WASHINGTON, July 8 (UPI) -- It sounds like a mathematical tongue twister, yet it is a vital question to determine where the economy and stock market are going: Do we live in an economy whose growth is primarily exponential, or primarily asymptotic?
For those who didn't spend their teenage years fooling around with this stuff (I was at a single sex British school, so no girls!) an exponentially growing economy is one where most things grow and grow and grow, by the same sort of percentage each year, so that if they double in 10 years, you can expect them to quadruple in 20, and octuple in 30. Information technology, in its various guises, has been a pretty good example of an exponentially growing industry since the 1970's.
An asymptotic economy, on the other hand, is one where things grow closer and closer towards a limit, without ever quite reaching it. The limit towards which the trend moves stays fairly constant, or maybe grows slowly along with say population. Steel usage, for example, has grown asymptotically in the last 50 years, at least in the advanced economies. Indeed, some studies have suggested that the total weight of the United States gross domestic product was less in 2000 than in 1900; in that sense, most bulky products have had asymptotic demand growth over long periods.
Products can change their characteristics. Automobile sales grew exponentially in the United States from their invention to about 1929, asymptotically thereafter. (To reduce the significance of that ominous date, one might take the transition point as 1926, the year that Henry Ford realized that he would have to introduce a new model after the Model T -- the significance of this change was immense; Ford's previous strategy was as if Microsoft had sold nothing but DOS operating systems from their 1981 introduction through 2000.) Outside the United States, automobiles were an exponential growth market in Europe through the 1960s, in Japan through the 1970s, and in India and China today.
The transition from exponential to asymptotic growth occurs when market saturation comes into play as a constraint on growth, so that the majority of demand arises from replacement buyers rather than from first time buyers.
In the U.S. economy as a whole, there are always mature products growing asymptotically -- or even tending to shrink, like wood products, whose use is less per capita than in 1900, although the mix has shifted towards paper and away from firewood and lumber. Since the Industrial Revolution, there have also always been exponentially growing products: textiles in 1800-1850, railroad mileage in 1830-1873, electricity usage in 1890-1950, plastics in 1930-1970 (remember the advice to young Benjamin Braddock in "The Graduate" -- plastics were still growing exponentially in 1967), personal computers in 1975-2000 and Internet information transfer from 1995 to 2005, 2010 -- we don't yet know. Eventually, however, all exponentially growing products, even those that have not previously slowed their rate of exponential growth much, become asymptotically growing products, in which the U.S. market is approaching saturation. Exponential growth in these areas, if it continues, is confined to non-U.S. markets, where incomes may be lower or initial take-up of new products slower.
The predominant characteristic of the U.S. economy at any time thus depends on the mix between exponentially growing and asymptotically growing products, and may vary from era to era. At some times, such as the 1860s or the 1920s, new and exponentially growing products and services play an important role in the economy. At other times, such as the 1930s, a number of previously exponentially growing products, such as the automobile, have moved to asymptotic growth, while new exponentially growing technologies, such as the radio or aircraft, may be too small an industry, such as radio, or too early in their life cycle, such as aircraft in the 1930s, to counterbalance a predominantly asymptotically growing economic base.
One fallacy of the 1990s to explode is that of the ever-increasing pace of change. Of course, there were a number of exponentially growing industries in the 1990s, whose expansion was very heavily publicized. Nevertheless, the overall share of exponentially growing industries in GDP was certainly below 20 percent and may well have been lower than at similar periods of rapid growth in the past, such as the 1920s. Qualitatively, if one compares the 33 years since 1969 with the period of double that length from 1903 to 1969 -- from the Wright Brothers to the Moon landings -- it is clear that change in people's everyday lives has not been particularly rapid. Most people's lifestyles in 1969, already heavily suburban, with high automobile penetration and relatively cheap jet air travel, were far closer to today's lifestyle than to that of 1936, 33 years before. In terms of family income, middle class families have benefited much less from the growth since 1969 than from that in 1936-69 -- most economic growth since 1969 has been swallowed up by the government, and by a small minority of the very rich.
In terms of life expectancy, also, in spite of the vaunted medical advances of the last 30 years, the improvement over the 20th century has slowed dramatically. U.S. birth life expectancy advanced from 48 years in 1903 by 13 years to 61 years in 1936, and by another 10 years to 71 years in 1969. Since 1969, however, it has advanced by only another 6 years to just under 77. So much for the last three decades' incessant emphasis on physical fitness and combating obesity, as well as the trillions spent on healthcare!
The three great exponential growth industries of the '90s were of course personal computers, mobile telephony and the Internet. In PCs, the U.S. market is close to saturation. Even if Moore's Law, doubling the capacity of PCs every 18 months to 24 months, continues to hold, consumer demand for additional PC capacity is simply not there, except to the extent that software producers such as Microsoft and America Online create it artificially. The transition from exponential to asymptotic growth in this sector has pretty clearly occurred in the West -- thus the recent anemic business results for Compaq and Gateway, and the slowing of growth even for Dell.
