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
For these utility functions, the marginal cost (in terms of utility) of an additional task is 2T/5 for high-ability workers and T/2 for low-ability workers; when paid the amount P per task (so that W = PT), the marginal benefit (in terms of utility) of an additional task is P regardless of the worker's ability. 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.)