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



V'(>) = - (1+ β + δ) φF'(l),                          (3.8b)

rn(f) = г* + а (п) = β
δa
F= rn(fι)fι = [г* + а (—)] —,

(3.8с)


(3.8d)


where С = δa and μ = (1 + β + δ) φ. The Hrst two steady-state conditions are quite
straightforward: equation (3.8a) describes the long-run
Hrst order condition for own
durable consumption, while equation (3.8b) is the long-run optimality condition for em-
ployment if it is the sole factor of production. In turn, equation (3.8c) describes the
steady-state maximum condition for foreign debt: the real return on debt in steady-state
equilibrium equals the given consumer-producer rate of time preference. Correspondingly,
this condition determines the steady-state stock of debt —, which is a function of the
world interest rate r
*, the domestic rate of time preference β, and the curvature of the
“risk premium” function α (
). Finally, equation (3.8d) is the steady-state version of the
current account balance in which the difference between long-run durable consumption
spending and output equals steady-state interest payments on the outstanding stock of
international debt.

Linearizing (3.7a)-(3.7d) about the steady-state equilibrium described by (3.8a)-
(3.8d), we obtain the following matrix differential equation

Z = Jsoez =

φ ■ ʌ

( (1 + β + δ)      O           1          O ʌ

^ φ φ ^

2

- cμ     - (1 + δ)       cμ          0

a a

μ

OOO  fra'

μ — μ

(3.9)

'

cμ        1     - (F'lμ cμ}  β + α'f )

— — у

where z = (φ, a, μ, —, /and Jsoe denotes the Jacobian matrix in the small open economy
(soe) case. To determine the stability properties of the equilibrium, we
Hrst consider the

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