3. Suppose there are two types of workers, k = G, B, differentiated by their productivity levels. Type G workers have productivity k = 2 and type B workers have productivity k= 1. The cost of achieving a given level of education is higher for type B than type G workers. The cost function of a type k to achieve education level e is cle; k) = * The utility function of a type k worker is u(w.e; k) = w-cle:k). (a) (10 points) Does a worker's education level affect productivity? If there was perfect information, what would be the optimal e, w be? (b) (15 points) Now suppose there is asymmetric information and the productivity level is known only to the worker. The type of the worker is not observable, but the level of education is. The firm believes that a worker with higher level of education than a threshold has higher productivity. Thus, it pays w(e) = 2 if e > e and w(e) = 1 if e