There are three types of workers in the world. I. ii. and Ill: each type has probability 1(3. The output of a type | worker is 100. the output of a type II is 8i], and the output of a type III is 4'3. Employers observe oniy the worker's level of education e. not her type t, and pay a wage to equal to the expected output given the beliefs about the worker's type (I. II or III} induced by her education. The worker's utility is the wage she gets minus the cost of the education. The cost of education for a type i is 5 per year. the cost to a type II is H] per year. and the cost to a type III is 20 per year. The worker can choose her years of education freely from [0. oo} - that is. she*s not constrained to integer amounts. [a] Find a pooling FEE in pure strategies. Specify beliefs. {b} Find the least years of education for each type for which there is a pure fully separating PBE {one in which each type gets a different number of years of education). If no fully separating equilibria exist. show this