The Stability of the "Morishima System".

Kennedy, Charles

This theorem will be proved if it can be shown that Morishima's theorem of the equivalence of dynamic stability conditions and Hicksian stability conditions for a subeconomy excluding the numeraire can be extended to an entire economy in which the sign rules hold. To establish this it is necessary to prove that: If the entire economy is Hicksian, every possible subeconomy formed by excluding the ith commodity as numeraire will also be Hicksian. This follows from the argument of the Lemma; If the entire economy is not Hicksian, every possible subeconomy formed by excluding the ith commodity as numeraire is not Hicksian. If the sign rules apply to the entire economy and there is some gross complementarity in the system, the ith commodity will be in one of the two subsets into which the set of commodities can be divided.

MATHEMATICAL economics; SAVINGS; COMMERCIAL products; MATHEMATICS; ALGEBRA; MATRICES (Mathematics); EQUILIBRIUM

Review of Economic Studies, 1970, Vol 37, Issue 2, p173

0034-6527

Academic Journal

10.2307/2296410