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 + M1eθrt + M2eθ2t                       (A13a)

a = a ■ A1eθ1t + A2eθ2t                           (A13b)

μ = μ + P1eθ1t + P2eθ2t                          (A13c)

n = n + Q1eθ1t + Q2eθ2t

(A13d)


where Mj, Ni, Pi and Qi, i = 1, 2 are constants (eigenvectors) corresponding to the stable
eigenvalues θ
ι 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 Mi, Ni, Pi in
terms of Q
i, i = 1, 2. These relationships, using (3.9a) and (A13a)-(A13d), are calculated
from the homogeneous system:

(14a)


(Jsoe - θl)x =

( (1 + β + δ) - θi        0             -1             0

M Mi

0

-cμ         - [(1 + δ) + θi]        cμ               0

Ni

0

0             0           -θi         -μα

Pi

0

-cμ               -1        - ( ʌ''lμ - cμ} (в + α'n} - θi J

Qi J

10 J

where x = (Mi, Ni, Pi, Qi),and where the constants in the small open economy (soe) for

i = 1, 2 are written as:

Mi =


Pi

(1 + β + δ) - θi


Pi
Φsoei)


-μ<QQi.
θiΦoei),


33




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