Regional Intergration and Migration: An Economic Geography Model with Hetergenous Labour Force

Pj
m_i =----j-----M

^j                   σ

^ V 1-σ 1^σ-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 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:

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