Ni =
cμμα
,/
θi [(1 + δ) + θi
1(i
Φsoe(θi)
Φsoe(θi)
) Qi = ΩSoe
(i
Φsoe(θi)
Φsoe(θi)
)q*,
(A14b)
where:
e.. μα
φ1'β+δ)- θi, ωs°∙ θθi [ θil ∙
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 — Φsoe(θ1)∖ , /ɪ - Φsoe(θ2)∖
h + Ωs1oe (θι) ——-ʌ-ɪʌ Qi + Ωs2oe (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:
Φsoe(θ1)Φsoe(θ2) [-(a - ao) + Ωs20e (θ2) ./Z ' (h - no)]
Q1 = Ωs1oe (θ1) Φsoe(θ2) [1 - Φsoe(θ1)l - Ω2oe (θ2) Φsoe(θ1) [1 - Φsoe(θ2)l,
_ [Φsoe(θ1)Φsoe(θ2)(a - ao) - Ωs1oe (θ1) Φsoe(θ2)[1 - Φsoe(θ1)l(n - no)l
Q2 = Ωs1oe (θ1) Φsoe(θ1) [1 - Φsoe(θ1)l - Ωs2oe (θ2) Φsoe(θ1) [1 - Φsoe(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.
34
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