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.