V'(>) = - (1+ β + δ) φF'(l), (3.8b)
rn(f) = г* + а (п) = β
δa — F (ŋ = 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
19
More intriguing information
1. Analyse des verbraucherorientierten Qualitätsurteils mittels assoziativer Verfahren am Beispiel von Schweinefleisch und Kartoffeln2. On Dictatorship, Economic Development and Stability
3. Industrial districts, innovation and I-district effect: territory or industrial specialization?
4. A Brief Introduction to the Guidance Theory of Representation
5. Job quality and labour market performance
6. The name is absent
7. The name is absent
8. Ultrametric Distance in Syntax
9. On the origin of the cumulative semantic inhibition effect
10. The name is absent