Reilly’s Law of Retail Gravitation

We’re in a good location to observe Reilly’s law – Libby attracts very little commerce from North County, and we’ve had a great example of how a political decision that minimizes travel at Roosville changes the retail industry. 

Reilly’s law best applies to the midwest plains – an area where mountains and rivers have minimal effect.  On the other hand, where 37 is the route to Libby, and 93 the route to Whitefish and Kalispell, the limits created by mountains and rivers kind of cancel out.   

From the web-site article: “Reilly realized that the larger a city, the larger a trade area it would have and thus it would draw from a larger hinterland around the city. Two cities of equal size have a trade area boundary midway between the two cities. When cities are of unequal size, the boundary lies closer to the smaller city, giving the larger city a larger trade area.

Reilly called the boundary between two trade areas the breaking point (BP). On that line, exactly half the population shops at either of the two cities.

The formula is used between two cities to find the BP between the two. The distance between the two cities is divided by one plus the result of dividing the population of city B by the population of city A. The resulting BP is the distance from city A to the 50% boundary of the trade area.

One can determine the complete trade area of a city by determining the BP between multiple cities or centers.

Of course, Reilly’s law presumes that the cities are on a flat plain without any rivers, freeways, political boundaries, consumer preferences, or mountains to modify an individual’s progress toward a city.”

The populations can be accessed readily – the census count for Eureka is 1,380. The Census lists Libby at 2,775, Whitefish at 7,751 and Kalispell at 24,558.  With Libby and Kalispell essentially equal distance from Eureka, the retail gravitation of Kalispell greatly overpowers Libby – even if we ignore the population that is outside the city limits (and north-county has a higher percentage outside town limits).  In terms of county solidarity, Libby just doesn’t attract north-county commerce.

A Science for Everyone, Community, Demography

Statistically Remote Doesn’t Mean Impossible

My post-Uvalde thoughts move toward hardening our own little school.  School shootings are always statistically unlikely.  The timeline at Uvalde shows that at 11:27, a teacher props the door open. It remains open for 6 minutes before the crazy little bastard enters the school.  He doesn’t close it – the door remains open and is the access point for police.  A safety protocol broke down.  The crazy little bastard had a six-minute window of opportunity.  Twenty-one people died and 17 more were wounded.  Six minutes.

In demography, our phrase is “Malthus only has to be right once.”  I listened to a Fed describing terrorist attacks  – “They have to get lucky once.  We have to get it right every day.”  The exercise showed how hard that was.  A teacher, secure in the misbelief that a statistically unlikely event wouldn’t happen, propped a door open.  For 6 minutes.  The crazy got in.  The statistically unlikely event happened.  We play poker hoping for statistically unlikely events to occur. 

It’s easy to look at the police failures – but the initial failure was the teacher who wedged the door open . . . secure in the belief that there was no risk in violating that simple safety protocol.  Staying alert, maintaining security against something that does not occur, day after day, is difficult. 

I can think of many situations where a teacher wouldn’t want to keep unlocking the door.  It’s Spring – the time when contracts are, or are not renewed.  We’ve had that this year at Trego – and seen a bit of hostility over it.  It gives me a perspective that, in Uvalde, the shooter gained access not through police failure, but through a teacher’s carelessness.  I can understand both carelessness and resentment.

I have forgotten the name of the teacher who left his female engineering students to be killed at the Montreal Polytechnique Massacre.  I hope he came to some sort of grips with his failure – I know I could not have accepted that decision had it been mine.  Perhaps the Uvalde teacher who spent 20 lives for easier access to the door can come to grips with that conduct.  I would hate to have to rationalize it had it been my blunder.

It is difficult to stay constantly on the alert for the statistically unlikely occurrence.  Years of boredom are eventually interrupted by a few minutes of stark terror.  Uvalde’s police, like Parkland’s, made poor choices – but the timeline shows that a teacher who propped the door open had the best opportunity to eliminate the shooter’s opportunity.  Was it just casual carelessness?  Was it carelessness coupled with resentment?  I do not know – but I have read the pricetag, and it was too high.

