Ex-Ante and Ex-Post Welfare Optimality under Uncertainty

It is widely believed by economic theorists that, if there were no transactions costs, and if all information about the economy were perfectly shared by all, then Arrow-Debreu commodity markets should bring about an ideal allocation. The basis for this belief seems clear. We have the two efficiency theorems of welfare economics which assure us that, in the absence of external effects, any competitive allocation is Pareto-efficient, and that any Pareto-efficient allocation is competitive, provided that appropriate lump-sum transfers are made. Of course, there are some reservations that need to be made: local satiation and non-convexities are well known to cause problems. But these are not the problems I wish to discuss here. To return to the usual argument, the next step involves noticing how, with commodity markets, the efficiency theorems of welfare economics carry over to an economy with uncertainty, as explained, for instance, in Chapter 7 of Debreu's Theorpj of Value. The fundamental value judgment that gives these efficiency theorems their normative interest is what may be called sovereignty. It is an assumption that the social welfare ordering should respect the preferences that govern consumers' market behaviour. It is a serious value judgment-more serious than most economists have been prepared to concede. But its seriousness increases when there is uncertainty. We know full well that individuals misperceive the probabilities of certain events, assuming that they even perceive any probabilities at all (see, for example, Kahneman and Tversky, 1979). Nor are we always willing to accept as appropriate the attitudes to risk of individuals who seem either extremely reckless or extremely cautious. Societies are often willing to make some gestures towards property owners who have not insured themselves adequately against damage from fire, flood or tempest, and not just because of imperfect insurance markets or even misperceptions of probabilities. In addition, the inequalities of income that arise when some individuals take more risks than others are not necessarily seen to be desirable, particularly if an individual has undertaken a useful but risky activity and has a very low income as a result of failure. Such gestures are examples of contingent lump-sum transfers. It seems clear that, if such transfers occur to a sufficient extent, they could supplant completely the securities markets which are usually sufficient to bring about Pareto efficiency. They may even be able to go further, and correct the imperfections of an Arrow-Debreu market allocation when individuals do misperceive probabilities or else have wrong attitudes to risk. This is the main question I wish to consider here. The idea that consumer sovereignty should not always extend to economies with uncertainty is not new: it can be found in work by Diamond (1967), Dr6ze