The second step of the consumer’s problem is to choose the optimal allocation of income
between A and M so that the utility is maximised
Maximising U = MμA1 μ subject to. PM + PaA=Y , gives us the uncompensated demand
for A and for each variety, mj :
A = (1 - μ )Y / Pa
(7)
mj =
-σ
p~r^μ μ
P-(σ-1) ‘
(8)
From the consumer’s utility maximisation problem we can also express the indirect utility
function, substituting (7) and (8) in (1) yields:
U = μμ (1 - μ )1-μY
PμP (1^μ)
(9)
the term PμPA°^μ) can be interpreted as the regional cost-of-living index in the economy.
What is the welfare effect of an increase in the number of variety? Assuming that all varieties
are available at the same price pi = pj, ∀j ∈ [1,..., n ], we can rewrite the manufacturing goods
price index as:
1-σ
Pr
1
1-σ
1
= Pn1-σ
12
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