Assets, Beliefs, and Equilibria in Economic Dynamics: Essays by Charalambos D. Aliprantis, Kenneth J. Arrow, Peter Hammond,

By Charalambos D. Aliprantis, Kenneth J. Arrow, Peter Hammond, Felix Kubler, Ho-Mou Wu, Nicholas C. Yannelis

This quantity includes a number of papers facing a vast variety of themes in mathematical economics, video game thought and fiscal dynamics. The contributions current either theoretical and utilized study. the amount is devoted to Mordecai Kurz. The papers have been offered in a different symposium co-hosted by means of the Stanford college division of Economics and by means of the Stanford Institute of financial coverage study in August 2002.

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Assume further that firms can identify annuity purchasers according to the group to which they belong. In a perfectly competitive market, annuities are then priced differently for each group, the analysis in Section 2 applying to each group separately. We focus on the effect of heterogeneity in survival rates and hence assume that wages are the same for both groups. Proposition 6. With full information and continuous annuitization, Ri > R 2. R Proof Applying (12) to each group, ci = c;(R) = J Fi (z)w(z)dz 0 T JFi(Z)dz o ' i = 1,2.

And, by second-order conditions, a' (R*) - Annuities and retirement 43 7 Lifetime and income uncertainty Suppose that individuals face lifetime uncertainty and are also uncertain about their future income. Income uncertainty may reflect, for example, the possibility of future disability. It is assumed that income uncertainty cannot be insured, presumably due to 'Moral-Hazard'. e. f p( B)dB = 1. o Consumption after the realization of B (at M), and the chosen retirement age, depend on B. Denote these c(B, z) and R(B), respectively.

When suppliers can identify the 'risk class' to which customers belong, competitive annuity prices differ by 'risk class' and a First Best allocation is attained (Yaari, 1965). ' Pooling leads to adverse selection, that is, annuities are purchased primarily by groups with high survival probabilities while those with low survival probability prefer to purchase fewer annuities. 2 In extreme cases, some 'risk classes' may choose not to purchase any annuities. In a Separating Equilibrium of this kind, the actions of individuals reveal (partially or fully) their characteristics (Rothschild and Stiglitz, 1976).

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