The moral hazard problem with high stakes

We study the moral-hazard problem when the agent's reservation utility is large, but so is the agent's value to the principal. We show that the principal's cost of implementing effort has a very simple limiting form. For large enough outside option, the principal's cost is convex in the action, so the optimally-implemented action is unique, and optimal effort rises with the agent's ability, and falls with the agent's wealth and outside option. In a competitive market setting where heterogenous principals and agents match, positive sorting ensues and effort increases in match quality, despite conflicting forces.