1. PAYG Social Security (15 pts). Suppose the following are the percentages of different age groups in China in year 2000, 2010 and 2020. Year 2000 2010 2020 Children Adults Senior (Age () - 24) (Age 25 - 64) (Age 65 and above) 0.39 0.54 0.07 0.33 0.57 0.09 0.29 0.59 0.12 In a PAYG social security, each adult is taxed fraction t of his/her wage and each senior receives fraction b of his/her wage before retiring. The social security system balances budget every year. Suppose all adults and seniors (before retiring) earn the same wage. (a) (5 pts) If each senior receives 40% of his/her wage before retiring, i.e. b = 0.4, what do the tax rates need to be in years 2000, 2010, and 2020, respectively? (b) (5 pts) If, instead, each adult is taxed 10% of their wage, i.e. T = 0.1, how much can seniors receive as a fraction of their wage in years 2000, 2010, and 2020, respectively? (C) (5 pts) Discuss how children's share of the population enters into your calculations in parts (a) and (b). What about for calculating the tax rate or replacement rate in year 2050