The value of a worker's marginal product is $50 per hour for high-ability workers and $15 per hour for low-ability workers.The preferences of high-ability workers correspond to the utility function U_H(E,W)= W - 4E,and the preferences of low-ability workers correspond to the utility function U_L(E,W)= W - 10E.By law,everyone is required to attend at least ten years of school.Three-fifths of the population has low ability,and two-fifths has high ability.What is the most efficient separating equilibrium? A) E_L = 13.5; E_H = 13.5 B) E_L = 10; E_H = 13.5 C) E_L = 13.5; E_H = 16.125 D) E_L = 10; E_H = 10

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Quizplus · Accepted Answer

To find the most efficient separating equilibrium, we need to find the level of education and wage rate for each ability type that maximizes their utility, given the value of their marginal product. For low-ability workers, their utility function is U_L(E,W)= W - 10E. To find the optimal level of education for low-ability workers, we need to determine the level of education where the marginal utility of education (i.e. wage increase from an additional year of education) equals the marginal cost of education (i.e. foregone earnings). The marginal utility of education is the derivative of the utility function with respect to education, which is -10. The marginal cost of education is the wage rate (which is $15) multiplied by the number of years of education, which is (E-10) multiplied by the discount factor (which we assume to be 1 for simplicity). So: MU(E) = MC(E) -10 = 15(E-10) E = 10 This means that low-ability workers should only complete the mandatory 10 years of education, since the marginal cost of additional education exceeds the marginal benefit. The wage rate for low-ability workers is then: W = 15(E-10) = 15(0) = 0 For high-ability workers, their utility function is U_H(E,W)= W - 4E. The optimal level of education is again where the marginal utility of education equals the marginal cost of education: MU(E) = MC(E) -4 = 50(E-10) E = 13.5 This means that high-ability workers should complete 13.5 years of education. The wage rate for high-ability workers is then: W = 50(E-10) = 50(3.5) = 175 Therefore, the most efficient separating equilibrium is for low-ability workers to only complete the mandatory 10 years of education and earn a wage of $0, while high-ability workers complete 13.5 years of education and earn a wage of $175. Choice B is the correct answer.

The Value of a Worker's Marginal Product Is $50 Per