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Government Workers and Economies of Scale

(Note: This entry was originally published on August 8, 2014.)

I had planned on my inaugural post being an eloquent essay on philosophy and political economy, encompassing the designs I had in store for this blog. Alas, I am lé tired.

But! A recent post over at the Wall Street Journal piqued my interest. Using data from the Bureau of Labor Statistics, Rani Molla charts the total number of government workers by state, as well as the government workers per 1,000 people.

Not surprisingly, the states with the largest populations (California, Texas, New York, and Florida) have the greatest numbers of government workers. Indeed, when the data is plotted, we see a clear, positive relationship between population and government workers – the larger the population, the greater the number of government workers.


However, when the data is adjusted for population, we see something quite different. As Molla points out, the states with the highest number of government workers per 1,000 people are those with relatively small number of residents (Wyoming, Alaska, North Dakota). What might account for this?


The answer might be simpler than you’d think, and it boils down to a basic concept of microeconomics.

Think for second – what jobs are performed by government workers? To keep it simple, let’s think about the jobs performed by the government workers in a single city. At the top of the list would be the mayor and members of city council, a city manager perhaps, and the various heads of city departments. Not too many workers overall. But no matter the size of the population, whether a city of 1,000 or 1,000,000, the number of mayors would remain constant (at 1). There would still be only a single city manager, a single chief of police, a single director of budgeting, or accounting, or human resources, and so on. As the number of residents increases, the number of workers performing certain job functions remains constant – a perfect example of economies of scale.

What about further down the pay scale? A larger city might require a greater number of clerks in its municipal courts, or a greater number of sanitation workers. And a larger number of employees in those areas might require a larger number of analysts in human resources to manage payrolls and benefits. Not to mention public safety – larger cities would  certainly employ a greater number of workers in the police force and fire department. In this case, we would observe what economists refer to as constant returns to scale: each marginal (additional) police officer or court clerk or sanitation worker would be capable of serving a roughly equal additional number of citizens within the city.

But what about other factors? When it comes to the government workforce within a state, which can serve as a proxy for the ‘size’ of government, some might argue that the more liberal a state, the higher the government workforce relative to the population. But is this relationship observed in the data? Perhaps unexpectedly, no.

Using the percent of a state’s vote in favor of Mitt Romney in the 2012 election as a proxy for the liberal/conservative leanings of a state, we can examine the relationship between politics and government employment.


In the graph above, states leaning toward Obama appear further to the left (such as California, New York, Massachusetts), while states leaning toward Romney appear further to the right (Utah, Wyoming, Oklahoma). Fitting a trend line to the data shows an ever-so-slight positive relationship; that is, the more conservative the state, the higher the rate of government employment.

But how can this be? Are not political conservatives the champions of ‘smaller’ government? Perhaps there is another factor that explains this observed relationship – such as the relative urban or rural nature of the population? Using population density as a measure of the ‘ruralness’  of a state’s population, we can examine the relationship more closely.


As we see, the lower the population density, the greater the number of government workers per capita. This is in line with the economies of scale described above – even the most-sparsely-populated states would require some minimum number of government workers to deliver public goods and services at even the most basic level. So, as the population converges to zero, the ratio of government workers to population rises.

But what accounts for the previously observed relationship between political orientation and government workforce? Plotting the relationship between political orientation and population density produces the following result:


As we can see, the more conservative a state (i.e. – the greater the percentage of the state voting for Romney in 2012), the lower the population density (the more rural the population). And as observed above, the lower the population density, the greater the government workforce relative to the population.

So what can we take away from this?

First, total government workforce is primarily a function of absolute population – the greater the number of people, the greater the number, degree, and complexity of socioeconomic interactions. Thus, the greater the need for public facilitators and monitors of these interactions, and the greater the demand for public goods and services.

Secondly, government workforces exhibit economies of scale – the greater the population, the smaller the number of government workers necessary to deliver those public goods and services relative to the population.

Finally, states with smaller populations, and thus lower population densities, have higher relative numbers of conservative voters, and at the same time, require higher relative numbers of government workers to provide public goods and services.


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Whither Wrong Things? (a work in progress)

The Man from Mars had been dead for 37 years.  Or rather, he had discorporated when the time had, grokking the fullness of the moment, when waiting was no more. His disciples, his water brothers, having shared in the non-wasting of food following his discorporation, had carried on their evangelism, spreading the teachings of the Church of All Worlds. The ranks of the ninth circle had steadily grown, to be sure, but not nearly so much as the ranks of casual All-Worlders drawn more to the more meditative practices, which allowed them to carry on with their daily lives rather in the same fashion to which they had long grown accustomed, but in a manner much less unhappy and conflict-ridden. Talking Martian and controlling objects with one’s mind was just fine for some, but for the average lay-All-Worlder, sharing water and a sense of inner peace was plenty.


