Clark County • Washington

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Background Information for Exponential Growth Spreadsheets

There is an underlying assumption in all growth planning under discussion for this county, which is not necessary and drives all resultant estimates of resources required to accommodate that growth. That is the assumption that growth must be planned for at some fixed rate of growth, which (like a compound interest process) gives you exponential growth and the horrendously large increases in population that a constant growth rate entails over time.

Using a fixed growth rate, any fixed growth rate, is basically tantamount to planning for failure, leading inevitably to a crisis when available resources (land, money, infrastructure) are inadequate for continued growth. At such junctures growth is abruptly curtailed with predictable economic repercussions throughout the economy, particularly those parts of the economy like the building construction industry which are dependent on growth.

There are other models for continuing growth, which can meet the population targets currently set by the state Office of Financial Management (OFM), but which lead to a more reasonable sustainable growth pattern which will not inevitably degrade our standard of living and destroy everything the residents of this County hold dear.

One is to grow with a fixed numerical increase in population each year, a simple linear increase in population which avoids the compounding effect of a fixed growth rate. The first Excel Spreadsheet attached (ExponentialGrowth.xls) compares the population levels each year over 5, 10, 20, and 40 year growth periods for various fixed growth rates. By manipulating the basic exponential growth equation for an x% Annual Growth Rate:

Base Population * ( 1 + x /100 )^N = Total Population at end of Year N

We can calculate the equivalent constant growth rate which will yield a given target population in a given year for a given base population in a preceding year. The Spreadsheet provides a comparison of the resultant populations for a number of different growth rates, including: the presently proposed 1.83% annual growth rate, the upper and lower-bound growth rates meeting the OFM maximum and minimum target values for the year 2020 (as defined in the FEIS), 2.433% and 1.127% respectively, and a linear growth increase value, expressed as a fixed percentage of the initial base population (for our purposes the Clark County estimated 2002 population from the FEIS).

The downside of the linear model shown in the first Spreadsheet is that in order to see substantially lower long-term population numbers, the annual increase in population from year 1 onward must be substantially lower than the 20 year historical, and presumably current, rate of growth. That would immediately and substantially impact the home building industry, resulting in significant job losses in that industry. That is in nobody's best interest.

The goal, as we move away from being a bedroom community for Portland, is to avoid abrupt growth transitions and consequent economic dislocations, gradually transitioning a portion of the home building industry's growth to building commercial and business developments that will provide jobs for Clark County residents; again at a steady numerical annual increase but not at a constant rate of increase. That may be accomplished by fostering public policies which gradually decrease the amount of annual increases in population and home building to some lower long-term sustainable level.

The 2nd Excel Spreadsheet attached (ExponentialSustainable.xls) provides a means of modeling the effects of such a policy, with a fixed rate of decrease in growth from the initial annual growth increment value to a lower, presumed to be sustainable, value for the planned-for annual numerical increase in population.

Both spreadsheets are protected (to prevent accidental changes to the calculation formulas) but live for real-time what-if explorations, with editable input values for initial percentage of baseline growth incremental value, rate of decrease of increasing growth, and sustainable annual growth increase value, depicted in BOLD text on the Spreadsheets (cells containing plain text are calculated values). Experimentation is encouraged. Particularly interesting percentage of base year population values to explore for the non-exponentially growing growth models are 1.25%, 1.5%, 1.83%, 2%, and 3%.

Lest anyone believe that these are academic distinctions with no real-world significance, I leave you with the following facts regarding one piece of the population growth infrastructure requirements: our schools.

Per the Clark County 2003 Population and Economic Handbook, there were a total of 67,406 pupils enrolled in Clark County public schools in 2002, which out of a total population of 370,463, works out to approx. 18.2% or 1 student per every 5.5 people (0.489 students per household, or about 1 student for every 2 households, for the reported population distribution of 2.69 people per household). At about 600 pupils per school, that works out to 1 school's worth of children for every 3300 person increase in population. That is approximately 3 new schools required for each 10,000 person increase in population.

Under the current proposed growth rate of 1.83%, the first 10,000 person, 3 school increase point hits in about 1.5 (more precisely 1.46876) years in 2004, more often thereafter. An increase of 100, 000 people, requires the building of 30 new schools; we hit that level of population increase in 13 years, and then again 11 years later.

By way of contrast, if we start with growth increasing by 3% of the baseline population annually (our historical average annual growth rate), with the annual increase value decreasing at a 20% annual rate to a target sustainable annual population increase value of 4000 people, the numbers are quite different. We hit the fist 10,000 person increase in population in 1 year, reaching the presumed sustainable 4000 person annual population growth value in 6 years, and a 100,000 person population increase in 20 years. Not perfect, but better.

Using appropriate baseline numbers, similar estimates can be created for all elements of our County infrastructure.
 

-WEM