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

G_i       = Gi  = -μf ^ttLi

(1+ β + δ) - ψi   φi(ψi)   ψiΦβψi)^,

_f _   c_μμf^tt    fl - Φ⅛Λ _l _ _ω fl - Φ⅛Λ _l

ⁱ   ψi [(1+ δ)+ ψi](^ Φ‰) Jⁱ ( φi(ψ.) J ^i,

(Allb)

where:
c                                          c                 c..μf^tt

"-    ^{l + β + δ}) - ^ψi,    ^ω! W = ψi     ^f . ψ_j ,

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 (W^l - Φ*^cy) L₁ + ⅛ (ψ₂)  ^l - фУ) L₂ = ao,   fc + L₁ + L₂ = ko,

V Φ^z(ψι) }               V Φ4Ψ2) }

(Al2a)

so that Li, L2 equals:

Φ⅜1)Φ⅜2) [-(a - ao) + ω^γ (ψ2) / ;  (k - ko)

Ω1 (ψi) Φ^r(ψ2) [l - Φ^r(ψ1)] - Ω2 (Ψ2) Φ^r(ψi) [l - Φ^r(ψ2)]

∣Φ^r(ψ1)Φ^r(ψ2)(a - ao) - Ω1 (ψι) Φ^r(ψ2)[l - Φ^r(ψι)](fc - ko)]

Ω1 (ψι) Φ^r(ψι) [l - Φ^z(ψι)] - Ω2 (ψ2) Φ^r(Ψι) [l - Φ^r(Ψ2)]

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.

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