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Boom or Bust: A Model of the Economic Impact of the Baby Boomers. Les Fletcher Brad Poon April 29, 2003 Math 164 Scientific Computing. Overview. Introduction Questions Model Description Results / Analysis Conclusion. Introduction.

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Boom or bust a model of the economic impact of the baby boomers

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

Les Fletcher

Brad Poon

April 29, 2003

Math 164 Scientific Computing


Overview
Overview

  • Introduction

  • Questions

  • Model Description

  • Results / Analysis

  • Conclusion


Introduction
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)


Questions
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?


Initial model
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


Initial model cont
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


Initial model results
Initial Model (Results)

  • Population growth is exponential!


Modification to model
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


New model with resource dependence
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


Population dependence on resources
Population Dependence on Resources

  • The population birth and death rates will now vary as a function of available resources:


Population dependence on resources cont
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


Population dependence on resources cont1
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



Results baby boom
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!


Should we encourage elderly to volunteer
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!


Should we push back age of retirement
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!


Conclusion
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