Resumen
In this paper we consider a class of pure exchange economies in which the
consumption plans may be restricted to be above a minimal level. This class is
parameterized by the initial endowments and the constraints on the consumption.
We show that the demand functions are locally Lipschitzian and almost
everywhere continuously differentiable even if some constraints may be binding.
We then study the equilibrium manifold that is the graph of the correspondence
which associates the equilibrium price vectors to the parameters. Using
an adapted definition of regularity, we show that: the set of regular economies
is 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 which
selects the given price vector. In the last section, we show that the above results
hold true when the constraints are fixed.