Microeconomics 2nd Edition by Douglas Bernheim

Exercise 1

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. Preferences correspond to the utility functions
for high-ability workers and
for low-ability workers. 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 an equilibrium exists.)