There is a fixed population of workers in the economy. Each worker has utility u(t,q, i9) = u (q g t), where t is the tax (if negative, then the subsidy), q 2 0 is income, and g is the cost a worker has to pay to earn the income. There are two types of workers, the low ability (9 = 9L 2':- D) and high ability (9 = EH > 9L)- The share of low ability workers is )3 E (0.1). Benevolent government offers a tax scheme {(tL, qL), (t3, qH)}1 and wants to maximize the total welfare 3110;, mg, 91,) + (1 )u(tH, qH, SH) subject to budt oonstraintBtL + (1 mtg 2 0 2 and incentive compatibility constraints which guarantee that low ability worker chooses (tL, qL) and high ability worker chooses (t3, q). 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. i) [3 points] Find the first besttax scheme Km, (1);). (he, q 11.)} (Le, when the government can observe the ability of each worker, so it does not have to take care of incentive compatibility constraints). 2) [Ti points] Find the second best tax scheme {(tL,qL),(tH,qH)} (is, 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. nth: There is no explicit formula for Cit.- 1In genereL a tee scheme is a function t = em], but since we only have two types, finding two pairs is sufficient i This means that the only source of financing for gevernme nt is workers