Comparative Statics in the Large : A Note

In this note, an abstract setting for discussing comparative statics in the large is presented to give a necessary and sufficient condition for the first Hicksian law to hold. This condition is gradually tranformed to the one through which we are able to see clearly the power of a theorem due to Gale and Nikaido. This theorem has been overlooked probably because it apparently does not involve the two systems to be compared. Moreover the condition for the theorem to be valid also guarantees the uniqueness of a solution to the equation systems under consideration. Some comments are also given to a recent contribution by T. Shiomura. His method of proof is based upon an advanced homotopy approach for fixed point algorithm. One important consequence of his results is that imperfect stability is enough to establish the first Hicksian law in general equilibrium models. This may, however, be shown using elementary calculus.

研究ノート (Note)