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

sufficient for optimality.

As in the closed economy model, we restrict the analysis to symmetric equilibria in
which identical agents make identical choices, implying, c + a ≡ C + A. Substituting this
relationship into (3.5a) and combining with (3.5c), we obtain:

U_c [c + a, s (1)] + ^{U [C + α}+ ⁽_a^1)] ’ ⁽¹⁾ = μ — φ = (β + δ)φ - φ        (3.6)

which repeats equation (2.11). The optimality conditions for work effort and international
borrowing in the symmetric state remain unchanged.

Consequently, the independent dynamics of the small open economy model corresponds
to the following system of equations

φ =(1+ β + δ) φ — μ                       (3.7a)

a = c (a, μ, φ) — δa                              (3.7b)

μ = μ [β — rⁿ(f)]                                (3.7c)

fι = rⁿ(n)n + c (a,μ, φ) — F [Z(μ)]                        (3.7d)

where we have substituted for c = c (a, μ, φ) in equations (3.7b, 3.7d) and I = I (μ) in
(3.7d).²³ A key distinction between the closed and small open economy models is the ability
of small open economy to borrow (and lend) from abroad. This is reflected in equation
(3.7d), which describes the (negative of) the current account balance. It is the difference
between domestic durable consumption, inclusive of interest service, and domestic output.

Letting φ = i = μ = fι = 0, the long-run equilibrium equals

Uc [(1+ δ>)i,_s (1)] + ^u∙ ^[(1+фф’ ^wμ'⁽¹⁾ =(β + δ)φ         (3.8a)

(1 ∣ δ ) a

²³This instantaneous consumption function, together with its partial derivatives, is the same as in the
closed economy framework, while for I = l(μ), ∂l∕∂μ = — (V'' + μF'') ¹ > 0.

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