対外債務と再生産可能資源輸出の動学的安定性
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概要
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The author has tried to study and analyze theproblems of sustainability and dynamic stabilityin the long-run equilibrium of a dynamical system in which there are two differential equationswith regard to population growth: a kind of renewable resource to be exploited and exported by domestic competitive firms and the accumulation of foreign debt through the international trade of that resource, and imported consumption goods and firms’ user costs in a small country. The fundamental model bodyof the dynamical system is formulated by utilizinga macroeconomic model of Rauscher [1989] with some alterations. Rather than using his method of the optimal control theory, the author altered the control variables by the functions that are dependent upon state variables and that have some economic possibility of a plausible value range in differential derivatives.The main results are two propositions obtained through the study of the fundamental dynamical system, which are equations (1.1), (1.2), (1.3), and (1.4) with relative assumptions and functions. Proposition 1 is a case similar to the result of Rauscher [1989], which asserts that the long-run equilibrium of the system becomes a saddle point that provides a unique path to approaching and reaching the one and only equilibrium point, at least in the local, when the economy tends to very positively exploit the resource to a large or even excessive extent. In contrast to Proposition 1, Proposition 2 asserts that the long-run equilibrium of the system becomes an asymptotically stable point that provides many paths to approaching and reaching the one and only equilibrium point, at least in the local, in a steady state (and also a more dynamic sustainable state than in Proposition 1) when the economy tends to conservatively exploit the resource to a moderate extent. The many paths make it much easier for the government to choose one path in practical cases such as through ordinary economic policies.
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