Delivered from Obscurity

In 1830, a rapidly growing settlement on the banks of the Mississippi River shipped more cotton than any other port in the region and was described as "the great steamboat depot of West Tennessee." It wasn't Memphis.

Like planets, cities have a gravitational pull. As a city grows, its gravity becomes stronger and it attracts people and economic activity. The more it attracts, the larger it grows. The larger it grows, the more it attracts.

A metropolitan statistical area (MSA) is the region that has fallen under the gravitational influence of the core city. The Memphis MSA spans nine counties in Tennessee, Arkansas, and Mississippi; these counties contain dozens of small, independent towns and municipalities, but their futures and fortunes are inextricably tied to Memphis.

After a city achieves a certain mass, it seems inevitable that it will become the core of an MSA. But before then, that role is up for grabs. Was it inevitable that, of all the settlements in the area, Memphis would be the one to achieve critical mass? Why is a town like Randolph, Tennessee, in the Memphis metropolitan area, rather than Memphis being in the Randolph metropolitan area? The answer is not so obvious.

A good place to start is geography. Did geography alone make Memphis the best candidate to become the dominant commercial center in the region? No. Imagine it's 1830, and you're given the task of choosing where in the  Mid-South to place a city. Before the urban geography was settled, the dominant industry was agriculture, so the most promising location would be one with favorable conditions for trading, warehousing, and shipping agricultural commodities. You would eliminate the cities without access to the Mississippi River. The river is/was prone to changing courses, so of the cities on the Mississippi, you would eliminate the ones not located on a deepwater channel where the river's course is fixed. Finally, the river is extremely prone to flooding, which makes storing commodities risky, so you eliminate the cities not on high ground. Memphis, high above a deepwater channel in the Mississippi on the Fourth Chickasaw Bluff, is still in the running. But Memphis is not unique in its geographic advantages.

You might consider planting your city near Randolph, Tennessee. Similar to Memphis, Randolph has a flood-safe location on the Second Chickasaw Bluff above the Mississippi River. The river runs deep at Randolph, which made it unlikely to change course. Randolph even had a slight edge: the city sat at the confluence of the Mississippi and a tributary, the Hatchie, navigable 70 miles inland. Memphis' tributary, the Wolf, was only navigable 10 miles inland.

An observer in 1830 might bet on Randolph. Not only did the city have similar, perhaps better, geographical advantages, but Memphis was crippled by repeated disease outbreaks. In 1830, Memphis had a population of 663. Randolph had a population of about 1,000. Randolph was a more important shipping center than Memphis and shipped more cotton.

But we know how this story ends. So what saved Memphis?

The Post Office. In 1829, near the peak of Randolph's commercial success, the postal service delivered a crippling blow to the fledgling regional capital: the main postal route was placed through Memphis, the sickly city to the South, rather than Randolph. The route connected Memphis and Nashville and brought mail thrice weekly. Randolph, with its once weekly delivery, instantly became more remote than Memphis. Mail, the only facilitator of long distance communication and economic transactions, was the lifeblood of the early 1800s economy, and the improvement in infrastructure that accompanied the development of the postal route drove people and activity through the city. Railroads soon followed. Memphis' gravity grew stronger, and was soon strong enough to attract economic activity away from Randolph. Randolph fell into Memphis' sphere.

This narrative glosses over a few facts about Randolph's decline. Shortly after the town was founded in 1823, a faulty land title cast doubt over the ownership of the land the town was built on. The promise of a canal connecting the Tennessee and Hatchie rivers never materialized. Attempts to attract a railroad failed. And to put the final nail in Randolph's coffin, federal troops burned the town during the Civil War. Twice.

The land title and the burning of the town were exogenous events that severly damaged Randolph's prospects. But other frequently cited factors in Randolph's decline occurred after the establishment of the postal route and may be symptoms rather than additional causes.

In the first decades of the 19th centuy, the region's burgeoning agricultural economy needed a commercial center, and two cities were at the tipping point. The postal route pushed Memphis to critical mass. Gravity did the rest.

Solow Act

Is Memphis on a long term path to prosperity?

As of the last Census, Memphis was the poorest large metropolitan area in the county. With Memphis' level of poverty, it will take more than a rising economic tide to lift the fortunes of the Bluff City; we need economic global warming with a subsequent rise in sea levels fueled by melting economic glaciers.

Tides are cyclical, but melting glaciers are a long run trend. And despite not experiencing the uptempo growth of similar sized cities like Austin and Nashville (maybe Memphis put its eggs in the wrong musical basket), Memphis' long run trend is lumpy but positive. But can we say anything more optimistic?

One theory of economic growth provides a glimmer of hope. Like other models of economic growth, such as the Malthusian model, the Solow growth model relies on a production function and a tendency towards a steady state point. A diagram of the Solow model is identical to a diagram of the Malthusian model, but with different axes: rather than labor on the horizontal axis and output/income on the vertical axis, the Solow model has capital per worker on the horizontal axis and savings/investment per worker on the vertical axis. And instead of a subsistence line, we have a balanced growth investment per worker line. Production remains a function of labor, capital, and technology, and still has diminishing marginal returns. (A few adjustments are needed to express the production function in per worker terms and to derive a savings/investment function from the production function, but the analysis remains essentially unchanged).

In this model, capital is key. The growth of the economy is determined by the growth of capital. At the steady state point, capital per worker is constant at the "balanced" level. At this level, the growth of capital is keeping up with depreciation and the growth in population. If we are to the left of the steady state point, the growth of capital is outpacing depreciation and the growth in population; therefore, capital per worker must be increasing (capital deepening). Capital is an input to production, so production per worker is increasing, and therefore saving is also increasing. So, we move along the savings function to the right. If we are to the right of the steady state point, the growth of capital is not keeping pace with depreciation and the growth in population, so capital per worker must be decreasing. Output per worker is decreasing, so saving is also decreasing, and we move along the savings function to the left. The economy tends towards the steady state, where saving is just enough to keep capital per worker constant.

What does this mean for Memphis? Among economies with the same production functions and the same access to technology, the model predicts convergence: poor economies should grow more quickly and catch up to wealthy economies. Workers in poor economies have less income and save less; because saving determines the growth of capital, capital per worker is lower. But because of diminishing marginal returns, the rate of return on capital is higher for the poor economy. Although workers in the poor economy save less, the higher return on capital means production/income per worker is growing faster. Faster growth in income means faster growth in saving, which means faster growth in capital per worker. Capital per worker will increase in the poor economy relative to the rich economy, until they are both at the same steady state point with the same income per capita.

It's reasonable to argue that cities in the United States have the same production function and access to technology, so we should expect convergence. If convergence were occurring, the cities (metropolitan statistical areas, or MSAs) with the highest income initially would grow more slowly than the cities with the lowest income initially. Lo, and behold! This is the case:

In fact, Memphis has outperformed the trend since 1969, growing slightly more quickly than its initial income would suggest.

The business cycle tides have not been favorable to Memphis, but if we bide our time, we may yet float to the top.

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.