In mobile telephony, if growth is still exponential it has slowed dramatically, and has produced a vast surplus of "bandwidth." The penetration of mobile telephones is now above 50 percent, and it seems likely that the third generation of technology, or 3G, revolution, that was supposed to increase greatly the percentage of people's income devoted to mobile telephony, will at least be delayed from its original timeframe, and may never arrive as more than a niche market -- for most consumers, the attraction of a tiny handset in transmitting and receiving information is limited indeed.
The Internet is a more interesting case. According to Monday's Wall Street Journal, information transmitted across the Net in 2001 was 891 petabytes, a figure so vast an unfamiliar unit had to be used to convey it. I believe the figure to be equivalent to 891,000 terabytes, a marginally familiar unit, 891 million gigabytes, a more familiar if novel one, or 891 billion megabytes, a unit with which we have become comfortable. The article was an impassioned plea for the government to unleash broadband technology, on the grounds that take-up of this technology has been much lower than predicted, a lapse that must, surely, be due to government regulation.
Or to market transition. If you think about it, the Internet now penetrates more than half of U.S. homes. These are not in general people thirsting for the knowledge of the Encyclopedia Britannica; they are people, often adolescent males, seeking to play Internet video games with really cool graphics, and to watch online the same type of low-IQ pap that graces the terrestrial TV channels. Of course, graphics require bandwidth, so in terms of petabytes consumer demand is still increasing exponentially, by 100 percent between 2000-2001. In terms of reality, however, it's just a modest increase in demand for the same type of programming to which U.S. consumers already devote on average 37 hours per week. There being only 168 hours in a week, with some needed for sleep, the shift down to merely asymptotic growth of petabyte usage, once TV-quality graphics are readily available, must be more or less imminent.
The dominance of the U.S. economy by asymptotic growth, likely to increase over the next decade -- though, by all means, to be reversed temporarily once the next "big thing" arrives -- has important economic implications. In an asymptotic growth economy, a productivity miracle, such as was lovingly and apparently largely falsely hailed by President Clinton and Federal Reserve Chairman Alan Greenspan in the late '90s, is not a blessing but a curse. If productivity growth were really to increase to say 4 percent per annum, in an economy most of which was growing only asymptotically, then the result would be not riches but a huge increase in unemployment. This was predicted by gurus in the 1960s, supposedly as a result of automation; it never happened. With a productivity miracle, it would be inevitable, and would cause enormous and probably wholly unmanageable social and political strains. Thank goodness, therefore, that the New Economy productivity miracle was a mirage.
As for the stock market, if the economy were growing exponentially, then it would indeed be attractive to reinvest in rapidly growing companies, forgoing current income. It might even be worth paying exorbitant sums in stock options to top management, with resulting dilution of your equity interest, to seize a greater portion of this exponentially growing pie.
In an economy whose growth is largely asymptotic, however, diluting one's stock interest by granting huge stock options to company management is the action of a madman. So, too, is forgoing current income in order to devote more and more of one's resources to a business which is growing only at the same rate as the economy -- one is simply putting temptation in management's way, thereby worsening the agency problems of public equity investment that have recently become only too apparent.
Instead, in an asymptotically growing economy, the primary need from stock market investment is dividends, to provide as high a steady income as possible, increasing with inflation and maybe a little bit with asymptotic growth, but above all secure against the inevitable hard times that will periodically occur. Accordingly, companies with low leverage, paying high and secure dividends, are the most attractive investments. The Capital Asset Pricing Model, recommending, for tax reasons, increased leverage and elimination of dividends is in such an economy simply waste paper -- the policy it recommends would increase investor risk, without any corresponding extra return.
From the above, it is I think clear that the United States is today primarily an asymptotically growing economy, and that investors should buy stocks only when they can obtain a high and secure dividend yield. For the 500 shares in the Standard and Poor's 500 Index to yield even 4 percent, at a payout ratio of 75 percent of earnings -- about the highest reliably possible, and well above current levels, even with earnings being depressed -- the S&P would have to trade just below 450. Monday, it closed at 976.98. That decline, from 976 to 450, is the bear market we still have ahead of us.
(The Bear's Lair is a weekly column which is intended to appear each Monday, an appropriately gloomy day of the week. Its rationale is that, in the long '90's boom, the proportion of "sell" recommendations put out by Wall Street houses declined from 9 percent of all research reports to 1 percent, and has only modestly rebounded since. Accordingly, investors have an excess of positive information and very little negative information. The column thus takes the ursine view of life and the market, in the hope that it may be usefully different from what investors see elsewhere.)
