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



time framework, the stock of consumer durables corresponds to:

- -∞


eδ(τ t)c(τ )rfιτ


(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:


Uc > 0,   Us > 0,   Ucc < 0,   Uss0,   UccUss U7cs0,   V' < 0,   V'' < 0,

(2.3a)


UscUc UsUcc > 0,


(2.3b)


lim Uc(c, s) = ,    lim Uc(c, s) = 0.

c0               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 e
ffort 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,
UsUc, 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 Fx, while “primes”
indicate that the derivative of a function of a single variable is being taken.




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