Transcript The Ricardian Model with a Continuum of Goods a(z)=unit labor requirement at home a*(z)=unit labor requirement abroad A(z)=a*(z)/a(z) ratio of Home to Foreign productivity of labor.

The Ricardian Model with a
Continuum of Goods
a(z)=unit labor requirement at home
a*(z)=unit labor requirement abroad
A(z)=a*(z)/a(z)
ratio of Home to Foreign
productivity of labor in good z.
A(1)>A(2)>A(3)>...
relative
wages
w/w*
A(z)
z
z
Which goods will be produced at home?
Z is produced at Home if wa(z)<w*a*(z) or
w/w*<a*(z)/a(z)=A(z)
for z : A( z)  w / w *
Demand Side
G(z ) = fraction of income spent on Home-made goods
 b(1)  b(2)  ... b( z)
wL  G( z)(wL  w * L*)
domestic
income
world
income
w
G( z ) L *
L*

 B( z )
w * 1  G( z ) L
L
relative
wage
L*
B( z )
L
w/w*
A(z)
z
z
GAINS FROM TRADE
I. Autarky
Country H
p A ( z )  wA a ( z ) w
wA
1

pA ( z)
a( z )
relative
wage
L*
B( z )
L
w/w*
A(z)
z
II. Free Trade
z
Country H’s Exports
pT ( z )  wT a( z )
wT
1
wA


pT ( z ) a( z ) p A ( z )
Country H’s Imports
pT ( z )  wT * a * ( z )
wT
wT
1
wA



pT ( z ) wT * a * ( z ) a( z ) p A ( z )
Country F’s Exports
pT * ( z )  wT * a * ( z )
wT *
1
wA *


pT ( z ) a * ( z )
pA * ( z)
Country F’s Imports
pT ( z )  wT a( z )
wT *
wT *
1
wA *



pT ( z ) wT a( z ) a * ( z ) p A * ( z )
An increase in Foreign Productivity
B( z )
2
L*
L
1
A1 ( z)
A2 ( z)
z
Home is better off because:
(1) consistent Home exports
p(z)=wa(z)
p’(z)=w’a(z)
(2) consistent Home imports
p(z)=w*a*(z)
p’(z)=w*’a*’(z)
w w'

p p'
w
w
1

p( z )
w * a * ( z)
w'
w'
1

p'
w*' a*'( z )
w/w* falls proportionally less than a*(z)
w
w'

p( z ) p' ( z )
Transitional goods
p(z)=wa(z)
w
1

p( z ) a( z )
p’(z)<w’a(z)
w'
1

p' ( z ) a( z )
w

p( z )
w'
p' ( z )