The third theorem of welfare economics

Résumé

Actively choosing to learn tends to involve market failure: if the new knowledge is not shared with everyone else, learning produces asymmetric information; if the new knowledge is welfare relevant and shared with everyone, learning essentially amounts to private provision of a public good, yielding externalities. I show that if there are more than two consumers, no other restrictions on preferences than completeness and transitivity, and no other restrictions on production technologies than their being nonempty and closed, an economy in which welfare relevant active learning is feasible cannot also be perfectly competitive. Thus, the first and second fundamental theorems of welfare economics do not hold for such economies.