A Science for Everyone, Community, Demography

Thoughts on Inflation

I’ve been watching monetary inflation since 1976 when I voted for Jimmy Carter.  I still don’t give Jimmy full credit for that spate of inflation – Nixon made the call that the US dollar would no longer be backed by gold in August of 1971.

1968 had been an interesting election – I recall the unhappy observation “Nixon, Humphrey, Wallace – three strikes and you’re out.”  The picture below brought back memories of a happier time, when I would add a million dollar Zimbabwe bill to a retirement card, so that my retiring colleagues would be millionaires as they left the university.  Ten bucks bought all the Zim million dollar notes I needed for a slew of retirement receptions.

Now the thing about inflation is that it taxes savers, and can move into being a tax on investors.  If we look at the value of gold during the California Gold Rush – 1849 – it was $18.93 per ounce.  That same value held through the Virginia City days, and basically took Montana from wilderness to statehood.  In 1920, gold finally topped $20 per ounce.  When Franklin Roosevelt was elected President, gold was at $20.69 per ounce – the next year, 1933, it was $26.33.  In 1934, it went to $34.69.

A couple of old Winchester catalogs, from 1900 and 1916, suggest that my Grandfather paid about $19.50 or a little more for his 1894 32 special rifle.  A glance online suggests somewhere close to $1,200 dollars today.  As I write this, gold is going for $1890.35 – roughly 100 times higher than when the rifle was made in 1902 along with the new, more powerful 32 special.  The cost of the rifle hasn’t kept up with gold.  Inflation or not, it’s kind of nice to look off the front porch and see the spot where my grandmother got a four-point in 1922.

At that turn of the century, land here was still available for homesteading – land here in Trego had little value.  Thirty dollars per acre was still a norm for accessible land in the 1950’s.  It’s another basis for calculating inflation – and if memory serves, Lee Harvey Oswald was paid 85 cents per hour in 1963. 

Median family incomes were somewhere around $500 per year in 1900, and had risen to about $3,300 by 1950.  Still, that half century was a time of many new developments and a greatly improved living standard.  Part of the change was that people could buy more – much like during our more recent inflationary times – along with the inflation of the eighties came the personal computer, the compact discs, video players etc.  Technical advances reduced the impact of inflation.

There is a certain irony in Putin’s decision to tie the Russian ruble to the value of gold.  Since that decision the ruble has gone up 6% compared to the US dollar.  He’s kind of the anti-Nixon, creating a stronger currency instead of a weaker one.  I guess that inflation often boils down to a handful of government officials making the decision to print more money.  I have a hunch inflation helps the folks who get the new dollars a lot more than it helps those who are trying to hang on to the existing dollars.


My Neighborhood Doesn’t Reflect My Nation

One of the advantages of social media is that folks with different views post their different opinions.  One of the disadvantages is that those different opinions come from different – often very different – locations. 

Let’s take climate change opinions for a simple example – I live just a touch south of the 49th parallel and a little over 3,000 feet above sea level.  Simple facts are that raising the sea level by a couple hundred feet isn’t going to affect my place.  Getting another three weeks of growing season is a positive thing for my garden.  If I were living in Paramaribo, just a little north of the equator and about 6 feet above sea level, my perspective would be different.  My greatest risk is wildfire – in Paramaribo even the dry season is rainy.

One of the readily available measurements of population is the percentage of foreign-born residents in a community.  In San Francisco, 34.4% of the population were born outside the United States.  Statewide, 26.9% of California residents were born outside the US.  Here in Lincoln County, Montana 2.6% of our population are foreign born (and I suspect half of those are Canadian).  It makes for a different point of view.

Race?  I live in a state where most of the population is white, and the second largest group is American Indian (6.6%).  Contrast that with Washington DC, where the Black population is 46.4% (compared to Montana’s 0.6%).  West Virginia somehow has the lowest percentage of foreign born residents and the lowest percentage of American Indian population.  Maine (94.6%) is the whitest state.  I have a hunch that who your neighbors are might affect your viewpoint.

18.7% of Montana’s population is over 65 – and five states are even higher.  Just 11.1% of Utah’s population is over 65.  (29.5% of Utah is under 18).  Who you see around you affects your perspective. More information is available at

Washington DC has the nation’s highest median household income – $92,266 . . . but it is skewed by race.  The median for Black households is $42,161, while the white median is $134,358.  Montana’s median household income was $65,712.  Mississippi came in last at $45,081.

