[30 points] The government of Cauria considers to choose one among three possible income tax reforms, as listed below. Y denotes an individuals yearly income, and is the income tax rate. Reform 1: No lump-sum transfer. Everyone pays income tax, of which the marginal tax rate for each income bracket is as follows. Annual Income Marginal Tax Rate Below 30 million 0% Between 30 million and 60 million 8% Between 60 million and 90 million 19% Between 90 million and 120 million 33% Over 120 million 48.5% Reform 2: Everyone receives a refundable tax credit of 20 million won. Everyone pays income tax at the rate 2= 40%. Reform 3: Everyone receives a lump-sum transfer of 20 million won. Everyone pays income tax at the rate 3, where 3 = 0.5 500 million ( + 1 ) (1) [15 points] Discuss the income tax progressivity of each reform. (2) [15 points] Evaluate the merits and shortcomings of each reform in the perspective of optimal income tax.