The value of a worker's marginal product is $40 per hour for high-ability workers and $5 per hour for low-ability workers.The preferences of high-ability workers correspond to the utility function U_H(E,W)= W - 5E,and the preferences of low-ability workers correspond to the utility function U_L(E,W)= W - 8E.By law,everyone is required to attend at least ten years of school.Three-fourths of the population has low ability,and one-fourth has high ability.What is the most efficient separating equilibrium?

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Quizplus · Accepted Answer

In a separating equilibrium, different types of workers choose different levels of education to signal their ability to employers. High-ability workers have a utility function of $U_H = W - 5E$, and low-ability workers have a utility function of $U_L = W - 8E$. Given the marginal products ($40 for high-ability and $5 for low-ability workers), high-ability workers will choose more education than the minimum required if it increases their utility by signaling their ability, thus earning a higher wage. Low-ability workers will not mimic high-ability workers beyond a certain point because the cost in terms of utility (due to their higher disutility from education, as shown by the coefficient of E in their utility function) outweighs the benefit of a higher wage. Therefore, the equilibrium involves high-ability workers choosing more education than low-ability workers, with low-ability workers sticking to the minimum required (10 years) because any additional education reduces their utility more significantly than it does for high-ability workers.

The Value of a Worker's Marginal Product Is $40 Per