West Virginia has the highest home ownership rate – 74.6%, while Montana’s rate is 69.7%.  Home ownership rate in Washington DC is around 42.5%.

Just a few spots where we can look at how our locality affects how we perceive the universe.

A Science for Everyone, Demography

Is Demography Really Destiny?

I’m looking at folks showing Russian, Ukrainian, and Chinese population pyramids, and ominously stating “Demography is Destiny.”  Of course I’ve been looking at Paul Ehrlich’s book The Population Bomb all of my student and professional life, and know what the population pyramid showed him in 1968 – and his interpretation sure as hell didn’t pan out.

Ehrlich predicted famine because of the rapid population growth.  Politicians looked at 9.2% of the population over 65, and knew that the Social Security System would be solid forever.  After all, “Demography is destiny”, right?

By 1970 – the year I turned 21 – the base of the pyramid showed where the trend was changing.  Lifespans had been increasing over the 20th century, and the 1970 pyramid showed that reproduction was slowing down.  Ehrlich had ignored the green revolution, and the politicians who could do simple math could realize that Social Security wasn’t going to be a cash cow.  We had passed the point where the Demographic Transition Model kicked in.  By the way – use to grab your own data – for years I’ve used spreadsheets to develop my pyramids, but these folks have put the data onto the net, helping make demography everyone’s science.

By 2000, the population pyramid had lost most of the resemblance to a pyramid, and even the most ignorant congresscritters could see the threat to Social Security.  Did I mention that Ehrlich’s training is in biology, and that his dissertation was on butterflies? 

I have no problem with the idea that “Demography is Destiny.”  The problem is that destiny is more readily observed in hindsight than in projecting today’s data into the future. 

I’m a rural demographer – well ahead of the curve in my specialized areas, but my areas are rural US – the real specialized areas are Hutterite and Reservation populations.  I can make some projections from the Russian, Ukrainian, and Chinese pyramids – but they basically start with, “Gosh!  There are a heckuva lot of old people in these countries.  There should be plenty of work for the younger generations.”

Seriously, go to, find the answers to your own questions.  In 1970, demography was based in the universities because their libraries held all the data.  Now, the data is online, and the science is open to everyone.  And I enjoy being able to share my science.

A Science for Everyone, Demography

Thinking Karl Marx

I suspect that today’s average leftist or socialist has left a bunch of Karl Marx’ writings unread.  The big thing to remember is that Karl spent a lot of years studying capitalism, identified a lot of systemic inequities, then proposed communism as an alternative.  Since the closest thing to his proposed communism at the time was the utopian socialist agenda, and utopian socialism wasn’t a major player, he didn’t have a lot of examples of the inequities that occur under socialism.

I tend to look at things from a demographic perspective – and I do use Marx’ Social Conflict Paradigm.  As we look at Marx’ terms, and attempt to fit them in with today’s political parties, we find a spot where his structure doesn’t match today’s parties.

Karl had divisions among the Bourgeoisie – the haute bourgeoisie and the petit bourgeoise.  Marx expected the concentration and centralization of capital would, sooner or later, put the petit bourgeoisie into the ranks of the working class (like the peasants would become the proletariat regardless of their attachment to the land.  The petit bourgeoisie basically hired laborers and worked alongside them.  The haute bourgeoisie on the other hand, didn’t work alongside the wage slaves they hired.

So if I look at the folks who drive the game, Soros, Gates, Musk, Zuckenberg, Dorsey, Pelosi, etc. qualify as haute bourgeoisie, while Rand Paul as an MD is a great example of the petit bourgeoisie.  I think Donald Trump might be a better fit as a petit bourgeoisie than as one of the haute bourgeoisie – the top cutoff line is definitely well above a million dollars.