In a sea-side city on the Florida Gulf coast, a 52-year-old woman in the midst of cleaning house one day went to retrieve a broom and pan from the closet. Walking back into the kitchen, she bumped into something that was not there, could not quite grok it, thought to herself “waiting is”, and went about her cleaning.

A week later, making her way into the kitchen, she walked round the something that was not there, and noticed a bulge in the side of her toaster. Puzzled, she picked it up, feeling along the sides, but could detect no anomaly; setting it down, the bulge reappeared. Again, she picked it up, but felt nothing out of the ordinary. Setting it down once more, she took a slice of bread from the cupboard, and inserted it into the misshapen toaster, depressed the lever, waited for the toaster to grok the fullness of the moment, and watched as the warm slice of bread sprang up from within the toaster. Confirming that the toaster was in perfect working condition, she retrieved the slice of bread, ate it (true to the teaching of non-wasting of food), and went about her day.

in the same building, a retired postal worker from Poughkeepsie living out his golden years in the sunny warmth of southern Florida, carried his bag of trash down the hall to the garbage chute, opened the door, stuffed the bag through the opening, and turned, expecting to hear the swoosh of the bag traveling down the chute. After a few steps, he paused, and listened – silence. He turned and walked back down the hall, opening the door and poking his head into the chute. There was his bag of trash, suspended a few feet below the door, wedged between the wall of the chute and…something that was not there. Retrieving a broom from his condo, he poked and prodded the bag until at last he dislodged it. Upon hearing the final thud as the bag fell three floors and landed in the collection bin, he returned to his afternoon ritual of crossword puzzles and light jazz.

In the building next door – an establishment occupied by tenants of a more discriminating taste – there lived a young couple recently returned from a year-long sojourn through the Old World, who, having sown their wild oats (both individually and in tandem, in the manner of the nearly-forgotten Fosterites), and secured gainful employment as an accountant and graphics designer, had settled in the Sunshine State to partake in the age-old tradition of establishing a nondescript nuclear family.

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Verse, old and new

(an old verse, written years ago)

a butterfly, so fragile, yet so elegantly able
to instill in us awareness of our oneness with that nature
that guides times across the eons, ‘cross the universe, winds blowing
upon which flutters softly
a fragile butterfly

(a new verse, hot off the press)

The spiny, reptilian lord surveys his domain:
from atop the strange cairn of neatly-stacked stones,
he keeps a watchful eye.
His blood, his throne, warmed by the sun,
change not his cold, hard gaze.
A rustling in the leaves, a tiny cock of his head:
Stand, fight, or fly?
Beware the lord of the sky!
tis nothing….
Flex once, twice, thrice!
Behold the scaly lord,
tread lightly thru his realm.

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Travels in the Realms of the Unpossible


In my economics lectures, I sometimes ask whether students are familiar with various concepts from science, particularly physics. The response is more often than not blank stares, due perhaps to the fact that science is, like, hard, and students would sooner forget it than dig deep into the recesses of memory. But in addition to the difficulties of science itself, it is difficult to imagine how the principles of a field as concrete as physics might be applied to a field as squishy as economics. An illuminating example is that of light cones.


In physics, a light cone represents the path that a flash of light will follow, unhindered, in response to some initial event, such as the striking of a match. Imagine being able to slow time down to a hyper-glacial pace, striking a match, and then observing the light of the tiny flame emanating in all directions, slowly illuminating everything around it. If you could take a three-dimensional snapshot at each subsequent second…each millisecond…each nanosecond…centered at the flame, and then view the entire collection of snapshots, you would observe a series of concentric spheres of increasing radius. As time moves forward, the sphere of light encompasses an ever-greater volume of physical space.

01-01 - FlameUnfortunately, when we think about the universe in terms of physical space and time simultaneously, what we call space-time, the human mind limits our ability to adequately conceptualize dynamic changes, such as the expansion of the match-flame’s light (it’s hyperspace, man). To keep things simple, we can reduce the dimensions of physical space from three to two, giving us a plane of physical space rather than the three-dimensional space that we observe in real life. We are effectively flattening physical space – think of the square that results from a flattened box. In addition to the two dimensions of space, we add a third dimension, time, measured along an axis perpendicular to the plane.

With this modification of space-time, the light from our match now expands in a two-dimensional circle, rather than a three-dimensional sphere, and as it moves forward along the axis of time, it creates a cone.

01-02 - Forward light cone But we are not confined to considering only the emanation of light that resulted from the striking of the match – we can also use this concept of light cones to think about what information and events caused the striking of the match. If space is measured both forward and backward in time…if the circle of light is allowed to both expand and contract, we end up with a pair of symmetric light cones – the Einstein-Minkowski representation of space-time.

01-03 - Past and future conesWith this model of space-time in mind, we can start to think about the confluence of factors that lead up to any singular moment of time in our lives, and from that point, we can explore the realm of possibilities, both past and future.

