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

According to (2.17), the expressions for c_μ and μ correspond to:

To calculate the stable eigenvalues ψι and ψ2, we substitute (2.19a, b)-(2.20), along
with the other relevant parameter values, into the appropriate elements of the Ja-
cobian matrix for the fixed employment economy, denoted by J^z. We then calculate
the eigenvalues of J^z, permitting the status parameter take on the following values:
η = (0.0, 0.2, 0.4, 0.6, 0.8,1.0). The results are given in Tables 1a and 1b, where we re-
port the absolute values, and, hence, the speeds of adjustment, of the stable eigenvalues,
I ψι I and I ψ₂ ∣∙¹⁷ We find in Table 1a for the case γ = 2.5 that greater values of η lead to
faster stable speeds of adjustment, although after η = 0.4, these increases are negligible.
In contrast, in Table 1b for the case γ = 0.4 higher values of the status parameter η result
in slower speeds of stable adjustment, although, as in Table 1a, the changes in ∣ ψι ∣ and
I ψ₂ I fall after η = 0.4. The reason for the distinct responses in Tables 1a and 1b is that
increases in η have opposite effects on the intertemporal elasticity of substitution—and,
thus, on the stable speeds of adjustment—depending on the value of the preference para-
meter γ. If consumer-producers have instantaneous preferences described by (2.17), then
the intertemporal elasticity of substitution, denoted by σ = σ(c + a), is equal to:¹⁸

(β + δ)c_μμ,     =   (c + a) ^γ + (c + a) ¹ η⅜^z(1)

^{(1 + β +} δ)^{(1 +} δ) à    [ɔ, (c + a)^-γ + (c + a)^-1 ηs'(1)j

¹⁷All numerical simulations are performed using Mathematica 4.1.

^l°If status depends on relative consumption, Fisher and Hof (2000a) show that the formula for the
decentralized intertemporal elasticity of substitution in the symmetric state is given by

V_e(c, 1) + c W (c, 1)_________

c [V_cc(c, 1) + c^-1V_cz(c, 1) - c'²∖z(c, 1)]

where U(c, C) = V(c, г), z ≡ c/С and C is the aggregate level of (non-durable) consumption. In (2.21) we
apply this expression to our specification in which consumption is a durable good.

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