capital stock (and, thus, steady-state output). These results represent an extension of the
Fisher and Hof (2000b) Hndings to the case of durable relative consumption.5 With regard
to the second issue, we Hnd that whether the speeds of adjustment rise or fall depends
on whether the rise in the degree of status preference raises or lowers the intertemporal
elasticity of substitution. Finally, we show that the long-run implications of an increase in
status considerations are generally extend to the small open economy model.
The rest of the paper is structured as follows. Section 2 describes the closed economy
model with durable consumption and derives its intertemporal equilibrium. The Hrst part
of section 2 outlines the general framework with endogenous employment, while the sec-
ond part of section 2 discusses the implication for the economy’s speed of adjustment in
the special case of Hxed employment. In section 3 we develop the small open economy
framework and analyze its dynamic and long-run properties. The paper closes with a brief
conclusion and a mathematical appendix that contains some results that are important
for our subsequent analysis.
2. The Model and Intertemporal Equilibrium
2.1. Variable Employment
We assume that the decentralized economy is populated by a large number of identi-
cal, inHnitely-lived consumer-producers.6 Without loss of generality, we specify that the
population is constant. In this framework, agents derive positive utility from aggregate
consumer durables, c + a, and status, s. In contrast, work effort, I, yields disutility. We
assume that durable consumption and status are additively separable from work effort in
the instantaneous utility function. Aggregate consumer durables consist of current goods
purchased at time t, c, and the inherited stock of consumer durables, a. For expositional
convenience, we refer to c as durable consumption and to a as its stock. In this continuous-
5Among other results, Fisher and Hof (2000b) show that an increase in the degree of status preference
increases the steady-state values of non-durable consumption, employment, and physical capital.
6We abstract from a public sector in this model, which means that we do address the question of optimal
policy in the context durable consumption externalities. We leave this issue for future work.