Hidden wealth and incentives

This paper analyzes the characteristics of optimal menu of contracts in the case that agents' wealth and actions are hidden from the principal. We first consider a benchmark case that the wealth levels of all agents are known to the principal, and we show that the power of incentives for agents with high wealth is greater than the one for agents with low wealth. The reason is that richer agents are less risk averse; providing high incentives for less riskaverse agents is beneficial to the principal. However, in the case that the agents' wealth is hidden, the principal will fail to achieve social efficiency because rich agents will act like poor agents. Thus, the principal must design another menu of contracts to prevent rich agents from mimicking poor agents. Ultimately, compared with the optimal menu of contracts derived when it was known, the power of incentives for rich agents is identical, but the power of incentives for poor agents declines.