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

We choose the following normalisation¹⁴ in order to simplify the wage equation and

the manufacturing price index:

β=—
σ

1

α = —
σ

(24)

From the pricing rule equation we get:   p_i = w_i and n_i = L_i. It is possible to rewrite

the price index as:

P=[ L{w∖^σ + L2 w' ^σφ ] '~^σ

P =[Lw2^σ> + L₂w2^{l σ}]^1-

(25)

and the wage equation as

ɪ ɪ

W1 =(σ-1)μ^σ [Y1 P1^σ-1 + Y₂P2^σ-1φ]^σ

ɪ ɪ

w2 =(σ -1) μ^σ [Y1 P1^σ-1φ + Y₂P2^σ-1 ]^σ

(26)

where φ = T ^σ = 1∣τ^{σ 1} (remember σ > 1). The parameter φ which is a function of the trade
costs can be interpreted as a parameter reflecting freeness of trade, ranging in between zero
for very high trade costs when τ →∞ (autarky), and one in the case of no trade costs, i.e.
τ = 1.

¹⁴ The scope of these normalisations, widely used in this literature, is to shift the analysis to the number of
manufacturing workers and their wages in each region in order to study the equilibria in the model and their
stability.

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