06 February, 2013

Musings On Growth

Lately, I've been doing quite a lot of economic data analysis; in particular, I have sifted through figures gathered from around the word for real GDP over the last three decades, and capital accumulation, production efficiency changes, and regional factors over the same period. Much of this data suggests a convergence of economies toward the most-developed economies. In other words, smaller, less developed economies grow (often exponentially) faster than more developed, larger economies. This produces a trend over time that would seem to indicate two factors which I would like to casually explore with this post:
a) economic growth over the long run seems to behave quasi-asymptotically 
b) convergence of economies implies that rapid growth might be inherently unsustainable
Before I begin discussing these ideas, I would like to point out that these thought are, unlike many of my other posts, not yet tested empirically, at least not so far as I was able to dig up with a cursory search. I am likewise not in the possession of enough relevant data to make such an empirical analysis myself. This is just, as the title suggests, a simple musing, rather than a rigorous analysis.
That having been said, there are some data which support these arguments. Growth rates, as measured in real GDP and real GDP per capita, over the past several decades, while showing great variability, seem to bear out the general conclusion that if a country started big, it grew more slowly in terms of percent change per annum; if it started smaller, it grew more rapidly in terms of percent change per annum. This means that large economies may have grown more in terms of absolute addition to real GDP, but their rate of growth was, on the whole, smaller than those of developing economies (especially the 'Tiger' economies of Asia and OPEC nations).
Given this, and given other observable indicators of economic growth (industrial development, capital accumulation, etc), it seems that there is some sort of marginal cost to continued growth. Economists and economically minded people are used to thinking in terms of margins, but for the relatively uninitiated reader, I will now go on a slight digression of margins (that those familiar therewith can skip by moving forward to the paragraph after next).
'Marginal' analysis is simply the analysis of the change that occurs in a given dependent variable when the independent variable is changed by 1 unit. For instance, Suppose that you are purchasing cans of soda. Each can costs $0.75. This means that the marginal cost of purchasing each additional can of soda is $0.75 - in other words, the additional cost you bear for each additional soda is $0.75. This is an example of a constant marginal cost. Now, suppose you are purchasing labor from a friend (you're paying him or her for their work). They might be willing to work 8 hours at a rate of $10/hour, but if you want them to work a 9th hour, they wish to be paid overtime ($15/hour). This means that the marginal cost of that 9th hour is not $10, but is $15- an example of increasing marginal costs.
It is commonly noted in microeconomics that marginal costs increase over time and marginal benefits decrease over time. Given the fundamental economic assumption of scarcity, this is inevitable- the more of a good is consumed, the more precious the remaining quantity of that good will necessarily become. Conversely, the marginal utility or marginal benefit goes down over time- a convenient way of imagining why is to think about how much pleasure you get from drinking a 6 pack versus drinking a case of beer. Once you drink too much, you puke; a clear example of a decreased marginal benefit from one additional can of beer.
This sort of thinking is what I wish to apply to economic growth. I am coming to the conclusion that increased economic growth in real terms has an increasing marginal cost and a decreasing marginal benefit over the long run. This implies that there is perhaps a steady state at which it would be most rational NOT to grow the economy, and perhaps it is this steady state toward which most economies seem to be converging.
There seems to be some logical basis for these thoughts. In the broad scope, it is commonly recognized that the pace of technological innovation and development is increasing at a rapid rate. One common measurement of the efficiency of technology, the doubling time for computer memory that can be produced at a given cost, has been increasing for the past 40 years. New innovations are being produced at a breakneck rate. Given most macroeconomic growth formulas (in which output is generally a function of capital, labor, investment, and technology), this would seem to imply that, ceteris paribus (all else being held equal), we should see increasing growth rates.
We do not.
Growth rates for most developed economies- the places where most of this innovation happens and where the benefits of those innovations are most strongly and immediately felt- have remained the same or even slowed, and they are certainly growing more slowly than less developed economies. It is my argument here that perhaps there is a decreasing marginal return for each unit of technological innovation; inversely, there is an increasing marginal cost for each little bit of growth that technological change adds to output. Cursorily, this seems to hold up to scrutiny. The jump in production efficiency gained from having no computers to having basic computers was large; the jump in production efficiency from the earliest computers to the ubiquitous desktop was large but smaller; the jump from desktops to faster and more powerful desktops modest, and smaller still. Yet the amount of resources spent on development of computers, and the rate at which new computing technology increases, has grown all the while. In real terms, the cost in resources (time, energy, etc) which must be spent for each additional 'unit' of technological innovation is rising over time!
The other factors of production are similarly limited. There is only so much capital to go around- it cannot increase forever. There are only so many natural resources to go around- they cannot increase forever. Historically, and in some cases currently, if there is a shortage of resources, more can be found somewhere at some cost. Think of today's situation with oil and fracking as representative. This process cannot go on forever- even if we eventually reach such a peak of efficiency that we are able to run an entire economy using only renewable resources like solar and wind power, there is only so much sun and so much wind! No matter how you think about it, the inputs which go into output are inherently limited and finite in nature, whether we have reach those limits or not.
All of this taken together supports the idea that economic growth over the long-run (and in this particular case, I'm talking about perhaps a century or more into the future) is going to slow asymptotically as it reaches this limit, whatever it is. This will be true for the world economy collectively, but it will be noticed most drastically by highly developed economies who will find that their present rates of growth are increasingly difficult to maintain, until they can't maintain them at all.
Eventually, this seems to imply that economics will become something that it has not been at any other time in human history: a zero-sum game. At this end-state when we have reached or are approaching the limits of resources and when further technological gains become massively costly, economic gains by smaller economies may begin to come at the cost of growth or even absolute size, in larger economies. This would promote a cutthroat growth expansion by all economies who seek to increase their share of the pie before the pie stops growing (or begins growing so slowly that the growth is negligible) which will only hasten the coming of a 0-development steady-state world economy.
This end-state need not be bleak; presumably, since all economies would have grown from today's size, quality of life and material wealth would have increased as well. No further growth does not mean  that there will be negative growth, nor does it mean that economies will collapse. There need not be a dystopia; this argument, if true, simply means that we may have to abandon our hopes of an ever-increasing utopia.
In conclusion, I reiterate that these are musings and speculations based upon no thorough or rigorous empirical or statistical analysis. These arguments are, however, interesting and have weighed on my mind for several weeks now. It will be interesting to see if any research is done into this area; perhaps even a model built for long-run growth which includes some of these conjectures.

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