By Jacques H. Drèze (eds.)
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Additional resources for Allocation under Uncertainty: Equilibrium and Optimality: Proceedings from a Workshop sponsored by the International Economic Association
The amounts of income in the two periods are Y1 and Y 2• These are exogenously given, Y1 with certainty, Y2 as a random variable. 1) The consumer maximises expected utility, E[U(Cb (Y1 -C1)(1 +r)+ YJ], with respect to C1 • This yields the first-order condition E[U1 -(1 +r)U2]=0. ) We assume that the second-order condition for a maximum is satisfied. As posed by Leland and Sandmo the problem is now: what is the effect on present consumption of a change in the probability distribution of future income such that it becomes 'more risky'?
Savage (, p. 154) also advances the view that' ... statistics proper can perhaps be defined as the art of dealing with vagueness and with interpersonal difference in decision situation'. One is thus naturally led to wonder about the integration of the theory with other work dealing explicitly with group decisions. The most important theorem on group decisions in economics is Arrow's impossibility theorem , which has drawn attention to the difficulties inherent in group decisions based on ordinal preferences (rankings) of the members.
This problem has been studied by Rothschild and Stiglitz [18a]. Let X and Y be two random variables with identical mean values. Then consider the following four specifications of the statement, ' Y is more risky than X': (I) Risk averters prefer X to Y; (2) Y has the same distribution as X plus noise; (3) the density of Y is more spread out than that of X; (4) Y has a greater variance than X. Rothschild and Stiglitz demonstrate that the first three specifications are equivalent in the sense that they induce the same partial ordering on the random variables; this ordering is weaker than the one induced by (4).
Allocation under Uncertainty: Equilibrium and Optimality: Proceedings from a Workshop sponsored by the International Economic Association by Jacques H. Drèze (eds.)