two positive eigenvalues ordered according to:
ψl < ≠2 < 0 < Ψ < ≠4∙
5.4. Solution for (φ, a, μ, к) in the Fixed-Employment Economy
The general stable solution to the differential equation system (A9) is represented by the
following expressions:
φ = φ + Eleψ1t + E2eψ2t (A10a)
a = a ■ Fleψ1t + F2eψ2t (A10b)
μ = μ + Gleψ1t + G2eψ2t (A10c)
к = fc + Lleψ1t + L2eψ2t
(A10d)
where Ei, Fi, Gi and Li, i = 1, 2 are constants (eigenvectors) corresponding to the stable
eigenvalues ψl and ψ2 of the fixed employment economy (I = I) and where φφ, a, μ, /ŋ are
the steady-state solutions derived from the system (A7a)-(A7c). Since only two of these
constants are independent, the first step in obtaining the complete solution is to solve
Ei, Fi, Gi in terms of Li, i = 1, 2. These relationships, using (A8) and (AlOa)-(AlOd), are
calculated from the homogeneous system:
(Jz - ψl)x
/ |
(1 + β + S) - ψi -cμ 0 |
0 - [(1 + δ} + ψi] 0 |
-1 - ψi |
0 0 -ff " |
∖ |
I |
Ei Fi Gi |
∖ | |
∖ |
T |
1 |
'k |
β - ψi |
) |
I |
Li |
/ |
0 ■ | |
0 | |
0 |
(A11a) |
∖0 J |
31
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