5. Spence Signaling When Education Enhances Productivity: While education can signal ability, many types of education (such as economics classes and program ming in R!) also teach valuable skills that increase as well as reveal a workers pro ductivity.Consider the model of education signaling ability that we analyzed in class but now assume that education, in addition to its signaling value, directly increases the marginal product of labor. Specically a worker of type or E {1, 2} who chooses education level 6 E 1R+ is worth or + 2A3 to each rm. The worker's utility is we/a when she acquires education a and is hired at wage to, and two rms compete so that, in any Perfect Bayesian Equilibrium in which both rms form the same belief p.03) 2 Pr[o: 2 He), the wage is w(e) = 2 ,u.(c) + 2A6. Assume that the fraction of type 0: = 1 workers in the economy is p = 1/2. [Note: There are two differences with the model from class: education is intrinsically valuable, and the cost of education is quadratic rather than linear in the education acquired] (a) Suppose o: is publicly observed. Solve the level of education and the wage for each type in equilibrium. (b) Suppose now, and for the remainder of the question, that o: is the worker's private information. Determine the level of education 8 chosen by the or = 1 type in any separating equilibrium. (c) For which values of A does there exist a pooling equilibrium in which both types choose 8 = 0? Does this equilibrium seem natural to you? (d) For which levels of A is there a PBE in which both types choose the same level of education as they would under public information? {6) Provide an economic explanation for your answer in part (d)