where к is a preference parameter1. Following Obstfeld and Rogoff (1998), Cj is an index
of consumption of Home and Foreign goods (for a representative agent) defined as follows:
r,7 ra-7
cj,H Cj,F
7Z(1 - 7)1-7
with
Cj,H =
CjF =
(7)
λ f1 λ-1
I (Cj,H(z)) λ
Jo
λ
λ-1
dz
P λ-1
I (Cj,F(z)) λ dz
Jo
λ
λ-1
, λ > 1.
It is clear that the elasticity of substitution across brands produced within a country is λ,
while the elasticity of substitution between Home and Foreign goods is I.2
The optimal consumption allocation of a representative individual across the
and Foreign good is respectively
Home
CjH=7 (pPh)
1 Cj ; Cj,F = (1 - 7) (Pf)
1
Cj
where
P = ph /F
H F
(2)
is the consumer price index (CPI)
and
Ph =
1 1 Ph (z)
L 7 Jo
1-λdz
1
1-λ
; pf =
ɪ [1 Pf(z)1-λdz
1 - 7 Jo
1
1-λ
,
(3)
are the Home and Foreign producers index, respectively.
2.3 Individual budget constraints
To complete the qualification of the individual’s problem, we consider the agent’s budget
constraint. Each j-th individual draws a salary for the labor type supplied to firms which,
in turn, distribute dividends evenly among their owners (all of the workers). Markets are
1Two conditions are to be satisfied by the utility function. The first is the disutility of work (^j < O,
log Lj ) < O, implying that log Lj < 1). The assumption к > a guarantees that in equilibrium O < log Lj < 1
holds (see equation (38)).
....... , „4 .. .. ., .. . ..... .. ..... ∕δ2V,- b
which implies logLj > O). The second is the concavity of the utility function in leisure ( £ = - ɪɪ(1
J J
2The parameter λ > 1 is the price elasticity of demand faced by each monopolist. The inequality
constraint ensures an interior equilibrium with a positive level of output. This relationship will become
apparent later when we solve for the optimal price setting.
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