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Under the expected utility paradigm, prudence (u′′′>0) is usually associated with the amount of risk premium an individual requires in order to renounce to a certain current outcome in favour of an uncertain future outcome. A prudent individual requires a higher premium the lower her initial wealth. However, when the individual has to make a costly investment before obtaining the outcome, she may prefer to delay that investment. This translates into a preference for latter, not earlier outcome. Consequently, prudence cannot be associated with a risk premium. In this paper we show that, for an individual who prefers to delay the investment, prudence is actually associated with the economic benefit granted by that delay. Specifically, a lower expected unit cost of acquiring the good is associated with a greater benefit of the investment delay if and only if u′′′ is high, and, with a uniform distribution, u′′′>0. We also show that the preference for facing a lower expected unit cost and/or a wider support of the unit cost increases with u′′′. We describe two applications of this result, namely, sequential learning in the delegation of a task and timing of investment decisions under multi-period uncertainty.
