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



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



(6)


11




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