Exceptional Argentina Di Tella, Glaeser and Llach - Thomas Piketty

K
c a
= 1−
α 1−α
T
A
( κ ) α
Using 1,2,4,5,6 and 8, we derive the following values for λ
aut
, κ
aut
and the autarky relative
domestic price p
aut
:
κ
λ
aut
aut
p
aut
φmβ
= (9)
φmβ
+ φaα
φm(1−
β )
=
φ (1−
β ) + 1−φ
−φ
m
β
=
α
β
α
( φ β + φ α )
m
( )
a
a
m
⎛
⎜
⎝
α −β
1−α
φa
(1−
β )
(( 1−φ
− βφ ))
a
m
⎞
⎟
⎠
1−β
ϒ
For autarky to be a steady-state equilibrium,
p
aut
has to satisfy:
( 1 −τ
) ≤ p ≤ π
π
aut
Otherwise, there are arbitrage opportunities for exporting and importing goods.
7.1.2 Equilibrium under Specialization
A specialized economy imports the secondary good and produces and exports the agricultural
good. The economy is specialized in the primary sector if there is no capital or labor employed in
the secondary sector; therefore: κ = λ = 0 . For this to be an equilibrium, the wages and capital
rental rate paid in the other sectors of the economy must be greater than what can be profitably paid
by the secondary sector.
β
1−β
⎡⎡1−
β ⎤ ⎡ β ⎤ ⎤
β 1−β
−1
d
mcm = ⎢⎢
⎥ + ⎢ ⎥ ⎥r
w M ≥ p m
(10)
⎢⎣
⎣ β ⎦ ⎣1−
β ⎦ ⎥⎦
d
Using 1,5, 7 and 10, setting λ = κ = 0 ,
m
pm
specialization is an equilibrium if:
β
1−β
⎡⎡1−
β ⎤ ⎡ β ⎤ ⎤
β
⎡
ϒ ≤ ⎢⎢
+ ⎥α
⎢
⎢⎣
β
⎥ ⎢
β
⎥
⎣ ⎦ ⎣1−
⎦ ⎥⎦
⎣
d
p = and pa
( 1−τ
) p a
= , we obtain that
( 1−φa
−φm
)
( φ ( 1−τ
) + φ )
m
a
⎤
⎥
⎦
1−β
( 1−τ
)π
Otherwise, there will be diversification. Naturally, ceteris paribus, for favorable enough terms of
trade, the economy will specialize in the production of primary goods.
7.1.3 Diversification and Trade
Using 1,2, 4,5, 7 and imposing
variables κ and λ .
d
p = p and p ( 1−τ
) p , we solve for the endogenous
d
m
m
a
=
a