question is about asymmetric information

Consider the adverse selection model, where the ability of each worker, 0, can be 1, 2 or 5. Workers observe their own abilities, but firms only observe the overall distribution of probabilities ( 1/3 , 1/6 , 1/2 ). Suppose that the reservation value is r(0) = 0.5+0.50. (a) What is the range of wages, for which all workers accept the competitive wage? What is expected productivity in this case? What is the range of possible wages for which a firm hires a random worker? Will there be a functioning labor market in this case? (b) What is the range of wages, for which no workers accept the competitive wage? (c) What is the range of wages, for which only lowest type workers accept the competitive wage? What is expected productivity in this case? What is the range of possible wages for which a firm hires a random worker in this case? Will there be functioning labor market? (d) What is the range of wages, for which only lowest and medium type workers accept the competitive wage? What is expected productivity in this case? What is the range of possible wages for which a firm hires a random worker in this case? Will there be functioning labor market in this case