well as intermediate goods and making a profit-maximizing investment. To find
such equilibrium we solve the model backwards. Each Y -firm chooses among
the different modes by computing the corresponding payoffs backwards given
an expectation on the choices made by all other Y -firms. These choices are
summarized by a certain value for the market potential A:
L
n)/px
(3)
A(m, n) = —,---:-----,----~~.-----
n/po + m/pE +(1- m
where m and n are the numbers of firms adopting modes O and E respectively.
Therefore, the conjectures made by firms are expectations on the market po-
tential variable A. Given A, investments, prices and quantities of final outputs
and intermediate inputs can be readily obtained.
4.1 Final exports
When a Y -firm decides to serve the market through the export of the final good
(mode X), intermediate production and transformation are both performed
abroad. Recall that in this case the intermediate input transforms one-to-one
into final output. Moreover, due to iceberg trade costs, an amount x of inter-
mediate input satisfies a final demand equal to xτ . The problem of the Y -firm
can then written as follows:
(4)
max∏x (x) = Πχ (x) = λ∕Aτ x — x,
x
where π and Π denote operating and total profits respectively. The profit max-
imizing intermediate production is then:
Aτ
~
(5)
The corresponding price can be obtained by substituting (5) into the inverse
1
demand function p = (A/y)2 implied by (2):
2 la∖
Px = - (6)
τ
while the associated profits are:
Aτ
(7)
∏x = ∏x = (px τ — 1)xχ = —
As it is intuitive, these results show that, under the final export mode,
outputs and profits fall while prices rise as trade costs increase (τ decreases)
and the market potential rises.