# On Some Properties of Logarithmic Utility Function

## S.M.Guriev, I.G.Pospelov, and D.V.Vedenov

We study a problem of consumer behavior with uncertain
prices and purchase moments. Between purchases consumer
receives constant income. At random moments the consumer obtains
an opportunity to spend part of his wealth. The consumer decides
how much to spend knowing the current price, distribution of prices
in future and distribution of future purchase moments.
The behavior is described by Bellman equation. We pay a special
attention to logarithmic utility. For this case we obtain asymptotical
formula is obtained. It also is shown that if and only if the
utility function is logarithmic, the consumer
choice does not depend upon probability distribution of prices:
nominal spending depends only on current wealth.

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