A Note on Risky Targets and Effort

Abstract

This note examines the effort choice problem of a decision maker (DM) who has to meet a target. The more the DM spends on effort, the more likely the target is reached. Besides the risk of missing the target despite his effort, the DM faces additional uncertainty in that both the target and the status quo are subject to exogenous shocks that are beyond the DM's control. We consider two cases: the additive case in which the DM's effort affects solely the likelihood of achieving the target, and the multiplicative case in which the DM's effort also has direct effect on the target and the status quo. Using the theory of monotone comparative statics and risk apportionment, we derive sufficient conditions under which the DM spends more on effort when the target experiences an improvement in risk via higher-order stochastic dominance.