Employers compete with each other to hire workers, who perform tasks. Workers have either high or low ability. An employer's total profits increase by $10 when a high-ability worker completes a task, and by $5 when a low-ability worker completes a task. For high-ability workers, preferences correspond to the utility function
UH (T, W) = W = T2/5
For low-ability workers, preferences correspond to the utility function
UL (T, W) = W = T2/4
In each of the following two scenarios, determine how many tasks each type of worker performs, the amounts of compensation they receive, and the levels of utility they enjoy. First scenario: employers can observe workers' types and the number of tasks each worker completes, so that workers are paid their marginal products. Second scenario: employers cannot observe workers' types or the quality of the tasks they perform, so that the market generates a competitive screening equilibrium. (You may assume that low-ability workers are so numerous that such equilibrium exists.)