Pj
mi =----j-----M
(3)
j σ
^ V 1-σ 1σ-1
Σ P
L i J
Equation (3) is the compensated demand function for the jth variety.
The minimum cost of attaining a fixed amount of M, can be expressed by using equation (3)
and summing over all the varieties as:
1
(4)
where the second part of the expression on the right-hand side can be easily interpreted as the
manufactured goods price index:
P = ∑ p^σ
1
1-σ
(5)
P measures the minimum cost of purchasing a unit of the composite index M, and can be
thought of as an expenditure function.
Demand for each variety j can be written as:
mj
Pj
P
-σ
(6)
11
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