Boom or Bust: A Model of the Economic Impact of the Baby Boomers

1. Boom or Bust: A Model of the Economic Impact of the Baby Boomers Les Fletcher Brad Poon April 29, 2003 Math 164 Scientific Computing

2. Overview • Introduction • Questions • Model Description • Results / Analysis • Conclusion

3. Introduction • The Baby Boomers resulted in a rapid increase of the world’s birth rate, which is only now skewing the elderly / youth ratio • eg. United States, Japan • We want to analyze the impact of this disproportion, particularly in the economic sector • Use actual U.S. demographic data to accurately model it’s population trend • ie. U.S. Department of Labor 2001 census report (http://www.bls.gov/cex/csxann01.pdf)

4. Questions • For what initial injection of a baby boomer birth rate will cause a significant collapse in the economy? • Should we encourage the elderly to do volunteer work in the economy as a means to remediate the problem? • Should we push back the age of retirement?

5. Initial Model • Break up population into sub-populations based on age • Youth (0-9) • Adolescent / Young Adult (10-19) • Adult (20-64) • Elderly (65-death) • Use time-continuous differential equation to model population change

6. Initial Model (cont.) Adolescent (Y) Youth (X) a : birth rate by adults b : death rate of youth c : ascension rate to adolescents d : death rate of adolescents e : ascension rate to adults Adult (Z) Elderly (E) f : death rate of adults g : ascension rate to elderly h : death rate of elderly

7. Initial Model (Results) • Population growth is exponential!

8. Modification to Model • Need to add some sort of “carrying capacity” limit to the model • Solution: Add a separate resource function and make births and deaths dependent on amount of resources available • Similar to consumer resource models

9. New Model with Resource Dependence • Define new resource function: • Therefore, at each time step we will have: • Resources consumed: • Resources available: c : consumption rate of resources p : production rate of resources

10. Population Dependence on Resources • The population birth and death rates will now vary as a function of available resources:

11. Population Dependence on Resources (cont.) • We need to define limits for the birth and death rates with respect to the availability of resources • For example, if there are no resources available, birth rates will go down and death rates will go up

12. Population Dependence on Resources (cont.) • Solution: Use a step-function inverse tangent! If (rc/ra < 1), then A = some lower limit else A = some upper limit A : max change s : sensitivity to change

13. Results (control group)

14. Results (baby boom) Now, at time t=100 years, increase the birth rate for 5 years to simulate a “baby boom” 6x original birth rate 7x original birth rate Population dies!

15. Should we encourage elderly to volunteer? • Increase production rate pE of elderly at time of baby boom (t = 100 years) to simulate volunteering: 50% more productive Population still dies out 75% more productive Population recovers!

16. Should we push back age of retirement? • Decrease ascension rate of adults to elderly so that the population is more productive for a longer time Extend retirement age to 70 Population still dies out Extend retirement age to 90! Population recovers!

17. Conclusion • We were able to construct a population model such that we could “tweak” parameters to simulate various economic recovery policies • Limitations to our model: • Baby boom did not actually reflect a youth / elderly disparity ratio, which was our original intention • Death rates are dependent on shared resources, as opposed to resources specific to each age group • No immigration / emigration factors are taken into account, which is a major factor in population trends