1. The value of a worker's marginal product is $50 per hour for high-ability workers and $18 per hour for low-ability workers. Let W denote the wage rate and Y years of education. The preferences of highability workers correspond to the utility function: U H (Y, W) = W 4Y. The preferences of low-ability workers correspond to the utility function: UL (Y, W) = W - 81'. By law, everyone is required to attend at least 10 years of school. The percentage of the population that has low ability is a. a. What can you say about the educational attainment of each type of worker in a separating equilibrium? b. Mathematically determine what would have to be true of a for the pooling equilibrium to be a Pareto improvement over some, but not all, separating equilibria. c. What critical assumption is necessary for years of education to be a successful signal and how is it represented in this