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

is influenced by several exogenous variables and it will change when the exogenous
environment changes. In the (θ^, k) plane it has a positive concave shape.¹³

Furthermore, in the long-run labor market equilibrium the steady-state employ-
ment rate is given by¹⁴

Therefore, the employment probability depends positively on labor market tight-
ness θ and on the matching-probability p(θ) and negatively on the separation rate
v. The higher the separation rate, the lower the steady-state employment rate.
Furthermore, the steady-state unemployment rate is determined as well as

1 = e(θ) + _w(θ),

where the steady-state unemployment rate u(θ) is defined as u(θ) := U∕L.

Thus, the steady-state for the labor market is described by an efficient factor al-
location function that defines all equilibrium combinations of labor market tightness
and capital intensity.

Steady-State of the Goods Market

As common in neoclassical growth models, the long-run steady-state is charac-
terized by a constant capital intensity, i.e.

k = 0                                 (23)

The steady-state of the goods market can be described by a balanced capital accu-
mulation function :¹⁵

ʌ

θ^β = ʌ. k“ - ^{(1 + c,s)} ʌ k
c,∙<∣Λv                 ^s

This function shows all combinations of labor market tightness and capital intensity
characterizing the steady-state in the goods market.

Furthermore, in the (θ, k) plane the balanced accumulation function has - until
the maximum is reached - a positive slope, in the maximum a slope of zero and
behind the maximum a negative slope.¹⁶

¹³See appendix.

¹⁴See appendix.

¹⁰For a detailed derivation of the balanced accumulation fuction see the appendix.

¹⁶See appendix.

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