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

The stability of the symmetric equilibrium is given by the relative strength of these
agglomerative and dispersive forces at work. For sufficiently high trade costs, imported
manufactured varieties are so expensive that it is profitable to have a symmetric equilibrium.
Conversely, at low trade costs the symmetric equilibrium is always unstable. Regional
economic integration has no impact on the location of industry until a critical level of
freeness of trade is reached. When this threshold of freeness of trade, the φ-break, is reached
the symmetric outcome becomes unstable since workers have an incentive to migrate. The
skill premium effect is peculiar to high-skilled workers, therefore the incentive to migrate and
the relative φ-break will be higher for this type of workers.

Formally a stable equilibrium is any point where:

(i)             the regional wage differentials are zero and {∂ω^u / ∂U_i, ∂ω^u / ∂S_i, ∂ω^s / ∂S_i, ∂ω^s / ∂U_i}

are all strictly negative. This is the case of a stable symmetric equilibrium where
S_i = U_i = 1/2;∀i∈ {1,2}. A positive increase in the quota of low or high-skilled workers in
the region, negatively affects the real wage differential. Agglomerative forces are dominated
by dispersive forces, therefore as a consequence counter-migration of manufacturing workers
will re-equilibrate the size of the regional manufacturing labour force;

(ii)            ω^u > 0, ω > 0 and S = U = 1 (or vice versa ω^u < 0, ω^s < 0 and S = U = 0), in the

case of a core-periphery equilibrium. The entire population of low and high-skilled workers
will be concentrated in the core. In this case we have the condition that in the core region
{∂ω^u / ∂U_i, ∂ω^u / ∂S_i, ∂ω^s / ∂S_i, ∂ω^s / ∂U_i} are all strictly positive.

(iii)            ω^u = 0, ω^s > 0 with S_i = 1 and U_i = 0 when a positive self-selection equilibrium is a

stable outcome. In this case high-skilled workers will be concentrated in the core region,

¹⁵ This adjustment mechanism assumes that entry and exit of firms occurs infinitely faster than migration. Firms
are therefore always in equilibrium.

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