Revisiting the First-Order Approach to Principal-Agent Problems

Abstract

Principal-agent problems are typically solved by the first-order approach (FOA) that replaces the incentive-compatibility constraint in the original problem with its first-order condition, resulting in a relaxed problem. The most celebrated condition that validates FOA is the Mirrlees-Rogerson Condition, developed for a risk-averse agent. We show that it fails to generalize to a widely studied setting of risk-neutral players and limited liability. Instead of justifying FOA, we propose a less stringent notion that only requires FOA to be valid for quota-bonus contracts (FOAVQB). This proposal is rationalized by our finding that quota-bonus contracts are optimal for the relaxed problem. We identify exogenous sufficient conditions that justify FOAVQB, thus ensuring the optimality of quota-bonus contracts for the original problem. These sufficient conditions are flexible enough to accommodate common instances where the agent's expected utility is non-unimodal in effort (besides those with a unimodal utility function), contrasting the literature that justifies FOA by finding conditions to guarantee unimodality.

Keywords: Principal-agent problems, Moral hazard, Limited liability, Quota-bonus contracts, First-order approach