The Impact of Optimal Tariffs and Taxes on Agglomeration

3 Equilibrium

Two kinds of equilibrium are determined by the model, a short-run equilib-
rium and a long-run equilibrium. The short-run equilibrium is characterized
by a given distribution of skilled workers, L and 1 - L, on the domestic and
foreign region. Then, the model ab ove determines prices and wages clearing
product and labor market. If these short-run prices and wages imply an in-
terregional real wage difference skilled workers face an incentive to migrate
to the region with higher earnings. Therefore, the long-run equilibrium is
reached if no incentive for migration exists anymore. This can be the case
either if real wages are equalized or if all skilled locate already in one region
(L=0 or 1 - L=0) such that any further migration is impossible.

Calculating the real wage difference, which is the crucial determinant
of migration, requires first the derivation of nominal wages. They can be
determined from the product market equilibrium by equalizing supply and
demand. Each firm produces an equilibrium amount of σw and faces foreign
and domestic demand for its variety which can be derived from the utility
function (1). Equalizing supply and demand yields that product market
equilibrium is guaranteed if:

σw = γYP ^σ-1 + Θ*γY *P *^σ-1

σw = ΘγYP ^σ-1 + γY *P *^σ-1

with Y and Y * defined by (7) and Θ defined by (3). Both equations depend
Iinerarly on the wage rates w and w*. Solving the system yields:

σγ ^[P^1-σTΘ* + P*^1-σT*^] + γ2(1 -L) [ΘΘ* - 1]

w = (σP*^1-σT* - γ(1-L))(σP^1-σT - γL) - γ2ΘΘ*(1 -L)L

(9)

σγ ∣ΘP*^1-σT* + P1^-σT^] + γ2L [ΘΘ* - 1]

w = (σP*^1-σT* - γ(1-L))(σP ^{1 σ}T - γL) - γ2ΘΘ*(1 -L)L

with P, T, Θ and the corresponding foreign variables defined in (3) and (7).

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