commodities
(4) < z < z(w)
,
where, taking (2 1
) with equality defines the borderline commodity
(5) z" = A
_1
(oj) ,
A ( ) being the inverse function of A( )
.
- 5 -
By the same argument the foreign country will specialize in the
production of commodities in the range
(4') z(00) < z < 1.
The minimum cost condition determines the structure of relative prices.
The relative price of a commodity z in terms of any other commodity z',
with both goods produced in the home country, is equal to the ratio of home
unit labor costs:
(6) P(z)/P(z') = wa(z)/wa(z') = a(z)/a(z') ; z < z, z* < z.
The relative
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