Bean Counting: Standard Choice in a Two-dimensional Incentive Problem By

1. Introduction This essay is an exploratory study of incentives with two-dimensional output. I consider a model in which workers allocate effort across two dimensions: quality and quantity. The monitor can observe quantity perfectly and without cost. While quality comes in divisible units, I assume that observable quality comes in two forms: normal and distinguished. If quality meets a fixed standard, then it is known to be distinguished. Otherwise, it is taken to be normal. With this information structure, workers choose to concentrate all of their energies into increasing quantity, or invest just enough to guarantee that their output is distinguished. I provide a characterization of the optimal mechanism that involves precisely this type of behavior. I use this characterization to investigate three other questions. First I ask: Does the inability to monitor quality increase the quantity of output? A naive version of the signpost phenomenon suggests that it would. With less incentive to invest effort in improving quality, workers would instead attempt to increase their observable output. This intuition turns out to be too naive. If quality and quantity are complementary, in a sense made precise below, then workers who produce low quality will also produce lower quantities as well. The naive intuition would be correct if the worker must allocate a fixed amount of energy to investments in quality and quantity. It neglects the possibility that the worker reacts to the limited observability by providing less of each component of output. In the leading case of my analysis, however, the optimal incentive scheme induces workers who provide low quality to provide lower quantities as well. The second question that I ask is: What incentives do different groups have to vary the level of quality that can be treated as distinguished? On one hand, the principal would like to obtain the most information about an agent from her limited knowledge of quality. On the other hand, agents with different abilities have different incentives. Agents who are barely willing to supply a distinguished quality level gain when the level decreases. Agents with higher abilities prefer higher standards. I give conditions under which the standard that maximizes the average payoff of those agents who choose to produce high quality work exceeds the standard that maximizes the average payoff of all agents. I also demonstrate a tendency for the preferred standard of the high-ability agents to exceed that of the principal. The …