A worker can exert two effort levels, solid and sloppy, which cause mistakes with probability 0.25 and 0.90. Whether a mistake occurs is observable, but effort is not. Very little computation is needed to answer this question. Potential workers are risk-neutral, and have a utility of zero if they are not employed. There are 60 identical firms.
Firms produce according to the number of employees they have who work.
Define by L the number of working employees. The probability of detecting shirking employees depends on the level of monitoring. Define by n the total number of employees per firm - both those who work and those who shirk. If employees work, their probability of being detected shirking is zero. Assume first that firms can control the level of q .