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

derivatives in (2.12a, b) are interpreted as follows: an increase in stock of durable con-
sumption a lowers its current level c. Indeed, as we show in the appendix, an increase in a
lowers c by one-for-one. In addition, current durable consumption depends negatively the
marginal utility of wealth μ and positively on the shadow value of the stock of durable
consumption φ. Regarding the short-run response of work effort, (2.12b) indicates an in-
crease in the shadow value μ raises work effort. Moreover, a given increase in the capital
stock к also encourages labor supply, since F_kι > 0, which is implied by constant returns
to scale production technology.

From the equations (2.11), (2.8b), (2.10d) and (2.8c), we state the independent dy-
namics of the economy:

φ =(1+ β + δ) φ - μ,                       (2.13a)

cl = c (a, μ, φ) — δa,                               (2.13b)

μ = μ [β — F_k (к, I (μ, к))] ,                           (2.13c)

к = F [(к, I (μ, к)) — c (a, μ, φ)] ,                          (2.13d)

where we have substituted for I = I (к, μ) in (2.13c, d) and c = c (α,μ, φ) in (2.13b, d),
respectively. Letting φ = a = μ = к = 0, the long-run equilibrium equals:

U_c [(1+ δ) α,s (1)] + ^{U 1(1 +} 1∖α^,/. ^wμ'⁽¹⁾ =(β + δ)φ        (2.14a)

(1 ∣ δ ) a

V' (Z) = — (1 + β + δ) φFι (k, Zj ,                        (2.14b)

Fk (^k, ^k) = β,

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