In: Statistics and Probability
The future of Social Security and Medicare generates a lot of
debate and political posturing. Analysts predict that, without
significant change, Social Security and Medicare funds will be
exhausted at some future date (the date depends on the expert). The
exercise asks you to use linear trends based on Social Security
Administration historical data in order to estimate when, if ever,
the funds will be in trouble (i.e., when disbursements will exceed
income).
Social Security income for the years 1990-2000 suggest that the
income trend can be estimated by the equation
y = 21.27x + 264.5
where x is the number of years since 1990 and y = annual income in billions of dollars. For the same years, the Social Security disbursements have the linear trend
y = 13.28x + 226.59.
(a) Find the point where income = disbursements. (Enter your answer as an ordered pair. Round your answers to two decimal places.)
(x, y) = |
(b) Does this suggest that Social Security is going broke?
YesNo
(c) What other factors might influence the trend that would cause
it to deviate from the linear trend?
The data for 1990 - 2003 is based on the populations that pay into
the Social Security fund and those that secure payments from the
fund. The relative size of these populations will change as Baby
Boomers retire. The Baby Boomers are the generation for which there
was a significantly higher birth rate. As they retire, the
population of Social Security recipients
will ---Select--- increase decrease and those paying
into the fund will ---Select--- increase decrease .
Thus, income will ---Select--- increase decrease and
disbursements will ---Select--- increase decrease . This
effect is not included in trends based on past income and
disbursements.