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



two positive eigenvalues ordered according to:

ψl 2 < 0 < Ψ 4

5.4. Solution for (φ, a, μ, к) in the Fixed-Employment Economy

The general stable solution to the differential equation system (A9) is represented by the
following expressions:

φ = φ + Eleψ1t + E2eψ2t                        (A10a)

a = a ■ Fleψ1t + F2eψ2t                           (A10b)

μ = μ + Gleψ1t + G2eψ2t                        (A10c)

к = fc + Lleψ1t + L2eψ2t

(A10d)


where Ei, Fi, Gi and Li, i = 1, 2 are constants (eigenvectors) corresponding to the stable
eigenvalues
ψl and ψ2 of the fixed employment economy (I = I) and where φφ, a, μ, /ŋ are
the steady-state solutions derived from the system (A7a)-(A7c). Since only two of these
constants are independent, the
first step in obtaining the complete solution is to solve
E
i, Fi, Gi in terms of Li, i = 1, 2. These relationships, using (A8) and (AlOa)-(AlOd), are
calculated from the homogeneous system:

(Jz - ψl)x

/

(1 + β + S) - ψi

-cμ

0

0

- [(1 + δ} + ψi]

0

-1

- ψi

0

0

-ff "

I

Ei

Fi

Gi

T

1

'k

β - ψi

)

I

Li

/


0

0

0

(A11a)

0 J


31




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