An Economic Theory of Secular Cycles by Ian Schindler is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

An Economic Theory of Secular Cycles

Ian Schindler
Toulouse School of Economics
CeReMath

Introduction

This post originally started as a comment to Ron Patterson's post Of Fossil Fuels and Human Destiny. Then I realized that I had too much to say for just a comment. It was also very much influenced by Gail Tverberg's work at Our Finite World. I would also like to respond to some of my colleagues who do not understand why I spend so much time worrying about peak oil.

Since 2010, I have been telling people that economists are a bit like the astronomers of the 14'th century in that they are hard working intelligent people but that their understanding of the economy is defective because the models they use to understand the economy do not apply to the economy, just like the geocentric theory of the universe under which the 14'th century astronomers labored obfuscated their understanding of the solar system. At first my criticism was limited to questioning the assumptions of neoclassic economics. The paper [5] was written with the aim of showing that specific arguments used in the peak oil debate, motivated by neoclassic equilibrium theory are deeply flawed. The paper is work in progress. The mathematics is finished and elementary. The interpretation is in progress. The main point is that neoclassical economic theory has led to a fundamental misunderstanding of the concept of cost share.

Being dissatisfied by current mainstream economics, this is also a research proposal, or more accurately an invitation to anyone interested to attempt to build an economic theory with different hypotheses to those of neoclassical economic theory with the aim of posthumous fame. That is, I will outline some basic principles of economics which I have observed and make conjectures as to how to piece these principles together to produce an economic theory which will be more useful in its predictive capabilities than neoclassical economic theory. I agree with the economist Ha-Joon Chang who says that 95% of economics is common sense.

A Specific Problem with Neoclassic Equilibrium Theory

"The Cost Share Theorem" from neoclassical equilibrium theory says that the importance of a cost in the economy is proportional to its cost share. The cost share of oil in the economy is roughly .05 or about 5%. The cost share of labor in the economy is over 50%. The cost share theorem says that a contraction in of 10% in oil production would have about the same effect on the economy as a 1% reduction in the labor force. This is completely false and the source of great confusion.

The cost share Theorem is derived from the assumptions:

There is an economic production function of a certain form describing GDP.
The economy is like a firm producing GDP which maximizes profits.

Theorem 3.1 in [5] requires far far weaker assumptions, the result requires only that the economy can be measured using monetary units and that one can take derivatives. It says that the dynamics of the cost share are much more important in determining the importance of a quantity in economic production than its size. Important quantities have a cost share with a small or negative derivative. This means that their cost share will decline in a growing economy and increase in a shrinking economy. This is intuitively obvious. If an important quantity increases, it enables the growth in other less important areas of the economy and thus the relative size of the cost share of important quantities declines. For example the oil industry enabled the growth of the internal combustion engine industry which in turn enabled the growth of transportation which enabled many other areas of the economy to grow. Below I describe Theorem 3.1 in English and explain the motivation for each statement.

The cost share theorem has led some to say that a decreasing cost share of oil during the 20'th century, indicates the economy is less dependent on oil for growth. Elementary algebra says that because the average price of oil was roughly constant, a decreasing cost share is a necessary condition for superlinear dependence. Thus a necessary condition for very strong dependence (a 10% contraction in oil production would cause a greater than 10% contraction in the economy) is used for justifying very weak dependence (a 10% contraction in oil production would cause a contraction in the economy on the order of .5 %). This is stated in Theorem 3.1 (1).
Item (2) describes special cases of (1).
Item (3) relates the dynamics of the cost share of a quantity to the importance of that quantity in the economy.
Item (4) says that the more important a quantity is in the economic production function, the lower the scarcity rent. Item (4) rebuts the argument that a decrease in oil production produces a rise in price which will cause the market to solve the problem. Intuitively, in the event of scarcity of an important quantity, economic production declines, thus damping the price rise. This suggests that peak oil is a low price problem, not a high price problem. Oil production will fall if production prices are higher than market prices.
Item (5) notes that factors with rising cost share are economic drags. For example the cost share of the financial industry rose between 1980 and 2000 while the economy and number of transactions increased. Item (5) says that this is the behaviour of an economic drag.
Items (6) and (7) give hints as to how to quantitatively measure the effects of different quantities and their prices on the economy. In fact I believe that GDP is a very poor measure of economic activity (see [2]).

One might think that the second hypothesis in the derivation of the Cost Share Theorem is the one that fails and that applied to a business neoclassical equilibrium theory does apply. This overlooks the fact that Theorem 3.1 was made with essentially no assumptions and hence also applies to the value produced from a firm. My conclusion is that neoclassical equilibrium theory does not apply to a growing or shrinking firm except under very special conditions. It might be useful in the analysis of a stagnating firm or economy. Theoretically this is to be expected, a system in equilibrium is in general, static.

Secular Cycles

In [7], Turchin and Nefedov describe cycles that are common to many former agrarian civilizations. The cycle begins with a period of growth, in population and living standards lasting on the order of 100 years. Then comes a period of stagflation in which population density approaches the carrying capacity of the land (population pressure increases) lasting on the order of a several decades. During the stagflation period peasants leave the countryside for cities, the difference between the elite and the commoners increases, and the price of food rises relative to wages. Food production and hence population cease to grow. At first the elite are somewhat better off in the stagflation period because wages are low and they can employ large numbers of former peasants who have left the countryside. As the stagflation period progresses, the ratio of elites to peasants rises (peasants have a higher mortality rate) creating competition among the elite. Social mobility increases, mostly downward as elites lose their status. Inter elite competition creates fissures which lead to civil war and the final crisis stage lasting a few decades in which population decreases and the state breaks down. There follows an intercycle lasting on the order of 70 years before a new growth period ensues.

