3. (This is Problem 9U9 in the textbook) Consider Spence's job-market signalling model with the following specications. There are two types of workers, 1 and 2. The productivities of the two types, as functions of the level of education, are W1[EJ = E and ME] = 1.5E. The cost of education of the two types, as functions of the level of educations, are cite = if and C2[El = '32. Each worker's utility is equal to his or her income minus the cost of education. Companies that seek to hire these workers are perfectly competitive in the labor market. {a} If types are public information [observable and veriable), find expressions for the levels of education, income, and utilities of the two types of workers. Now suppose that each worker's types is his or her private information. {b} Verify that if the contracts of part (a) are attempted in this situation of information asymmetry, then type 2 does not want to take up the contract of type 1, but type 1 does want to take up the contract intended for type 2, so \"natural\" separation cannot preval. (c) If we leave the contract of type 1 as in part (a), what is the range of contracts (education-wage pairs) for type 2 that can achieve separation? (d) Of the separating contracts, which one do you expect to prevail? Give a verbal but not a formal explanation for your answer. (e) Who gains or loses from the information asymmetry? How much