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 ₊ E_le^ψ1^t + E₂e^ψ2t                        (A10a)

a = a ■ F_le^ψ1^t + F₂e^ψ2t                           (A10b)

μ = μ + G_le^ψ1^t + G₂e^ψ2t                        (A10c)

к = fc + L_le^ψ1^t + L₂e^ψ2t

where Ei, Fi, Gi and Li, i = 1, 2 are constants (eigenvectors) corresponding to the stable
eigenvalues ψ_l 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
Ei, Fi, Gi in terms of Li, i = 1, 2. These relationships, using (A8) and (AlOa)-(AlOd), are
calculated from the homogeneous system:

(J^z - ψl)x

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