Consumption: Beyond Certainty Equivalence

This paper discusses the recent research on the consumption function that has attempted to relax the assumption of certainty equivalence. While there remain many open questions, both theoretical and empirical, it is clear that the assumption of certainty equivalence can be misleading. Under more plausible specifications of preferences toward risk, uncertainty lowers the level of consumption, increases the expected rate of growth of consumption, and increases the response of consumption to news about income. Moreover, changes in the amount of uncertainty are a potentially important source of fluctuations in consumption.

A new North American snake of the genus Natrix

http://deepblue.lib.umich.edu/bitstream/2027.42/56579/1/OP140.pd

A synopsis of the king snakes: genus Lampropeltis Fitzinger

http://deepblue.lib.umich.edu/bitstream/2027.42/56526/1/OP087.pd

Discovery of the eggs of the four-toed salamander in Michigan

http://deepblue.lib.umich.edu/bitstream/2027.42/56565/1/OP126.pd

A new snake of the genus Arizona

http://deepblue.lib.umich.edu/bitstream/2027.42/56589/1/OP150.pd

Three new snakes of the genus Lampropeltis

http://deepblue.lib.umich.edu/bitstream/2027.42/56520/1/OP081.pd

Na atomic order, Co charge disproportionation and magnetism in Nax_{x}CoO2_{2} for large Na contents

We have synthesized and characterized four different stable phases of Na ordered Na$_{x}$CoO$_{2}$, for $0.65<x<0.8$. Above 100 K they display similar Curie-Weiss susceptibilities as well as ferromagnetic $q=0$ spin fluctuations in the CoO$_{2}$ planes revealed by $^{23}$Na NMR data. In all phases from $^{59}$Co NMR data we display evidences that the Co disproportionate already above 300 K into non magnetic Co$^{3+}$ and magnetic $\approx$Co$^{3.5+}$ sites on which holes delocalize. This allows us to understand that metallic magnetism is favored for these large Na contents. Below 100 K the phases differentiate, and a magnetic order sets in only for $x\gtrsim 0.75$ at $T_{N}=$22 K. We suggest that the charge order also governs the low $T$ energy scales and transverse couplings

59Co NMR study of the Co states in superconducting and anhydrous cobaltates

$^{59}$Co NMR spectra in oriented powders of Na$_{0.35}$CoO$_{2}$ and in its hydrated superconducting phase (HSC) Na$_{0.35}$CoO$_{2}$,1.3H$_{2}$O reveal a single electronic Co state with identical $T$ independent NMR shift tensor. These phases differ markedly from Na$_{0.7}$CoO$_{2}$, in which we resolve 3 types of Co sites. The large T variation of their spin susceptibilities $\chi ^{s}$ and the anisotropy of the orbital susceptibility $\chi ^{orb}$ allow us to conclude that charge disproportionation occurs, in a non magnetic Co$^{3+}$ and two magnetic sites with about 0.3 and 0.7 holes in the $t_{2g}$ multiplet. The data are consistent with those for the single Co site in the anhydrous and HSC phase assuming the expected Co$^{3.65+}$ charge.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev. Let