There are two types of workers, H (high skilled) types and L (low skilled) types. Workers' utility function is: = () () for L types = () () for H types where () is the compensation schedule posted by firms, () is the cost of acquiring an education of e years for an H type, () is the cost of acquiring an education of e years for an L type. Suppose that () = 0.5 2 and () = 0.75 2 . Suppose that the value of the marginal product of an H type is 6 and the value of the marginal product of an L type is 3. Suppose that 1/3 of the workers are H types, but an employer cannot directly distinguish an H type from an L type.

Find a separating equilibrium and derive the equilibrium compensation schedule posted by firms at this equilibrium. Compare the equilibrium investments in education made by both types with respect to the levels of investment that they would make in the case of full information.