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

pends positively on c, while (2.3c) describes the limiting behavior of the marginal utility of
consumption. Regarding status, we assume that it depends positively on relative durable
consumption, denoted by z ≡ c + a∕C + A, and takes the following “ratio” functional form:

^s ≡^{s (z)}=^s ɑ+A) ’     ^s' > °’ ^s" ≤ ^{o,                 (2л)}

where C + A is the average (or aggregate) level of durable consumption in the economy.
Given the specihcation of status in (2.4), we impose an additional condition of the function
U ^(c’S^):.

This condition guarantees that there exists a negative relationship between the (flow) of
durable consumption goods and its shadow value. Finally, the agent possesses a constant
returns to scale production function that satisfies the following standard neoclassical prop-
erties of positive and diminishing marginal physical productivity in capital, k, and labor,
Z:⁹

у = F(k’Z);     F_k > °’   F_kk < °’   F₁ > °’   F_ll < °’             (2.6)

where у represents output. In addition, the consumer-producer accumulates physical cap-
ital according to:¹⁰

____, _

k = F(k, Z) — c.

⁹The constant returns of scale property implies that the production function obeys the following rela-
tionships:

Fki > 0,  F_kkFu = F⅛ι,  F_kkFi - F_kiF_k = F_kk(y∕l),  F_kiFi - FuF_k = F_kι(y∕l).

¹⁰To keep the exposition of the model as simple as possible, we do not specify that physical capital is
subject to depreciation. It would, of course, be straightforward to do so, although none of our qualitative
results would be affected.

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