Abstract
Allocations in a random economy described by an integrably bounded, closed and convex valued, measurable consumption multifunction and a monotone, continuous utility function are studied. The notions of efficiency and optimality of allocations are introduced and compared. Through the use of price systems belonging to L X ∗ ∞ = (L X 1) ∗ , a necessary and sufficient condition for optimality is obtained. Also for the case where the allocation belongs to L X ∞, it is shown that the efficiency prices can be chosen to be in L X ∗ 1 , although (L X) ∞ ∗ L X ∗ 1 . Finally, approximate optimality and efficiency are considered and also some stability results are proven when the consumption multifunction or the utility function vary in a certain sense. This work is based on the theory of normal integrands of Rockafellar.
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