Fred Thompson - Econ 101: Economic Growth

I was desperately trying to find time to post and, hooray, along comes Fred Thompson to save the day with a great post on economic growth theory. Thanks Fred.

Patrick Emerson in an earlier blog post wrote:

“But children are also resources in and of themselves: they are the ones who will have to come up with the solutions to the resource issues and I have faith that they can and will do it. Within each child comes the potential for being a vital part of the world's human capital resource that will solve global warming, find new renewable energy technologies, will invent more efficient ways to produces goods and services that use fewer resources, and so on. They are the ones that will create the new resources with which humanity will thrive. In fact, during the recent explosion in human population, living standards have risen considerably.”

Patrick eloquently explains the conclusions of contemporary economic growth theory. I am going to ratchet this up a bit and try to explain the theory itself and how these conclusions were reached.

This story begins with the notion that capital and labor are combined to produce goods and services. The more goods and serves you can produce/consume the wealthier you are. We call the mathematical representation of this process a production function. Once upon a time, most economists believed that the rate of capital accumulation determined the productivity and wealth of an economy. That is, if you added more tools, plant, and equipment, you could make the labor force more productive. The faster you accumulate capital the faster economic output will grow.

Then, in the early 1950s, a guy named Robert Solow was playing around with production functions and discovered something very interesting about them. Beyond a certain point you cannot increase output per unit of labor input by adding more capital. The implication is that once the optimal labor capital combination has been reached an economy can grow no faster that the rate at which the labor force expands. Moreover, in the real world, where resources can and throughout history have been depleted, this implies that output per worker must fall, ultimately to below subsistence levels.

However, when Solow looked at the available data he found that output actually grew faster than could be explained by the growth in labor and capital. In mathematics a result that isn’t explained by a model’s variables is called a residual, in this case, unexplained growth. By definition a residual must be explained by a variable that is outside (or exogenous to) the model. Solow hypothesized that this particular residual was due to technological improvements that made capital and labor more productive. The implication is that, if technology complements labor and capital in a production function, as long as it grows faster than the rate of resource depletion, the economy can continue to grow in wealth and population.

So what determines the rate at which technology grows? In exogenous growth theory, once you have reached the limits of investment in human as well as physical capital, the rate of technological innovation ought to be about the same as the rate of population growth. Ultimately, however, this implies that, since the rate of resource depletion speeds up as the labor force grows, while technology is a linear function of population size, all technological innovation does is to put off the eventual crash to a later date. This is, of course, the kind of model that drove the Club of Rome’s doomsday results. Folks talk about these formulations in terms of limits to growth (in wealth and population). In fact, almost any kind sustainable human future is incompatible with this kind of model. Every conceivable set of choices eventually leads to declining wealth and eventually a population crash.

Unsatisfied with this approach, economists, including, most prominently Paul Romer, built mathematical models (or production functions) that included (or endogenized) technological advancement as an explanatory variable. In so doing they made a surprising discovery: the payoff to investment in technological advancement is different than the payoff to investment in capital. Because in theory, technological advancement can be freely shared with all users, it is characterized by increasing returns to scale. This means that even if the rate of technological innovation is a direct or linear function of the size of the population and, thereby, the workforce, its payoff increases at an increasing rate when you increase workforce size.

For example, if every unit of the workforce invents something that makes work ten percent more productive and you have one workforce unit, productivity is increased ten percent. If you have two units, you can produce 21 percent more stuff; ten units, 160 percent; and 100 units, 1,378,000 percent.

The implication of this theory is that population growth is not inimical to increased economic wealth. Moreover, there are almost an infinite number of sustainable growth paths both in terms wealth and population (although not all growth paths are sustainable). I think the best growth paths are those in which everyone is well educated and technologically innovative. Indeed, where being smart, technologically literate, and innovative are universally admired personal qualities. But the status quo will probably suffice.

I also like plenty of open spaces, clean rivers, blue skies, old-growth forests, and pristine beaches. I don’t like crowds and can barely tolerate cities. But these are aesthetic preferences, not matters of survival. We all have to make trade offs, individually and collectively. Generally, however, richer is better. And, because aesthetic preferences are normal goods, richer also means that they are more likely to be realized.