DURABLE CONSUMPTION AS A STATUS GOOD: A STUDY OF NEOCLASSICAL CASES



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
L
i 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) = a
o 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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