Exceptional Argentina Di Tella, Glaeser and Llach - Thomas Piketty

Short Run
In the short run, all factors of production are reallocated only within the sector where they were
previously employed. Given the Cobb-Douglas production function and the zero profit condition,
we know that the flow of earnings accruing to landlords is equal to a fraction of the value of the
total production of the primary sector. Given that land is not reallocated, the percentage increase in
the rental rate for land is equal to:
t = a a
+ y a
Since, in the short run, the allocation of capital in the primary sector does not change, the following
capital rent equation holds:
k
a
= aa
+ ya
Similarly, in the manufacturing sector, the following capital rent and wage equations hold:
k = m + y
m
m
m
l
m
= mm
+ ym
Finally, total expenditure on services has to equal the total wages paid in the sector. Noting that the
production of services has to equal consumption, we find that:
l
n
= cn
+ nn
Let us now consider the effects of an increase in the international price of the primary good. Given
that there is no factor reallocation, the output of the three goods remains constant. Without
government intervention, the domestic price of the primary good and the return to the factors
employed in the primary sector increase in proportion to the increase in the terms of trade. Since
the agents owning those resources are wealthier, they increase their demand for services, which
drives up wages in the tertiary sector. Workers in the service sector enjoy an increase in their
nominal wages that is proportional to the economy's degree of specialization: χ
a
. Finally, the
factors employed in the manufacturing sector do not receive any increase in their remunerations.
The consumer price index rises, since the prices of both the primary and the tertiary goods
increase. Proposition 2 summarizes these results.
Proposition 2 In the short run, an increase in the international price of the agricultural
good (i.e., an improvement in the terms of trade) raises the real remuneration received by
landowners, capitalists in the primary sector and service workers. However, it reduces the real
remuneration of workers and capitalists in the manufacturing sector.
Notice that the real effects of an increase in the international price of the agricultural good are
identical to those of a decrease in the international price of the manufactured good. Agents may
demand policies that will protect them from changes in international prices. Proposition 3 deals
with the effects of taxes on exports.