A rational foundation of procrastination

We introduce a search-theoretic framework that induces a time preference of a decision-maker who conducts a costly search each period. As a result of optimal decision-making, the induced time preference conforms to well-known empirical and experimental evidence.
First, the induced discount factor increases over time unless the increase in risk aversion caused by the search cost dominates the reverse hazard rate of the search. Hence, any increasing or constant relative risk aversion utility function exhibits procrastination; and if a search cost is small, so does regardless of risk attitude. For a risk-neutral decision-maker, the time preference is stationary if and only if the search is a Bernoulli process. Second, we show that the discount factor increases in fall-back value. Furthermore, if the reverse hazard rate dominates the increase in risk aversion, the wealth effect diminishes, which offers a theoretical foundation of the assumption of Becker and Mulligan (1997).
We further investigate the role of search technology. With a lower search cost, the decision-maker discounts more future value. Better technology in terms of stochastic dominance may make them more patient, but it will eventually them less patient as the deadline approaches.