Consider the model of job market signaling explored. More specifically, consider the mode of analysis that is attributed to Spence, where workers choose education levels in anticipation of the wages they will receive. We explored both separating and pooling equilibria, where we assumed that each type of worker chooses one and only one level of education in equilibrium.

(a) Are there any separating equilibrium where one type (or both) chooses more than one level of education? By a separating equilibrium we mean that if one type chooses a given education level with positive probability, then the other type does not.

(b) Is there any pooling equilibrium where both types choose more than one level of education? By a pooling equilibrium we mean that every education level chosen by one type with positive probability is chosen by the other type with positive probability.

(c) A hybrid equilibrium is one inwhich some education levels are chosen by one type only and others are chosen by both types. Are there any hybrid equilibria? If so, how many different "types" of them can you construct?

(d) What is the maximum number of education levels that a low-ability worker can choose with positive probability in any equilibrium? What is the maximum number of education levels that a high-ability worker can choose with positive probability in any equilibrium? Justify your answers.