Prudent Job Search and Consumption Sensitivity

This paper connects classical preference theory to quantitative job search and savings models. We treat job acceptance as a choice between stochastic income lotteries. By integrating Decreasing Absolute Risk Aversion (DARA) and Prudence (DAP), we derive five contributions. First, we prove the standard positive wealth effect on reservation wages is driven by the gap between the risk premium (equating total utilities) and the prudence premium (equating marginal utilities), while resolving value function concavity. Second, a unified theorem shows the wealth effect depends on the stochastic dominance of on-the-job search (OJS) versus unemployed search. We uncover a novel "Investment Fund" regime: when OJS is superior, reservation wages decrease with wealth as agents purchase access to high-growth states. Third, this explains consumption puzzles, showing the high MPC of the unemployed is an endogenous response to background risk. Fourth, we demonstrate an isomorphism between labor and savings: the reservation wage exhibits the same prudence-driven diminishing sensitivity as the consumption function. Fifth, borrowing constraints amplify wealth sensitivity without altering qualitative risk rankings.