where n is the number of varieties produced, mi consumption of each variety and ρ a
parameter representing the intensity of the “love for variety” in the manufacturing sector. The
constant elasticity of substitution between any two varieties is σ ≡ 1/ (1 - ρ), (σ >1).
The consumers maximize (1) subject to the following budget constraint:
n
PAA + Σ mP = Y
1
where Y is income and Pa, Pi respectively the prices of the homogeneous product and prices
for each variety of the manufacturing aggregate.
A two stage budgeting procedure can be applied. The first step in the consumer’s problem is
to choose each mi in order to minimise the cost of attaining a given M:
σ
n
÷ σ-1
∑ m σ
σ-1
min ∑ pimi s.t. M =
1
-1/σ
-, p- , l,
=τπ- = — therefore
j-σ Pj
m m m .....mi
the first-order conditions. imply —-
mj
( P-
t p
mj
and by substitution of this last equation in the budget constraint we obtain:
n n
∑p
ʌɪ-ɑ
σ-1
mj ~σ~
σ
σ-1
which implies:
10
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