where x = (Ei, Fi, Gi, Li)tand where the constants for i = 1, 2 are written as
Gi = Gi = -μf ttLi
(1+ β + δ) - ψi φi(ψi) ψiΦβψi),
f _ cμμftt fl - Φ⅛Λ l _ ω fl - Φ⅛Λ l
i ψi [(1+ δ)+ ψi](^ Φ‰) Ji ( φi(ψ.) J i,
(Allb)
where:
c c c..μftt
"- l + β + δ) - ψi, ω! W = ψi f . ψj ,
are the solution coefficients for the Hxed employment case. To solve for the constants
Li and complete the solution of (AlOa)-(AlOd), we use the fact that the stock of durable
goods and physical capital evolve continuously from their initial conditions, a(O) = ao and
к (O) = ko. From (AlOb, d) this gives us the two equation system
'a + Ωξ (Wl - Φ*cy) L1 + ⅛ (ψ2) l - фУ) L2 = ao, fc + L1 + L2 = ko,
V Φz(ψι) } V Φ4Ψ2) }
(Al2a)
so that Li, L2 equals:
Φ⅜1)Φ⅜2) [-(a - ao) + ωγ (ψ2) / ; (k - ko)
Ω1 (ψi) Φr(ψ2) [l - Φr(ψ1)] - Ω2 (Ψ2) Φr(ψi) [l - Φr(ψ2)]
L2 =
∣Φr(ψ1)Φr(ψ2)(a - ao) - Ω1 (ψι) Φr(ψ2)[l - Φr(ψι)](fc - ko)]
Ω1 (ψι) Φr(ψι) [l - Φz(ψι)] - Ω2 (ψ2) Φr(Ψι) [l - Φr(Ψ2)]
(Al2b)
Substitution of equations (Al2b) into (Allb) and the resulting expressions into (AlOa)-
(AlOd) yield the stable solutions for (φ, a, μ, k) in the Hxed employment case.
32
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