Problem 3: Screening [25 points]. There is a tted population of workers in the economy. Each worker has utility u(t:, q, H) = u (q 2: t), where t is the tax [ifnegative then the subsidy). q 2 0 is income. and 2 39 is the cost a worker has to pay to earn the income. There are Mo types of workers, the low ability (6 = 6L 2: O) and high ability (9 = 9H 2: HQ. The share of low ability workers is ,8 E (0.1). Benevolent government offers a tax scheme {(tL, qL), (TIH, qH)}1 and wants to maximize the totalwelfare [Bary qL, BL) + (1 )u(c, qH, 91,.) subject to budget constraint tL + (1 Mob. 2 l} 2and incentive compatibility constraints which guarantee that low ability worker chooses (Q, {is} and high ability worker chooses (EH, qH). We assume the government can force the workers to pay taxes, so there is no need for individual rationality constraints. In addition, assume u(-) is increasing and concave. 1) [3 points] Find the first best tax scheme {(cL, qL), (EH. qH)} (i.e., when the government can observe the ability of each worker, so it does not have to take care of incentive compatibility constraints). 2) [1? points] Find the second best tax scheme {(tL,qL),(tH,qH)} [i.e., when the asymmetry of information is taken into account}. Compare the second best taxes with the first best taxes for both types. Comment on the differences. as: There is no pc formula for (1