The difference between the proletariat and the lumpenproletariat is the difference between the skilled and semi-skilled workforce and the chronically unemployed.   Marx studied capitalism – but, born in Prussia in 1818, lived under the late stages of feudalism instead of something more similar to our system where votes select the leadership.  The university system at the time was just beginning to break away from church dominance – Marx hypothesized about a more ideal social system during a time of tremendous social change.  There is a bit of irony in the fact that Karl Marx could complete a Ph.D. but never hold a job other than journalism.  We live in a time when many, like Marx, are highly educated but do not find particularly great employment.

Marx saw the haute bourgeoisie, the petit bourgeoisie, the proletariat, and the lumpenproletariat.  He didn’t foresee the emergence of a highly educated class that crossed into all those four groups.  That intelligentsia with minimal capital is a fifth group that screws up Marx’ hypothesis – largely by taking jobs in the bureaucracies of government and education.  Max Weber studied bureaucracies after Marx died.  To understand Marx, we need to remember he wrote hypothetically of a world that he understood largely from his studies of capitalism.  The new educated class may not have the property to fit well with the petit bourgeoisie, but they give orders and make good incomes.

So if we look at today’s politics, we see the left, the left – as home to an alliance of haute bourgeoisie and the lumpenproletariat – something that Marx’ dialectic did not predict.  While Karl did see the petit bourgeoisie learning that their best interests were shared with the proletariat, he never saw the petit bourgeoisie allying with the working class proletariats to become the dissatisfied republican voters.  The educated class that Marx didn’t consider can either give orders like the petit bourgeoisie, follow orders like the proletariat workers, or be fundamentally as hard to employ as the lumpenproletariat – but they tend to identify with the left. 

Some of Marx’ writings and thoughts created a solid foundation for my own work.  I appreciate the good work he did.  On the other hand, he died 140 years ago.  There are many things he did not foresee – and a college educated proletariat subgroup is one of them.  The college educated lumpenproletariat was likely even harder for Marx to envision. 

A Science for Everyone, Demography

Wells-Barnett Becoming Barbie

I note that Mattel is making a Barbie doll that honors Ida Wells-Barnett.

They note that she was a journalist, suffragette, and had a role in founding the NAACP – to me, her unusual strength was the use of statistics in her research on lynchings.  She deserves mention in her early role in social research and reliance on statistics.  Still, the article doesn’t include the quote that I find easy to remember:

I’m a Montanan.  My state’s legal tradition begins with vigilantes hanging a crooked sheriff and his minions.  In 1884, Granville Stuart organized another vigilance committee – now known as Stuart’s Stranglers – to end rustling.  In a short time, Stuart’s Stranglers killed at least 20 rustlers, and numbers up to 100 are written in some accounts.  By the end of the Summer, Granville Stuart was president of the Stockman’s Association.  Stuart’s activities, despite the poor record keeping, made 1884 the highest year for lynching white men in the US. (My readings suggest that the first recorded use of the numbers 3-7-77 was by Stuart’s Stranglers and not by the Vigilantes of Montana 20 years earlier)

Douglas Linder has published the data series Ida Wells started (maintained at Tuskegee) on lynchings by state and race. Clicking the link will give you an idea of how solid the lady’s research was – and how racist it was in some areas.

I’ll be looking for the Barbie – but I want mine to be holding a lever action Winchester.  She may not have been granted a graduate degree – but her work was important in developing American Sociology.

A Science for Everyone, Community, Demography

Our Communities by ACS Numbers

I listened to a comment about the median household income in Trego – and defaulted to my professional statement before retirement – “That’s American Community Survey data, and it’s not very good for small communities.”  When I checked it, the $36,458 median household income for Trego translates as “somewhere between $27,478 and $45,438.  ACS data has its uses, but it has to be used with a lot of caution.

So here’s a little ACS data on our communities – you can check for margin of error (MOE) here.   I wouldn’t recommend using any of the numbers without reviewing MOE – but just sharing the data shows the variance.  It’s safe to admit that my household was one selected for the ACS. With two retirees at home, I didn’t hurt Trego’s school enrollment rate, I raised the percentage of bachelors degree or above, kept the employment rate down, and raised the median age.

