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

then

φ'₁'(k) < O

is implied. ■

Proposition 5 Using (1), (3) and (20), the steady-state employment rate e(θ) =
^{is im}p^lied.

Proof. Equation (20) can be written as

E = O ^ M = vE

and using (1) and (3), then

M* = VE

Mi — Me = vE
M _ M

p(θ)L = (v + p(θ)) Ê.

Therefore, e(θ) := = = follows. ■

Proposition 6 Using (2), (Ib), (8), (18), (19) and (23), the balanced accumulation

function θ^β = -⅛-

^d C_vQ XU

k^a

k-+=)λ^ =: φ_ι(k) is implied.

Proof. Using equations (18), (19) in efficiency units, then

x = (1 + cis') y + c_υv.

(27)

Define V := V∕ΛE and use (2) and (8), then

(Ê + v ) Λ

V = ʌ--J-θ^,.

(28)

Substituting (7b) and (28) in (27), then

у = ιu—

1 + C∕s

k^a

^λo

θ^β .

• ∙ Z ^ ^ ∖ ∙

Define k := K/ [ΛE], then k = K∕ΛE — ( Λ + EJ k. Use K = I = sY, i.e. use (19),
then