да __ 1 ∂c _ 1 ду _ _ 41)(1+ β + δ) Fkk Fl{y∕l') > θ
(2.18b)
∂η δ∂η δ∂η (1 + δ)l∆
9к= _ Fki дУ_ _ F (1) δ (1+ β + δ) FkiFi > o ⇒ д (y∕Q _ дк=0
∂η Fkk ∂η (1 + δ)α∆ ∂η ∂η ,
(2.18с)
where13
∆ _ (β + δ) δV"Fkk — (1+ β + δ) Fi [7 [(1 + δ)h]-(1+γ) + 21 Fkk(y∕y) > 0.
(1 + δ)a2
The signs of the expressions in (2.18a)-(2.18c) can be directly explained: a higher weight on
status considerations causes consumer-producers to place a greater value on consumption
at the expense of leisure, which is reflected in (2.18a) in the higher long-run levels of μ and
<y. This leads, in turn, to an increase in work effort y, which, since Fki > 0, causes physical
capital y to accumulate. Nevertheless, the steady-state capital-labor ratio y, determined by
the rate of time preference β and the curvature of the production function, is independent,
according to (2.18c), of changes in the status preference parameter η. The long-run rise
in output у leads, as indicated in (2.18b), to an increase in durable consumption c and its
steady-state stock a. Our results represent, then, an extension of those of Fisher and Hof
(2000b), who in their model non-durable consumption show that “status consciousness”
leads to “too much” consumption, work effort, and physical capital accumulation relative
to a socially planned economy in which status considerations do not play a role.14
2.2. Fixed Employment Case
In order to explore in greater detail the dynamic properties of the durable consumption
model, we simplify the framework by assuming that employment fixed. The description
of the fixed employment version of the model, along with its optimality conditions and
13In calculating (2.18b) and ∆, we have used the fact that (FkkFi — Fkiβ) = Fkk (j//ŋ-
14See Fisher and Hof (2000b) proposition 1 and section 4, pp. 10-12. In the context of our model, the
social planner would set c + a = C + A, implying that (2.17) becomes:
U(c + α,s) = (1 — γ)-1 (c + a)1-γ + ηs (1) , γ > 0, η > 0.
In this case there is no relative consumption externality arising from status preference.
12