Production functions that combine material, capital, labor, and energy in a single algebraic expression reveal how entrenched economic methodology misapprehends reality. Everyone familiar with natural resource economics has seen equations like Y = F (M, K, L, E), where Y is the maximum level of output obtainable during a period via implied technique (F), from a given amount of raw material (M), capital services (K), labor (L), and energy (E).

Can energy be considered just another element in the input vector? Can it be treated as an independent variable in the same category as capital and labor? Hardly, yet discussions about the impact energy prices have on economic performance begin with such formulations. They show up in print and pixel, adorn slides and blackboards as symbols of pure logic cleansed from heterodox critique and the trappings of popular rhetoric. Explicit and abiding reliance on them — as if they were axioms of Euclidean geometry — bears some responsibility for separating science from common reason and for abetting the unbroken effort to rationalize away the dangers inherent in losing the world’s easiest accessible and most potent energy carrier — crude oil.

Differentiation and simple manipulation of production functions are used to calculate the energy elasticity of output, the price elasticity of energy, the elasticity of substitution among resources, or losses incurred as a result of increasing energy/oil/gasoline prices. Factor proportions (intensities) are ever-present terms in all such calculations. They are the bait that fugitives from independent thinking keep swallowing year after year.

Namely, the shares of energy, oil, and gasoline in the GDP are low, particularly in developed economies. U.S. energy expenditures, for example, stayed below 10 percent of the GDP during the past two decades while the national petroleum bill remained in the 4-6-percent range. Economic commentary revolves around these numbers, celebrating their lowness as a triumph of technology and the relentless drive for profit.

The small share of natural resources in aggregate expenditures is not one hundred percent good news. The neoclassical prediction apparatus is false.

Low energy shares indicate increased specialization. The variety of products and services widens and production becomes more “roundabout,” i.e., the vertical chain of intermediary stations lengthens. But beware! The study of biological evolution has shown that nature selects against rapid growth accompanied by a high degree of specialization. Growing demand on depleting resources brings inflexibility in a way that is ignored by conventional economics.

The reciprocal of those low energy, oil, and gasoline shares would be an equally important indicator to describe the state of the world. It would show the extent to which material welfare has become vulnerable to the availability of extrasomatic energy in adequate quantities and at non-disruptive marginal costs. Detachment from nature is an illusion, not liberation. If the perspective of analysis is appropriately wide, factually relevant losses always appear to follow gains previously presumed to be pure.

To appreciate why the significance of energy/oil price hikes is understated and spuriously quantified when a function such as the one quoted becomes the theoretical basis of econometric work, we need to climb to a higher altitude of abstraction.

Production is a process whereby labor expands somatic energy to mobilize extrasomatic energy for the purpose of operating physical capital, which, in turn, represents the potential to perform tasks beyond human biological ability and capacity.

“E” in the production function stands for the medium of transmission that labor deploys to animate physical capital. It is the electricity used by the carpenter, the auto worker, the supermarket clerk, the dentist (all expanders of somatic energy, i.e., labor) to operate the chain saw, the assembly line, the store, and the high-speed drill. It is gasoline (with its energy stored in chemical bonds) which, upon burning, allows the driver to steer the truck, the car, the tractor.

Extrasomatic energy can be measured in units of Human Energy Equivalent (HEE) — a good yardstick of economic development. At the dawn of civilization HEE was zero. It grew gradually over tens of thousands of years and accelerated during the industrial age. According to ecological economists M. Common and S. Stagl, the average per capita HEE is now around 20, with a huge spread of above 90 for the most and below 10 for the least developed countries.

It is clear that without an uninterrupted flow of extrasomatic energy from the environment into the economic system, the scientific-technological know-how symbolized by “F” would be “lifeless.” However, given the low share or intensity of “E,” it is much less obvious how unbreakable the historical correlation between the level of output and extrasomatic energy really is. Conserving carriers and enhancing their productivity (efficiency) — although desirable goals — help only within narrow limits and temporarily.

If a heuristic analytical model had to be chosen to illustrate the relationship between “E” and the rest of the inputs at the global level, perhaps the Leontief production function, which presumes fixed proportions (i.e., between “E” and all other factors) and no substitution between the two vectors would best describe the unique role extrasomatic energy plays.

“E” is not simply one of the guys among factors of production.

Treating “E” as if it were on equal footing with other resources is what philosophers call a “category mistake,” a term psychiatrists borrowed to characterize symptoms of mental illness, e.g., the man goes to the cleaners and orders a Big Mac.

In contrast to raw materials, capital equipment, and labor skills, which can be arbitrarily varied as technology evolves or changes in response to relative factor prices, energy is an irreplaceable complement with a high degree of homogeneity. Substitution among its specific forms (i.e., heat, chemical, mechanical, electromagnetic, or nuclear energy) is limited and very slow.

A significant shift among the ways work (change in kinetic energy) is obtained affects the entire industrial infrastructure. The spectrum of difficulties facing the introduction of electric cars on a mass scale (substitution of electromagnetic for chemical energy) is a telling example.

