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

where:

e.. μα

^φ1'^β+δ)^- θi,      ^ωs°∙ ^θθi [           θ_il ∙

are the solution coefficients for the small open economy case. To solve for the constants
Qi and complete the solution of (A13a)-(A13d), we use the fact that the stock of durable
goods and net debt evolve continuously from their initial conditions, a(0) = ao and n (0) =
no. From (A13b, d) this gives us the two equation system

_z /ɪ — Φ^soe(θ₁)∖              ,    /ɪ - Φ^soe(θ₂)∖

h + Ω^s₁^oe (θι) ——-ʌ-ɪʌ Qi + Ω^s₂^oe (θ₂) ——-V² Q₂ = ao,    n + Qi + Q₂ = no,

^{1 V 1}' у  Φs°e(θ₁)   J ^{2       2 V 2,} у  Φs°e(θ₂)   ) ^{22 θ,                  22     θ,}

(A15a)

from which we solve Qi, Q2 as:

Φ^soe(θ1)Φ^soe(θ2) [-(a - ao) + Ω^s2^0e (θ2) ./Z ' (h - no)]
^Q1 = Ω^s₁^oe (θ₁) Φ^soe(θ₂) [1 - Φ^soe(θ₁)l - Ω2^oe (θ₂) Φ^soe(θ₁) [1 - Φ^soe(θ₂)l^,

_ [Φ^soe(θ₁)Φ^soe(θ₂)(a - a_o) - Ω^s₁^oe (θ₁) Φ^soe(θ₂)[1 - Φ^soe(θ₁)l(n - n_o)l

^Q2 = Ω^s₁^oe (θ₁) Φ^soe(θ₁) [1 - Φ^soe(θ₁)l - Ω^s2^oe (θ₂) Φ^soe(θ₁) [1 - Φ^soe(θ₂)l ■

(A15b)

Substitution of equations (A15b) into (A14b) and the resulting expressions into (A13a)-
(A13d) yield the stable solutions for (φ, a, μ, n) in the small open economy with an upward-
sloping supply function of debt.

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