Unemployment cycles

setting C 3 = 0, and we obtain:
⎡
⎢
⎣
u t − u ∗ i
γ t − γ ∗ i
θ t − θ ∗ i
⎤
[ ⎥
⎦ = [v(λ C1 exp(λ 1 t)
1) v(λ 2 )]
C 2 exp(λ 2 t)
=
⎡
⎢
⎣
⎤
v 1 (λ 1 ) v 1 (λ 2 ) [ v 2 (λ 1 ) v 2 (λ 2 ) ⎥ C1 exp(λ 1 t)
⎦
C 2 exp(λ 2 t)
v 3 (λ 1 ) v 3 (λ 2 )
]
]
Productivity Induced Dynamics
˙u = δ(1 − u) − um(θ(Ω)) (47)
˙γ = um(θ(Ω)) − (δ + λ(Ω)m(θ(Ω)))γ (48)
[ (
m(θ(Ω))u
λ
˙θ(Ω) =
× − θ(Ω)c ) (
c(1 − η(θ(Ω)))(u + λ(Ω)γ) u m(θ(Ω)) + J − ˙u γ )
u + ˙γ − (py − w(Ω))
(
c u + λ(Ω)γ
+
− λ(Ω)γ )
]
J (r + δ + λ(Ω)m(θ(Ω))) + (1 − π(Ω))∆ θ (Ω). (49)
q(θ(Ω)) u u