“E” may be comparable to the energy living organisms need to exist.

Life’s intrinsic tendency toward copious variation is accompanied by a supremely universal process of sucking free energy from the environment. In the context of the production function, while the economy is wide open to the development of possibilities in one sense, it remains virtually closed in another. We can create infinitely many things in infinitely many ways, but the actual production process remains bound to the requirement of metabolizing energy sources in proportions that remain largely insensitive to market signals.

Energy carriers (or, for that matter, any other natural resource, e.g., oil as material input, copper or timber) saved through conservation or efficiency appear to the economic system as new reserves. The incentive to draft them into production is bound up with an overweening pressure for output maximization, a momentum unstoppable by environmental advocacy. GDP growth rate — the higher the better — remains the single most important indicator whereby national governments are judged. More output is associated with job creation and improved living standards.

If the fuel efficiency of combustion engines doubles, twice as many vehicles will be produced. If energy-efficient buildings will be constructed and people become conscious about using electricity in their homes, the natural gas saved will show up on supermarket and department store shelves as refined product inputs in tens of thousands of consumer goods, from electrical appliances to shiny plastic dishes, aspirins and their containers, all the way to the asphalt on the parking lot.

Upon giving due consideration to the structural inelasticity among forms of energy and the sustained tendency to gobble up substances saved through “conservation and efficiency,” we can see that the demand for the medium of transmission from somatic energy to physical capital is bound to grow, making the world economy increasingly vulnerable to its price and availability.

The rising value of extrasomatic energy becomes a drag on growth.

Energy derived from nonrenewable sources is slated to demand increasing bundles of resources, making them unavailable to produce what the world really wants. Costs will increase across the board. In Econ-101 speak; supply curves will shift upwards to the left, indicating smaller amounts being supplied at any given price. In practical terms, washing machines, as well as the electricity to run them, will become more expensive.

Having entered the temporal zone of peak oil — a period of history when the nearness of the de facto maximum of worldwide oil production exerts a decisive influence on global economic performance — is the “leading indicator” that the depletion of material resources has begun to constrain the spontaneous multiplication of productive activities.

Indeed, it would be salutary for the international community to remember that oil is not just another commodity traded along with bauxite, coffee, pork bellies, and gold.

It is interesting (that is, if you are into “econ lit”) to look back at the struggle of economists in the 1950s to reconcile the mathematics of smooth and endless expansion with the Leontief technology that allows no substitution between some groups of resources. It is a credit to their perspicacity that they saw the inevitability of chaotic developments and breakdowns when the neo-orthodox conditions of virtually uninterrupted growth change into the current ones; that is, when Leontief’s growth-limiting, fixed-proportion, numerically-based model acquires practical relevance.

Depletion of conventional oil challenges economic organization.

The question is plain but historic: Can existing institutions (including property relations and forms/patterns of distribution) and a largely short-run profit-based problem-solving mechanism generate the dynamism required to break through the growth-constraining rise in the share of extrasomatic energy in the global production function?

Those who say “yes” emphasize the plethora of business opportunities that the need to rely on more expensive supplies of oil (e.g., from the arctic region and deep seas), unconventional oil (i.e., shale, sand-based crude, liquids obtained from coal, biomass, and natural gas processing), and alternative sources of energy will bring. They believe that private entrepreneurship, man’s engineering genius, and a minimalist government is the best medicine to cure any shortage — if such ailment exists at all. History shows an inevitable progress toward the ever-more plenty.

Market debacle in energy transition

Dismissal of this pious first principle begins by underscoring that the era of cheap extrasomatic energy is over and that such a critical juncture was in the cards all along. The coupling of unlimited material ends with the means of limiting each other’s gains to achieve it (i.e., gladiatorial rivalry for shares in markets that were once imperfect but by now are venal) defines a system that is indifferent to the finiteness of space, material endowments, and absorbing capacity. And as the statistics of highway fatalities illustrate, inattentiveness and full-tilt rush is a combination with consequences.

The motive of maximizing private gains is a winner as long as society’s explicit goal is the mass-provision of goods and services. Firm-level competition tends to optimize the employment of factors and the resultant dynamism keeps the engine of resource expansion humming. But when the implicit need to supply more expensive energy begins to affect economic performance, the market-signal-based nexus between wants and their satisfaction loses traction; it becomes a fortuitous hash of stop-and-go actions and wait-and-see inactions.

Without that much maligned and dreaded public interference (some form of government handout), the last thing that would emerge from a corporate boardroom is the decision to secure a loan (pledging real property and blue chip stocks as collateral) in order to invest in solar energy that could be sold profitably only when the price of oil rises to the same level that upended the economy in late 2007.

When the exchange value of “E” reaches output- and employment-damaging heights, the system is unable to direct resources released by the setback toward the broad goals of energy and environmental sustainability.

