Problem 1 Let's assume our community has both high productivity workers (where their marginal product of labor is 45) and low productivity workers (where their marginal product of labor is 25). (a) What would be the wage if we had perfect infermatiOn? (b) Now, let's assume there is asymmetric information. If we know that our community is made up of 40% of high productivity workers, what is the competitive wage? (c) Let's assume we've decided to offer a wage of $45 if a worker has at least 4 years of college. If they do not have at least 4 years, we will offer a wage of $25. If each year of college costs $6, what will each type do? (d) Let's now assume the rm will offer the wage of $45 for any worker that obtains some 8* level of education. Further assume that the cost of education is now $2 per year for the high- productivity worker and $4 per year for the low-productivity worker. For what levels of 6* will each type go to college? What is the separating equilibrium? (c) It turns out the rm was wrong about the labor supply composition. In reality, the labor supply consists of 10% high-productivity workers and 90% low-productivity workers. What is the competitive wage is this case? How does it differ? Explain