The Second Fundamental Theorem of Positive Economics

Welfare Economics is fortunate that there are two Fundamental Theorems of Welfare Economics. Positive Economics on the other hand is seemingly endowed with none. One of the fundamental results of Positive Economics is that a competitive equilibrium exists under fairly general conditions; this then may be called the First Fundamental Theorem of Positive Economics (FFTPE). The existing results on uniqueness and stability of competitive equilibrium are far too restrictive to be up for consideration as a Fundamental Theorem. It is to reexamine this question that we revisit the question of stability of competitive equilibrium. It is shown that if, for all distributions of the aggregate endowment, the matrix sum of the Jacobian of the excess demand function plus its transpose, evaluated at the equilibrium, have maximal rank then equilibria will be locally asymptotically stable. When this condition is not met, it is shown how redistributing resources will always make a competitive equilibrium price configuration stable and this need not involve redistributing endowments so that trades do not exist at equilibrium. This last result is quite general and the only requirement is that the rank condition referred to earlier hold at zero trade competitive equilibria and consequently may qualify to be called the Second Fundamental Theorem of Positive Economics (SFTPE). audience. The searching queries and pointed interjections from Professor McKenzie, kept the audience enthralled and subsequently led to a revision and a shift in focus. I am indebted to Kazuo Nishimura and Makoto Yano for providing me with an opportunity to submit this paper for the McKenzie memorial issue. A very helpful and encouraging set of comments from a referee is gratefully acknowledged. Help from H. Karun in editing the document in its current form is gratefully acknowledged.