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
σ1/ (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

÷  σ-1

m σ


σ-1


min pimi s.t. M =

1

-1/σ

-, p-          , l,

=τπ- = —  therefore

j   Pj


m m m .....mi

the first-order conditions. imply —-
mj

( P-
t p


mj


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

n   n

p


ʌɪ-ɑ


σ-1
mj ~σ~


σ

σ-1

which implies:


10




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