Trego CDPFortine CDPEureka CCDRexford Town
Median Age60.527.950.153.3
Median Household Income$36,458$68,036$40,827$30,481
Bachelor’s Degree or more26.10%19.20%22.40%0.00%
School Enrollment97.80%72.30%81.90%100%
Employment Rate40.20%59.50%38.30%20.60%
Housing Units2831773,71673
Occupied Housing Units2371442,79646
Children under 189.30%32.50%22.10%13%

It looks like the Fortine sample drew some younger respondents.  Eureka CCD with a larger population and larger sample is probably closer to correct, and the town of Rexford data is probably close to useless because the small sample size almost guarantees sampling bias

Community, Demography

Trego and the American Community Survey

Montana’s American Community Survey is composed from the final interviews conducted with 10,138 households in the state.  Since Montana has 519,935 households, the chance of any household being in the final interview is 10,138 out of 519,935 = 0.0195, right around 2% of the population is included in the survey.  Since Tregp shows 295 households, we can guess that our community data is assembled from somewhere around 6 completed interviews.

This table about sample sizes is from

As you will note, a population of 250 calls for 152 samples, and that the break is in the lower right corner – while a sample of 382 covers a population of 75,000, 384 is good for a million.  I’m not going into details about sampling – this is a blog, not a stats class. If enough people ask for the stats instruction, I’ll do another article.  Suffice to say, we can expect the numbers on the ACS to be pretty vague in small communities. So let’s look at the ACS data:

The top of the page shows:

Total Population                                           515

Median Household Income                          $36,458

Bachelor’s Degree or Higher                       26.1%

Employment Rate                                        40.2%

Total Housing Units                                      283

Without Health Care Coverage                   9.0%

Total Households                                         249

As we go further down the page, we start to encounter the variance – the range the number represents.  That 515 population is taken from the decennial census not the ACS. 

Median Age:    60.5 +/- 3.2 years 

16.8% of Trego folks speak a language other than English at home – plus or minus 15.4% so that’s somewhere between 6 and 166.  Probably not a particularly useful piece of information.

That Median Household Income turns out to be plus or minus $8,980: the number can be as much as 24.6% off either way.  It can be as low as $27,478 or as high as $45,438.  As we move into the full chart on that number, we see that the number of households lists the margin of error as plus or minus 67.  Could be as low as 182 or as high as 316. 

That 26.1% of Trego residents with a bachelor’s degree or more has a 12% margin of error – it could be as low as 14.1% or as high as 38.1%,  It shows 8.1% of our residents holding graduate or professional degrees, but doesn’t give a margin of error there.

The school board will be pleased to know that 97.8% (plus or minus 6.6%) of our kids are enrolled in Kindergarten to 12th grade.  Might even surprise the County Superintendent.  Pretty sure some kids out there are home-schooled.

That 40.2% employment rate (+/- 12.9%) looks low – but I guess it fits right in with a median age over 60 and 31.1% (+/-9.4%) disability. 

And finally, there are 48 women 15 to 50 years old – but the margin of error is 38, so it translates to somewhere between 10 and 86.

The ACS data is good – but the sample for Trego was small, and not checking the limitations lets us make blunders.

Community, Demography

4% Growth for County 57

The 2020 Census numbers have been released, and we’re looking at data we can begin to use.  I’m hoping to get the data at a school district level later on – but for now, we have county level data, CCD level data, and Census tract level data.

First – Lincoln County’s population dropped by a tenth of a percent.  Second, the population in the Libby CCD dropped by 1.2% (now 9,772), population in the Troy CCD dropped by 3.9% now 3,435), and population in the Eureka CCD increased by 4.0% (now 6,470).   North County is now officially 89 residents less than a third of the county’s population.  3,435 of the people represented by the Troy Commissioner reside in the Troy CCD, while 3,124 reside in the Libby CCD.  This is a trend worth watching.

Housing data is available at the county level – and it may give us some insight on rentals in the area.  Housing units in Lincoln County decreased by 4.0% – occupied housing units increased by 0.5%, and unoccupied housing units decreased by 19.6%. 

In County 57 – the Eureka CCD – housing unit numbers are:

 2020 #2020 %2010 #2010 %Change
Total Housing Units3,716 3,771 -1.5%

All these statistics are in comparison with the 2010 Census. 

It’s going to be fun as future releases will show even more usable data.