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

√

- -∞

_e^δ(^{τ t})_c(_τ )rf_ιτ

(2.1a)

and accumulates according to:

a = c — δa

(2.1b)

where δ is the rate of depreciation of consumer durables.⁷ We specify that each agent pos-
sesses the following general instantaneous utility function over own durable consumption,
c + a, and status, s, and work effort I:

U (c + a,s) + V (Z),

(2.2)

where U and V have the following properties:

U_c > 0,   U_s > 0,   U_cc < 0,   U_ss ≤ 0,   U_ccU_ss — U⁷_cs ≥ 0,   V' < 0,   V'' < 0,

(2.3a)

UscUc — UsUcc > 0,

(2.3b)

lim U_c(c, s) = ∞,    lim U_c(c, s) = 0.

c→0               c→∞

(2.3c)

According to (2.3a), the representative agent derives positive, though diminishing, mar-
ginal utility from own consumption and positive and non-increasing marginal utility from
status, with the instantaneous utility function U jointly concave in c and s.⁸ In addition,
work effort generates disutility and V is concave. The condition (2.3b) imposes normality
on preferences, i.e., the marginal rate of substitution of status for consumption, U_s∣U_c, de-

⁷This specification of durable consumption is found in Mansoorian (1998, 2000).

⁸We use the following notational conventions. In general, we suppress a variable’s time dependence,
i.e., x ≡ x(t). The time derivative of x will be denoted by x; a steady-state value by x. Unless otherwise
indicated, the partial derivative of a function F with respect to x will be denoted by F_x, while “primes”
indicate that the derivative of a function of a single variable is being taken.