When a principal sets a target level and agents reaching it receive a bonus

A common incentive pay scheme sets an output target level that, if achieved, a fixed bonus is awarded. Such commission-based bonuses are most common in sales teams. The principal determines the target level and the bonus size. The agent then selects their effort level. We first solve the agent's problem, and then substitute that solution in the principal's problem. We analyze such a scenario for additive and then for multiplicative noise. Our contribution is the analytical derivation of target level and bonus size, usually determined by intuition. We also compare the expected consequences with those of a 'standard' Principal-Agent model where the principal's benefit depends on the absolute achievement.