Question

Consider an overlapping generation set up with pay-as-you-go social security system in a hypothetical economy. There are 100 old retirees and 103 young workers at the current period. Old retirees earned $1,000 each when they were young. Young workers now earn $1,040 each. Suppose that the population growth is constant and there is a fixed payroll tax of 15%, which is used to finance the pay-as-you-go social security system. (a) what is the population growth rate, n? (b) How much is the total contribution of young workers to the social security system in the current period? (c) How much each retiree can receive from the social security system? (d) How much was the contribution of each old retiree when he or she was young? (e) What is the implicit return on the social security system?

Answer 1

Answer:

a) 3%

b) the new workers contribute 16,068 dollars

c)$160.68 each

d) the old workers contribute 15,000 when they made his contribution

e) rate of return 7.12%

Explanation:

growth rate: the increase in the workforce:

103 new workers / 100 retired - 1 = 0.03 = 3%

103 workers x 1,040 each x 15% = 16,068

assuming no other employee:

$16,068 pension fund / 100 retired persons = 160.68 dollars each

100 workers x 1,000 each x 15% = 15,000

e) the old retire contribute:

1,000 x 15% =  150

they receive 160.68

rate of return:

160.68 / 150 - 1 = 0.0712