Suppose the following are the percentages of different age groups in US in year

2000, 2010 and 2020.

Year Children Adults Senior

(Age 0 - 24) (Age 25 - 64) (Age 65 and above)

2000 0.39 0.54 0.07

2010 0.33 0.57 0.09

2020 0.29 0.59 0.12

In a PAYG social security, each adult is taxed fraction 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 60% of his/her wage before retiring, i.e. b = 0.6, what do the tax rates need to be in year 2000, 2010, and 2020, respectively?

(b) (5 pts) If, instead, each adult is taxed 10% of their wage, i.e. = 0.1, how much can seniors receive as a fraction of their wage in year 2000, 2010, and 2020, respectively?

(c) (5 pts) Discuss the pattern you find in parts (a) and (b). What does it tell you about the shortcomings of PAYG social security? What can be done to improve the situation?