and (3.8b)-(3.8d) with respect to η, we calculate the following long-run comparative statics
expressions for
ŋ:
φφ. - χ.1 ∂μ _ F (1) α (1+ β + δ) [V '' + (1+ β + δ) φF "]
дП “(1+ β + ? ∂n - (1 + δ)+Γ > 0,
(3.11a)
∂2 _ 1 dC _ s, (1) α'(1 + β + δ)(F')2
(3.11b)
⅜ - δ∂n - (1 + δ) αΓ >
dn
dη
|
d I _ |
F (1) α' (1+ β + δ)(F')2 > 0 |
⇒ |
_ ~ | ||
|
dη |
(1 + δ)<!Γ , |
∂η |
∂η |
(3.11c) | |
(3.11d)
where
Γ - —a' (β + δ) δ [v'' + (1 + β + δ) φF"]
—a' [7 [(1 + <5)h]-(1+7) + z^ɪʌɪ?- 21 (1 + β + δ) F "F ' < 0.
(1 ∣ δ)2
How do the small open economy results in (3.11a)-(3.11d) compare to those calculated
in (2.18a)-(2.18c) for the closed economy case? As in the closed economy framework, a
greater degree of status preference raises the shadow values φ and fl and causes a long-run
increase in work effort (, along with durable consumption c and its aggregate stock 2.
These results, then, represent an extension of the Fisher and Hof (2000b) findings that an
increase in the degree of status preference leads to a long-run increase in consumption,
work effort, and output to the small open economy. One key distinction between the small
open economy and closed economies is, of course, the ability of the small open economy
to finance its durable consumption by borrowing from abroad. In this model, however,
the steady-state increase in durable consumption is exactly offset by the long-run rise
in domestic output, which implies that there is no change in the steady-state stock of
21