A consumer with diminishing marginal utility in consumption, who can search for lower prices, will balance the gains from spreading consumption evenly through time against the benefits of delaying consumption until lower prices are revealed. Optimal programs of consumption, savings and price are characterized for a general formulation of this problem. Intertemporal substitutability is measured by relative-risk aversion. Small relative-risk aversion is sufficient for the intuitive solution: As the best current price rises, more search and less consumption is done. The general model is adapted to special cases. Among other things, this shows that linear utility and sequential search implies calculable reservation prices and consumption only when search stops. However, this characterization is a consequence of the restriction to linear utility. Outside of this context reservation prices and consumption may not be calculable.
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