Malthusian Memphis?

Other mid-sized cities are flourishing. Is Memphis stuck?

It’s the year of the mid-sized city, but Memphis seems to have missed the boat. Austin, Raleigh, Charlotte, and Oklahoma City, to name a few, are turning heads with their rapid growth. Nashville, Memphis' Elvis-stealing neighbor, is America’s new “it” city.

Even Des Moines is getting attention. Des Moines. “When you come from Des Moines you either accept the fact without question and settle down with a girl called Bobbie and get a job in the Firestone factory and live there forever and ever or you spend your adolescence moaning at length about what a dump it is and how you can't wait to get out and then you settle down with a local girl named Bobbie and get a job in the Firestone factory and live there forever and ever.” (Bill Bryson) Despite all of this, an alarming number of people are using words like “thriving” in the same sentence as “Des Moines." 

Surely no Memphian, proud or otherwise, is content to watch Des Moines pass us by.

Memphis hasn't experienced anything near the income or population growth of its similar sized sister cities. Why is Memphis missing out on all the fun? Could Memphis be suffering from Malthusian stagnation?

In the grim Malthusian model of long run economic growth, fertility and mortality steal away any increases in income and leave just enough resources to sustain life. The model has two building blocks: the subsistence line and the production function.

The subsistence line shows the amount of output/income, Y, needed to sustain a given number of people, N. Let’s make everyone work in this model, so “people”, “workers”, and “employment” are interchangeable. Income per worker (Y/N) is constant along the subsistence line. Above the line, income per worker is greater than required for survival; people have enough to eat and then some. We can support more children, so why not? Birth rates increase. Everyone is well fed, so death rates decrease. Both factors cause population to grow. But below the line, life isn't as rosy. Income per worker is below the amount needed to survive. None of us can afford another hungry mouth to feed. Birth rates fall. Everyone is struggling to feed themselves, so starvation and disease lead to an increase in death rates. Both factors cause population to shrink. Population growth in the bountiful years will steal away our surplus until we all have just enough to survive, and population decline during the occasional potato famine will ensure the lucky ones will have just enough to survive.

The second building block, the production function, shows the amount of output/income (Y) that the economy can generate with a given number of workers (holding other factors fixed). The crucial feature of the production function is diminishing marginal product of labor: if a farm with one employee hires a second, production will increase by a greater amount than if that same farm had one thousand employees and hired one more. So the production function flattens out as employment increases.

The combination of the subsistence line and the production function paints a pessimistic picture. Suppose the economy starts at a point to the left of the subsistence line. Resources are abundant; each worker has more than he needs to survive. The surplus encourages population growth and therefore more workers. The additional workers generate additional output, but diminishing marginal returns to labor means each one adds less than the one before. So the economy moves along the production function towards the subsistence line until everyone has just enough to survive (the production function determines how much output a given number of workers can generate, so it is along this curve that the economy moves). Now suppose the economy is at a point on the production function to the right of the subsistence line. Resources are scarce and the population decreases, which decreases production. But because of diminishing marginal returns, the decreases in production will be of lesser magnitude than the decreases in population as we move left along the curve. Income per worker will rise until everyone has just enough to survive. The economy will settle on the steady state point no matter where it starts. In the steady state, income per person doesn't grow. Population doesn’t grow. There is no economic growth.

But it gets worse. Imagine a new technology is invented or imported that makes every single Memphian more productive. The same number of workers can now produce more output, so the production curve pivots upwards. Surely this will generate economic growth and make us all better off? Alas. For the same reasons as above, the economy moves along the production function to the subsistence line. Total production increases. Population increases. But income per person returns to its depressing pre-invention level. We waste away in Malthusian stagnation.

Inescapable poverty with no income growth and no population growth. It does sound eerily familiar.

You can breathe a sigh of relief, though, because Memphis has clearly non-Malthusian properties. Although real income growth stalled during the recession, both real income per capita and population in Memphis have shown steady long-run growth trends, which isn’t allowed under Malthus. In fact, Malthusian stagnation doesn’t really characterize any existing economies. (It does, however, do a good job of describing the world from, say, the Neolithic revolution up until around 1800. So give Thomas some credit).

Memphis may not be enjoying the growth and prosperity of Nashville or Austin (or even boring Des Moines), but it’s fairly safe to say that we’ve avoided the Malthusian stagnation that characterized medieval Europe. So that’s something. Let’s give ourselves a pat on the back.