Discrepancies between ex ante and ex post efficiency under identical subjective probabilities

Starr (1973) showed that, if people have different subjective probabilities, ex ante and ex post efficiency conflict. Conversely, under the simple preferences that he considered, the discrepancy between ex ante and ex post efficiency disappears when subjective probabilities are identical. Here I consider identical subjective probabilities, but more general preferences. First, risk attraction is admitted. Second, I dispense with the double requirement (dubbed IZU) of additive separability and state-independence of the utility of zero-date consumption, an unrealistic requirement when modeling the investment in durable goods. I find that, under IZU, and as long as ex post preferences satisfy the natural assumption of quasiconcavity (and satisfy some technical qualifications), an ex ante efficient allocation is indeed ex post efficient, but the converse is not necessarily true under risk attraction. If, on the other hand, IZU is violated, then one can have ex ante efficient allocations that are not ex post efficient, and vice-versa, even under risk aversion.