Consider an overlapping generation set up with pay-as-you-go social security sys
ID: 1111332 • Letter: C
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?
Explanation / Answer
a). Population growth rate (n) = New Population (n1) - Old population (n0) / Old population (n0)
n = n1 - 203 / 203
n = n1/203 - 1
b) Current Contribution of Young Workers = Total Salary of Young workers * 15/100
= (1040 * 103 * 15/100) = 16,068
c). Each retiree can recieve = Total Contribution by Young Workers/number of retirees
= 16,068/100 = 160.68
d). Contribution of Each old retiree = Salary of 1 retiree * 15/100 = 1000*15/100 = 150
e). Implicit Return is the total economic benefit that has been derived from the scheme. The implicit return in this case could be better financing opportunities for the old people after they have retired due to social security scheme.