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



Equilibrium of the Goods Market

In the closed economy households consume and save a constant fraction of their
income and the equilibrium for the goods market is characterized by

I = S = βY

(19)


with S as savings and s as the saving rate.

4 Steady-State Solution

Analyzing the steady-state solution, the long-run equilibrium for the labor market
and the steady-state for the goods market are derived separately and can be charac-
terized by a efficient factor allocation function respectively a balanced accumulation
function.

Steady-State of the Labor Market

The steady-state of the labor market is deduced by using the flow condition of
the labor market. This condition requires that the inflows are equal to the outflows
and, therefore, the change in employment is zero:

E = O « V1-βVλ 1 = vE.


(20)


Furthermore, due to neglecting on-the-job-search, the flow of new created vacancies
is identical to the employment flow, i.e. V = E = O, and because of a constant
labor force, the employment and unemployment levels are constant in the long-run
equilibrium, i.e. E= — Ù = O. These conditions imply that steady-state labor
market tightness is also constant, i.e. 0 = O, and that the steady-state growth rates
of unemployment and vacancies are zero, i.e. V = Ù = O.

Using these conditions, the efficient factor allocation function for the stationary
labor market can be derived:12

θβ =


ʌo (1 — ɑ)(l — β )(1 — ω)


<⅛0λ[(ɪ) k“-1 + v — λ


ka =: Φ1(k).


(21)


It shows all combinations of capital intensity and labor market tightness that reflect
the long-run equilibrium of the labor market. The steady-state of the labor-market
12For the detailed derivation of the efficient factor allocation function see appendix.

18



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