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

which implies that we can rule out the case in which all the eigenvalues are positive. Thus,
the equilibrium of (2.15) is a saddlepoint with two negative and two positive eigenvalues
ordered according to:

ωι < ω2 < 0 < ω3 < ω4.

Using standard methods, we can solve (2.15) for the paths of (φ, a,μ, fc). This procedure
is outlined in the appendix. While a detailed analysis of the solution paths of (φ, a, μ, fc)
is beyond the scope of this paper and is left for future work, the methods used by Eicher
and Turnovsky (2001) can be employed to do so.

We next investigate the implications of status preference on the long-run equilibrium
of the economy. To do so, we choose a convenient specihcation of U(c + a, s), similar to
that employed by Rauscher (1997), in which own consumption (inclusive of its durable
stock) is additively separable from status:¹²

^{u (c + a},s⁾ = ⁽¹ - -) ^{1 (c + a)1 γ +} η_s(j^c + °_a

We interpret the parameter η as a measure of the “importance” of status for consumer-
producers, or the as the “degree” of status preference. Under the specihcation (2.17), the
steady-state condition (2.14a) becomes:

K¹ + δ)a]^-γ + '     =(β + δ)φ.

(1 + o)a

Differentiating (2.14a') and (2.14b)-(2.14d) with respect to η, we calculate the following

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∂^φ = (1 + β + δ)

∂η

¹²Rauscher (1997) restricts his attention to non-durable consumption. In addition, we retain in this part
of the paper the general specification of the disutility of work effort V(Z) stated in (2.2) and (2.3a). The
conditions γ > 0, η > 0, in (2.17) guarantee c_μ < 0, which is a sufficient condition, given the other model
assumptions, that the equilibrium of (2.15) is a saddlepoint.

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