The equilibrium manifold with boundary constraints on the consumption sets - Bonnisseau, Jean-Marc; Rivera, Jorge (Estudios de Economía, 2016)
In this paper we consider a class of pure exchange economies in which theconsumption plans may be restricted to be above a minimal level. This class isparameterized by the initial endowments and the constraints on the consumption.We show that the demand functions are locally Lipschitzian and almosteverywhere continuously differentiable even if some constraints may be binding.We then study the equilibrium manifold that is the graph of the correspondencewhich associates the equilibrium price vectors to the parameters. Usingan adapted definition of regularity, we show that: the set of regular economiesis open and of full measure; for each regular economy,there exists a finite odd number of equilibria and for each equilibrium price,there exists a local differentiable selection of the equilibrium manifold whichselects the given price vector. In the last section, we show that the above resultshold true when the constraints are fixed.