Equilibrium of a production economy with noncompact attainable allocation set

In this paper, we consider a production economy with an unbounded attainable set where the consumers may have non-complete non-transitive preferences. To get the existence of an equilibrium, we provide an asymptotic property on preferences for the attainable consumptions and we use a combination of nonlinear optimization and fixed point theorem on truncated economies together with an asymptotic argument. We show that this condition holds true if the set of attainable allocations is compact or, when preferences are representable by utility functions, if the set of attainable individually rational utility levels is compact. This assumption generalizes the CPP condition of Allouch (2002) and covers the example of Page et al. (2000) when the attainable utility levels set is not compact. So we extend the previous existence results with non compact attainable sets in two ways by adding a production sector and considering general preferences.