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)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.) Youth (X) Adolescent (Y) Adult (Z) Elderly (E) 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 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 rate7x original birth rate Population dies!

15. Should we encourage elderly to volunteer? Increase production rate p E 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