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.
Back to Sergei Guriev' homepage.