1. Notes on Social Security
Two important factors:
(i) Rate of population growth.
(ii) Ratio of the length of working years to retirement years.

2. Steady-state picture assuming a population growth rate of 10% over 10 years and a 4 to 1 ratio for working years to retirement.
Retired
Working
(65-75)
55-65
45-55
35-45
25-35 1
1.1
(1.1)2
(1.1)3
(1.1)4
(1.1)5
(1.1)6
etc.

3. This gives a ratio of working persons to retired persons of
This means that if each working person contributes one $ in taxes, each old person can receive about $5 dollars in retirement.

4. Now suppose life expectancy changes to 80 years so that people will leave for 15 years in retirement rather than 10 years (if the retirement age remains as 65). This will change the ratio of working persons to retired persons to:
Consequently, if the tax payments do not change, $1 tax per worker can finance only $3.4 in retirement benefits.

5. Now consider a reduction in population growth rate from 10% to 5% over a 10-year period. The picture will change as follows:
Retired
Working
(65-75)
55-65
45-55
35-45
25-35 1
1.1
(1.1)2
(1.1)3
(1.1)4
(1.1)4(1.05)
(1.1)4(1.05)2
(1.1)4(1.05)3
(1.1)4(1.05)4
(1.1)3(1.05)
(1.1)4(1.05)5
etc.

6. Or Retired Working (65-75) 55-65 45-55 35-45 25-35 1 1.1 (1.1)2 (1.1)3
(1.1)4
(1.1)3(1.05)
(1.1)2(1.05)
(1.1)2(1.05)2
(1.1)(1.05)
(1.1)(1.05)2
(1.1)(1.05)3
1.05
(1.05)2
(1.05)3
(1.05)4
etc.

7. The development of the ratio of working people to retired people:
to to to to
This implies that a one-dollar tax payment by working people can only finance a retirement benefit of about $4.53.

8. Importance of the alternatives
Suppose the rate of return on investment is 20% (over a 10-year period). the implication of this is that if one saves $1 during his/her working years, he/she will get
Compare this with 4.53

9. Another way to see the comparison is in terms of present values. Thus
Present value of tax payments
Present value of benefits
Net present value