Ecology as a comprehensive and multifold obstacle to economic growth is revealing its presence by nullifying efforts to overcome it. Nothing keeps oil prices somewhere between the obscenely high and the tolerably modest in order to encourage investment in nonconventional oil and other energy sources. The financial crisis, which is closely tied to self-feeding excesses in oil trade, has weakened both ability and appetite to underwrite energy infrastructure development. Fiscal and monetary policy pedals have been pushed and are being pressed to the metal to no avail.

The jury is still out — but not much longer — on the aptitude of national governments to escape from economic policy traps and overcome institutional rigidities (vigilantly guarded by trenchant private interests) in order to steer the structure of energy supplies in the desired direction.

A fundamental rift separates the present from the past.

The singularity inherent in having left the sans souci puberty of ingesting and egesting nonrenewable resources as if they were poured from a magically self-replenishing container (call it the “Global Strategic Energy and Material Reserve”) broke the symmetry between the past and the future.

The relevance of projecting forward what lies backward has waned. But, of course, the recognition that the world economy has about as much chance to outgrow its already manifest resource and environmental limits as a mud ball has to fly through a cement wall (the textbook example of inelastic collision) will be a slow and messy process.

Some measure of hope may nonetheless be derived from the growing moral and logical intuition that humanity must reorganize its relationship with nature. (And how could this occur without reorganizing relationships among its own ranks?)

The beautiful otherness of an eternally cycling, forever growing economy unimpaired by earthly constraints

Stashing quickly- and slowly-diminishing nonrenewable resource inputs as equivalents into ordinary production functions is the first innocent step contemporary mainstream economics, which may be characterized as “neoclassical” for the past threescore years, makes toward disprizing concern over oil as the front barricade to economic growth.

Without a blink of the eye, flows from an apparently declining reservoir are put side by side with labor and capital services. The human biomass, from where labor flows; and buildings, machinery and equipment, which render capital services, also comprise natural resources but these are relatively abundant, i.e., they do not decline, degrade, or disperse at an alarming rate. (Much of the human body is made up of oxygen, carbon, and hydrogen; and contemporary capital goods are built mainly of abundant reserves of iron and bauxite. There is plenty of silicon to manufacture semiconductors.)

Would you trust a physician who believes that the healthiest, rather than the sickest, part of the organism determines life expectancy? This is the analogue of assuming seamless substitutability between rapidly and barely diminishing resources.

The second step is to consider these algebraic expressions (originally applied to optimizing activities at the level of industrial firms or plants) the valid representation of an infallible, self-programmed and self-correcting navigational equipment that guides society toward long-run equilibrium. Reliance on the so-called Constant Elasticity of Substitution (CES) functions in general equilibrium models, used to analyze national economies as well as the world economy, is the prime example.

Relative factor shares and substitutability among factors are of central importance in CES functions (of which the Cobb-Douglas format, the workhorse of neoclassical modeling, is a special case). Thus, the ability of a specific enterprise to increase the productivity of a factor (any factor, hence energy and oil) is subtly stipulated to be possible everywhere and all the time.

Under the banner of rationalism, resource scarcities are automatically rendered harmless by the interaction of market forces and technological development. Such is the conviction that breeds a hypertrophied, compulsive fixation with ever greater details within the protective enclosure of a fictitious economy in which the Earth plays the supporting role of standby reserve and fodder for consumption.

The passionate cry “peak oil is wrong!” heard from traditional economists is a proximal diagnostic of disorderly reasoning. By itself, the peak of worldwide oil production (whether it has already occurred or not) cannot be “wrong.” There must be a maximum in a time series that shows the flow-per-period history of a nonrenewable resource. The obstinate persistence of not understanding this betokens insensitivity to social and ethical problems, the 18th century Promethean metanarrative about the Invisible Hand’s munificence — accompanied by theological background noises — notwithstanding.

Taking the part for the whole

A recurring practical way to smear away the relevance of natural resources in the economic process is to cite the “post-industrial” character of high-income OECD countries. It takes a savant to atrophy reality so transparently. The majority of the planet’s population is now industrializing. Before you can have a respectable car service sector you must first have cars, roads, and gas stations.

Being economically advanced by itself implies the maintenance of a high-fixed-cost industrial infrastructure made up not only of the most abundant elements in the Earth’s crust. Hence, the world’s appetite for exhaustible resources, with fossil fuels as the top exponent, is accelerating rather than decelerating when global factors of production are at or trend toward full employment.

One may be inclined to ascribe the splendid intellectual self-incarceration of contemporary economics to “discourse” — postmodern philosophy’s explanation of how an internally coherent conceptual universe attached to the academic merit system prevents minds from seeing that a fading epoch’s moribund ideology postures as State-of- the-Art science, armed with a positivist research agenda.

But complete exoneration is no longer possible, not when the world population is pushing seven billion; not when data on proven oil reserves and their rates of depletion are compared to projections about the number of motor vehicles doubling in two decades — not with the air we breathe.