Conjectures and Predictions

In [5] secular cycles are interpreted qualitatively with respect to food production. The same analysis can be carried out not only in agrarian societies, but also in modern industrial societies. The main conjecture is the following, to be understood very broadly:

Conjecture 4.1 Free cash flow is spent on sex, drugs, rock and roll, and conquest.

An immediate consequence of Conjecture 4.1 is that since free cash flow leads to sex (in a broad sense), enough free cash flow leads to growth. One can loosely call drugs and rock and roll our culture (about which we are a bit ambivalent).

We also make the following conjecture motivated by [5, Definition 3.1] (worded specifically for oil, but which can be easily generalized to other quantities).

Conjecture 4.2 The price of oil depends on the amount of capital which transforms oil into useful work (in other words into sex, drugs, rock and roll, and conquest).

We believe that oil companies never talk about a problem in supply in order to encourage the purchase of turbines, internal combustion engines, etc. because without such purchases, the price of oil would drop.

Conjectures 4.1 and 4.2 suggest the following scenarios for secular cycles for the oil age:

The Growth Phase

The tool for measuring this phase is Equation (3.5) in [5]. Production of oil encourages the production of oil consuming capital. If the price of oil drops, producing oil consuming capital becomes a sexy business which grows. As this business grows demand for oil increases making oil production a sexy business. As long as profits are good and the business stays sexy you have growth in oil production. This describes the growth feedback cycle in oil production. The greater the profits, the more sex, drugs, and rock and roll. This creates diversity in the economy which in turn gives workers opportunities. Abusive employers have trouble keeping quality workers. Aggressive investors will produce the most profits as they will produce the most oil, drugs, and rock and roll.

The Stagflation Phase

Stagflation is characterized by increasing oil prices relative to wages while quantities increase marginally if at all due to the decreasing quality of oil reserves (the sweet spots are produced first). The tool to study this phase is Equation (3.6) in [5]. The phase is also characterized by decreasing profits. For example if we change units to energy, the EROEI of oil dropped from around 100 during the growth phase to 20 at the beginning of the stagflation phase. When EROEI is 100, you invest a barrel of oil, you get back 100 barrels of oil. After using a few barrels on food, say 80 barrels can be used for sex, drugs, rock and roll, and conquest. When EROEI is below 20, investing a barrel of oil will only yield 15 barrels to use for sex, drugs, rock and roll, and conquest (of course efficiency has improved so you get more sex, drugs, and rock and roll per barrel). Profits first begin to fall in oil consuming industries. They stagnate and then fall in the oil producing companies. The cost share of oil increases (in family budgets) as the economy loses it's ecodiversity. Wages fall as the choice in jobs falls. More and more companies lose their sex appeal. As stagflation continues, some producers become more aggressive as historically this produced higher profits. Some of these aggressive investors have trouble meeting their debt obligations. Stress and competition increases. The first thing to go is the sex. The drugs and delusions are the last to go.

Oil becomes less and less affordable. It is important to understand that oil becomes less affordable in several ways:

Higher oil prices.
Lower wages due to less ecodiversity.
Unemployment due to decreasing ecodiversity and a changing economy.

The pain is not evenly spread. An elite class develops that can buy influence and take advantage of the pain of others to live extravagantly.

Note that our intensive agriculture is very much an oil consumer [4] and will also suffer from lack of profits as food becomes less affordable. In France, for every three retiring farmers only one farmer takes up the trade.

If investors maximize their profit, then the cost share theorem will become increasingly valid. That is, the cost share of oil will tend towards its elasticity or relative importance in the economy.

Contraction Phase

In the contraction phase, the lazy investor is the most successful. That is the investor who takes on no personal risk, but buys the assets of formerly aggressive, bankrupt investors. The feedback cycle that characterized the growth phase goes into reverse. As the affordability of oil decreases, the market for capital transforming oil into sex, drugs, and rock and roll goes into reverse. This drops the price of oil below production prices and the oil producing business loses it's sex appeal (note that decreased wages reinforce this process).

We then reach a bifurcation point in history. The solution is not unique. Civil war is a possibility. Substitution of energy sources is a possibility, (as the oil based economy replaced the whale economy of the 19'th century [1]), but time is running out and most of the world seems unaware of the problem. Oil independent parallel economies can also appear and eventually become sexy enough to replace the oil economy, but not before a lot of pain ensues. In fact all of these possibilities are already occurring to some extent.

Recommendations

We believe that empirical evidence puts the beginning of the stagflation phase in 2005. We recommend a change in vocabulary to those who report oil statistics. Rather than: "oil production has not yet peaked". We recommend the more informative phrase: "stagflation continues". Stagflation is currently having a great effect on economies around the world. The effects will be greatly magnified when we transition into the contraction phase.

We believe that economic models should be broad enough to encompass the biosphere. The 19'th and 20'th century produced economic growth, but at great cost to the biosphere. We are embracing permaculture and hoping for the best. Those in permaculture have been working on the problem for 40 years. They have a good understanding of the biosphere and very encouraging results. Note that Conjecture 4.1 could be used for Darwin's theory of natural selection, it applies across species.