Global invertibility of excess demand functions - Enrique Covarrubias (Banco de México, 2013)
In this paper we provide necessary and sufficient conditions for the excess demand function of a pure exchange economy to be globally invertible so that there is a unique equilibrium. Indeed, we show that an excess demand function is globally invertible if and only if its Jacobian never vanishes and it is a proper map. Our result includes as special cases many partial results found in the literature that imply global uniqueness including Gale-Nikaido conditions and properties related to stability of equilibria. Furthermore, by showing that the condition is necessary, we are implicitly finding the weakest possible condition.
Keywords: C62; C65; D51; D52; D58; 330; excess demand function; invertibility; uniqueness; Jacobian; proper map