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

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

min ∑ p_im_i s.t. M =

1

m m m .....m_i

the first-order conditions. imply —-
^mj

and by substitution of this last equation in the budget constraint we obtain:

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