Global Comparative Statics for Models with Hicksian Imperfect Stability

概要

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This note is to provide a bridge between traditional local analysis for comparative statics and its global counterpart. Many economists vaguely believe that it is possible to obtain a global result by applying consecutively a series of local results. This belief is not well founded in models where parameters enter in a not-so-simple way. An example is given to show that local analysis is after all local. In the proof of the first main theorem, a consecutive use of a well known local result is employed. Some necessary assumptions are explicitly stated. Then this theorem is applied to establish another main theorem in which a simple repetitive application of local analysis may break down because some required properties cease to hold. This two-stage approach seems to be useful in tackling with other types of equations. As an application of our theorems, a general equilibrium model with Hicksian imperfect stability is taken up. A comparative statics result due to Hicks is extended to the case of global changes. An interesting point to note is that when dealing with global comparative statics, the old system plays no explicit role. Only the new system matters together with the new and old equilibrium values. Understanding this point is important when we come to consider such real situations as involve technical changes in which new processes as well as new commodities turn up.
岡山大学の論文