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

fi = rⁿ(n)n + с — F (Z)

and the No-Ponzi-Game condition limt→∞ ne^-rnt ≥ O, together with the initial stocks of
durable consumption and net debt: a(O) = no > O, n(O) = no > O. The current-value
Hamiltonian for this problem corresponds to
where μ now corresponds to the shadow value of international assets. As in the closed-
economy framework, consumers make their choices taking the aggregate levels of durable
goods and their stocks as given. Furthermore, agents make their consumption∕savings
decision holding the interest rate on bonds rⁿ(n) constant. This implies that the Hrst
order conditions are equal to the following expressions

и и           , .₁ U₄ [c + a, s (г)] s' (1)            ,                        , _ .

^uc ^{[c + a,s (г)] +}                        =^{μ - φ,                 (3}.5^a)

O + Ji

V '(Z) = —μF '(Z)                                  (3.5b)

φ = (β + Φ)φ — U_c [c + α,s (г)] - ^{U [c +} "'ɪ⁽/^{)] s}'⁽¹⁾,            (3.5c)

O + √/

μ = μ [β — rⁿ(n)]                              (3.5d)

The optimality conditions (3.5a)-(3.5c) for the open economy have an interpretation simi-
lar to their counterparts (2.1Oa)-(2.1Oc) for the closed economy. The exception is equation
(3.5d), which describes the optimal path of the shadow value μ if the stock of net debt
is chosen optimally. Our speciHcation of preferences in equations (2.3a)-(2.3b) guaran-
tees that the Hamiltonian (3.4) is jointly concave in the control variables c and Z and
the state variables a and n. This implies that if the limiting transversality conditions
lim_t→∞ aφe^-∣^βt = lim_t→∞ nμe^-βt = O hold, then necessary conditions (3.5a)-(3.5d) are

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