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

intertemporal equilibrium, is given below in the appendix. Examining the steady-state
system in (A7a)-(A7c), it is clear that the per-capita values of (c, a, ŋ are independent of
the parameters of the instantaneous utility function U (c + a, s'). Indeed, they are solely a
function, as in the standard neoclassical framework without status preference, of the time
rate of preference β and the properties of the per-capita production function y = f (fc).
With respect to the steady-state equilibrium, shifts in the status parameter η only influence
the values of the costate variables ft and φ>.¹⁵ Nevertheless, changes in the importance that
status consciousness individuals place on the relative consumption of durable goods do
affect, through their influence on the values of c_/( and μ, the stable speeds of adjustment
of the economy toward steady-state equilibrium. Investigating the relationship between η
and the stable eigenvalues, denoted ψι and ψ2 in the special case of fixed employment, is
the focus in this part of the paper.

To do so, we choose the following very simple numerical parameterization of the neo-
classical economy with durable goods:

β = 0.04,      δ = 0.10,      y = fc⁰∙³⁶

Substituting these values in the steady-state equilibrium conditions (A7b, c), we obtain
the solutions for the long-run stocks of physical capital and durable goods and the (flow)
of durable consumption (=output):

~

1 = 31.0,     a = 34.4,     c = y = 3.44.

In this exercise we retain the parameterized functional form for U(c + a, s) given in (2.17)
and specify two alternative values of the preference parameter γ: γ = 2.5 and γ = 0.4.¹⁶

¹⁵Using the parameterized instantaneous utility function (2.17) and differentiating (A7a) with respect
to η, we And:

— = (1 + β + δ)^-1 — = -,----^-P--ʌ- > 0.

∂η                 -η (β + δ) (1 + δ) a

¹⁶The available empirical evidence supports an estimate of γ that is closer to 2.5 to 0.4.

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