Qualification-Mismatch and Long-Term Unemployment in a Growth-Matching Model

φ

Figure 3: Steady-State of the Economy.

After deriving the equilibrium conditions for the steady-state labor market re-
spectively for the steady-state goods market separately, both determine together the
overall steady-state, i.e. the efficient factor allocation function and the balance cap-
ital accumulation function simultaneously define the steady-state values for θ and k.
In Figure 3 the steady-state search equilibrium (θ , k) is graphed at the intersection
of both functions. Due to the shape of both functions the steady-state exists and is
unique.

Once the steady-state search equilibrium (θ , k) is determined, the steady-state
values for the matching probability p, the steady-state employment respectively un-
employment rate ë respectively й can be derived. The steady-state employment and
unemployment levels are fixed as well: E = e(θ)L and U = ü&)L. Furthermore,
steady-state labor market tightness determines the equilibrium unemployment du-
ration ë and the steady-state fraction of the long-term unemployed φ (see Figure
3).

Beside the determination of the steady-state labor market variables, the growth
and accumulation process is fixed. In the long-run equilibrium the capital stock,
the production and income levels grow with the rate of technical progress, i.e. K =
ʌ ʌ ʌ
.v = γ = л.

Stability of the Steady-State

The transitional behavior of the labor market tightness is characterized by the

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