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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