Let us leave our light cones for a moment, and turn to economics.


In the field of economics, we spend a great deal of time studying how individuals make decisions, particularly when confronted with a scarcity of resources.

Think for a moment about all of the decisions you make in a single day. The very second your alarm clock sounds, and you snap (or drift) from the perceived space-time of the dream-state to the space-time of consciousness, the decision-making gears in your brain are set in motion. Will you turn the alarm off and get out of bed, embarking on your daily rituals of preparation? Or will you hit the ‘snooze’ button? What would you gain or lose in either case? Turning off the alarm and foregoing additional sleep would allow you to start the day off ‘right’, ready and raring to go. Hitting snooze, on the other hand, would allow you a few more precious moments of sleep.

But what is the scarce resource in this case? It is time itself, perhaps the only resource that is universal to man and all living creatures. As Diogenes Laertius records in Book V of his Lives and Opinions of Eminent Philosophers, a favorite expression of the Peripatetic philosopher Theophrastus was “that time was the most valuable thing that a man could spend.”

01-04 - Skeleton and hourglassOur decisions at any point in time are based on a multitude of factors. We analyze the information we know (or…suspect we know) about our present circumstances, both material and abstract. We then weigh that information against our personal preferences, thinking about the consequences of any decision, both personal and social. All of these inputs are taken in or recalled by our brain, the numbers are crunched, and a decision is made.

01-05 - Gear Head\With this model of decision-making in mind, we can construct a synthesis of these theoretical concepts, both physical and economic.


As we move forward through time, we are constantly making decisions. Are we ignoring the past as we progress? No! We survey all of the past events and experiences that have led us up to a particular choice-moment in space-time, relying heavily on the lessons and accumulation of information gleaned from our past experiences to make optimal choices moving forward. Economists refer to this backward-looking approach as adaptive expectations.

In making any decision, we rely not only on past information, but also on what we can reasonably expect to follow from whatever choice is selected; we can’t truly predict the future, but we can at least define some limited realm of future possibilities, forming what economists describe as rational expectations. Weighing our options, we project forward all of the possible paths that might result from our decision based on past experience. Thus, in any singular moment in our personal niches of space-time, we are both backward- and forward-looking.

01-06 - JanusAnd so, with eyes to the past and the future, cognizant of our present state of being, we progress through space-time. There exists a finite number of possible paths that could converge on a particular moment, and from that singular moment, there extends a finite number of possible paths forward. Any events that might transpire that lead not to that moment, or follow not from that moment, are beyond the realm of the possible for the individual experiencing that moment. And so individual travelers we are, drifting through the realms of the possible and the unpossible.

01-07 - Realm of UnpossibleBut we are not alone! As we move forward through life, our paths cross with those around us, perhaps for only a single moment, or…perhaps for many moments.

I board a bus, and for the better part of an hour, I share a series of consecutive moments with the driver and the other passengers. Our paths have crossed, converged, and remain intertwined for the duration of my trip. When I reach my stop, I disembark, and our paths diverge – I proceed into my own future of possibilities, and the driver and passengers into theirs, never to cross again…or will we?

Having once crossed paths, we have established a realm of shared possibilities. That shared realm might itself be finite, existing for period of time that will come to an end once our paths reach a point of critical divergence.

A man I have seen before on the bus wearing worn clothes, now wearing a hospital bracelet. What unfortunate incident sent him to the hospital? Will this alter his future path? Is it possible that this will be the last time our paths cross? Our paths having converged, will we now, individually, wander into our separate realms of possibilities?

Or the girl I see each day in the dining hall, dining alone. What series of events have led to these solitary suppers? Will she always break bread for one? Or will some day she dine with a companion?

01-08 - Divergent ConesThere is nothing that guarantees that our paths will remain intertwined. But neither is there anything that will prohibit our paths from crossing again in the future. At every moment in time, our decisions will alter our unique future realms of what’s possible. Maybe I will never see the man on the bus again. Maybe his future is bleak. Or maybe it is beautiful. I may never know.

Sometimes, however, we might encounter another person, and the resulting collision realigns our individual paths such that there is a future realm of shared possibilities. It does not necessarily mean that we will be attached at the hip for all eternity, but certainly our lives will be lived in a common space across time. Perhaps two people will fall in love, choosing to join their lives, two flashes of light in the universe, growing and fading in tandem, binary stars revolving around a common center of gravity. But still, nothing is guaranteed. A lifetime together is possible, but there still exists for each of them a separate future realm of possibilities. And like two stars, they could slowly drift apart over time into far-flung corners of the universe, never to cross paths again.

01-09 - Convergent ConesThis is how I see people, wherever I go – fellow cone-headed travelers in space-time. Every mind I encounter is a universe unto itself, with a rich history and future distinct from my own, perhaps but for a single shared moment. It is a beautiful thing.

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