Exceptional Argentina Di Tella, Glaeser and Llach - Thomas Piketty

L λ = m
L
K κ = m
K
That is, λ is the share of workers employed in the manufacturing sector and κ is the share of
units of capital employed in that sector. We seek to characterize the steady-state ratios κ and λ
as functions of the technological and preference parameters, factor endowments and exogenous
variables: terms of trade π and the ad-valorem tax rate on exports τ .
Since land is used only in the primary sector, its outside opportunity cost is zero. Given our
technological assumptions, the marginal product of the first infinitesimal unit of capital employed
in the primary sector is infinite; therefore κ < 1, i.e., the primary sector always employs some
capital.
The demand for capital in the primary sector solves the following first-order condition for profit
optimization of the representative firm in the sector:
⎛ 1 ⎞
α⎜
⎟
⎝1−κ
⎠
1−α
p
d
a
=
ra
K
α 1−
K T
α
A
(1)
d
where p
a
is the domestic price of the agricultural good and r
a
is the return to capital in
the primary sector. Similarly, the demand for land in the primary sector, given the land rental rate,
q , is given by:
α qT
1 − p d a
=
(2)
α 1−α
K T A
( α )( 1−κ
)
If some capital is also employed in the secondary sector, then the demand for capital in the
secondary sector satisfies:
⎛ λ ⎞
β⎜
⎟
⎝ κ ⎠
1−β
ϒp
d
m
rm
K
= (3)
α 1−α
K T A
d
where p
m
is the domestic price of the manufactured good and r
m
is the return to capital
in the secondary sector. The demand for labor in the sector is given by:
where w is the wage rate.
β
⎛ κ ⎞ Lw
(1 − β ) ⎜ ⎟ ϒp d m
=
(4)
α 1−α
⎝ λ ⎠ K T A