General consumption constraints and regular economies

Private ownership economies with externalities and existence of competitive equilibria: a differentiable approach

“…The following theorem is a consequence of the homotopy invariance of the topological degree. Following Chapter 4 in Milnor (1965), and more recent contributions by Villanacci and Zenginobuz (2005), del Mercato (2006) and Bonnisseau and del Mercato (2008), our homotopy approach is based on the theory of degree modulo 2. The reader can find a survey of the degree theory, for example, in Geanakoplos and Shafer (1990) and in Villanacci et al (2002).…”

“…Our main theorem (Theorem 8) states that the set of competitive equilibria with strictly positive consumptions and strictly positive prices is non-empty and compact. We prove Theorem 8 following the seminal work by Smale (1974), and more recent contributions by Villanacci and Zenginobuz (2005), del Mercato (2006) and Bonnisseau and del Mercato (2008). That is, we use:…”

“…But, it implies that at the end of the arc the set of equilibria associated with the given economy is non-empty and compact. This is a kind of standard technique used in many contributions in general equilibrium theory, see for instance Villanacci and Zenginobuz (2005), del Mercato (2006), Mandel (2008), Bonnisseau and del Mercato (2008), Kung (2008), and Ericson and Kung (2015). However, the work of adapting this technique to economies with externalities on the production side is non-trivial and it requires some ingenious adjustments, because the production sets are not required to be convex with respect to the consumption and production activities of all the agents (for more details, see Subsection 4.2).…”

Generic regularity of differentiated product oligopolies

“…Several variations of the economic environment have been considered: Incomplete markets are covered by Geanakoplos and Polemarchakis (1986). Restrictions on portfolios and consumption are considered by Cass et al (2001) and Bonnisseau and del Mercato (2008), respectively. Economies with a public good are the subject of Villanacci and Zenginobuz (2005).…”

“…Economies with a public good are the subject of Villanacci and Zenginobuz (2005). Nonstandard preferences are the focus of Bonnisseau (2003), who considers consumers without ordered preferences, Biheng and Bonnisseau (2015), who consider ambiguity-averse consumers, and Bonnisseau and del Mercato (2010), who consider consumption externalities.…”