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

5.5. Solution for (φ,a,μ,n) in the Small Open Economy

The general stable solution to the differential equation system (3.9a) is represented by the
following expressions:

φ = φ + M₁e^θrt + M₂e^θ2^t                       (A13a)

a = a ■ A₁e^θ1^t + A₂e^θ2^t                           (A13b)

μ = μ + P₁e^θ1^t + P₂e^θ2^t                          (A13c)

n = n + Q1e^θ1t + Q2e^θ2t

where Mj, Ni, Pi and Qi, i = 1, 2 are constants (eigenvectors) corresponding to the stable
eigenvalues θι and θ₂ of the small open economy and where (φ, a, μ, n) are the steady-
state solutions derived from the system (3.8a)-(3.8d). Since only two of these constants

are independent, the first step in obtaining the complete solution is to solve M_i, N_i, P_i in
terms of Qi, i = 1, 2. These relationships, using (3.9a) and (A13a)-(A13d), are calculated
from the homogeneous system:

(J^soe - θl)x =

where x = (M_i, N_i, P_i, Q_i)^,and where the constants in the small open economy (soe) for

i = 1, 2 are written as:

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