because it generates interior intertemporal equilibria with saddlepath dynamics.21 More-
over, incorporating (3.1), together with durable consumption goods, into the neoclassical
small open economy model yields a fourth-order differential equation system, as in the
case of our closed economy model. This characteristic makes our closed and open economy
specifications more directly comparable.
The other modification of the basic model is the assumption that employment I is
the sole factor of production so that: y = F(Z), F' > 0, F'' < 0. The reason why we
abstract from physical capital in the small open economy extension is for the sake of
analytical tractability and because its dynamic behavior, in the absence of specifying an
installation-cost, Tobin’s q framework for physical capital, is not particularly revealing.22
Taken together, these two modifications imply that the accumulation of net debt is given
by
fι = rn(n)n + c — F (Z)
(3.2)
where, as before c is the level of current durable goods. The consumer-producer’s maxi-
mization problem in this small open economy contest becomes
subject to
max
c + ■• ' )+ v (Z)
e-βtdt J.
(3.3a)
a = c — δa (3.3b)
21The recent papers of Fisher and Hof (2003) and Fisher (2004a) have an extensive discussion of the
conditions required for the small open economy to possess interior equilibria, particularly the circumstances
in which an interior equilibrium is attained without imposing equality between the world interest rate and
the domestic rate of time preference, r* = β. This issue is also addressed in the standard references of
Barro and Sala-i-Martin (1995), ch. 2, and Turnovsky (1997), chs. 2 and 3.
22It is straightforward to show that the condition β = r* must be imposed for the small economy Ramsey
model, in the absence of other modifications, to achieve an interior steady state and possess saddlepath
dynamics. If the domestic economy also possesses physical capital к, then this condition implies that к
is always at its steady-state value. In terms of our model with durable consumption goods, it can be
demonstrated that the only variables that exhibit non-degenerate dynamics are the stock of consumer
durables a and the stock of net debt n. All other variables always equal their steady-state values.
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