Diatribes of Jay

This is a blog of essays on public policy. It shuns ideology and applies facts, logic and math to economic, social and political problems. It has a subject-matter index, a list of recent posts, and permalinks at the ends of posts. Comments are moderated and may take time to appear. Note: Profile updated 4/7/12

02 July 2008

Innumeracy, Economics and the Great Accommodation

[Note that this essay was first posted in July 2008. For an application of this reasoning to current oil and gasoline prices, click here. For evidence from the Wall Street Journal that Peak Oil already passed in 2009 or 2010, click here. (You many need a trial subscription to read the article.)]

Supply and Demand
Elasticity of Demand
What’s Happening Now
Conclusion: Malthus and the Great Accommodation


We Americans are an innumerate people. I don’t mean we are so numerous we can’t be counted. I’m sort of making up a new word. “Innumeracy” is to math as illiteracy is to reading.

Most of us can read and write. We wouldn’t still be the world’s leading society if that weren’t so. But when confronted with the simplest precepts of mathematical/quantitative science, many of us have no clue. This sad fact applies not just to the average high-school graduate, but also to the journalists who inform us and the lawyers who govern us. Most of them chose their professions in part because they didn’t like math.

We all had high-school algebra, and most of us who went to college had some exposure to calculus. Yet when we encounter a nonlinear phenomenon—something that simple arithmetic or percentages can’t explain—we turn back to superstition or instinct. We become like savages who hear the roll of thunder and think the gods are angry.

So it is with our current economic predicament. We look at the rapid rise of prices for oil, food, copper, aluminum, cotton, corn and iron, and we become confused. How can prices double or triple, we ask, when global demand has increased by percentages lower (often much lower) than triple digits?

We look for demons. Speculators, hedge-fund managers, OPEC or some other evil spirit must be at fault.

Unfortunately, solving these problems is not nearly as simple as exorcising demons. In order to understand why the prices of everything we need most are rising rapidly, you need to understand at least three things: (1) the law of supply and demand; (2) the elasticity of demand, which is often nonlinear: and (3) how increases in demand can make prices respond in a nonlinear fashion.

Supply and Demand

The economic law of supply and demand expresses a simple and fundamental fact of life: the more of anything you have, the less of it you want, and the less you are willing to pay for it. Think of a kid with an allowance on a hot summer day. For the first nice, cool ice cream cone, she might give up all her weekly “pay.” But what about the second or third one? As the kid becomes satiated, the amount she’ll bargain for the next ice cream cone becomes smaller and smaller. As the quantity available increases, price goes down.

Another effect on demand is substitution. For most things in life, there are substitutes. Aluminum can make electrical wiring almost as well as copper. Bricks can make solid buildings about as well as stone. As the price of copper or stone rises, electricians and builders switch to the substitutes—aluminum and brick. Sales of copper and stone go down as a result. So the quantity sold goes down as the price goes up because potential buyers switch to cheaper substitutes.

In the case of our kid, she can save her allowance by following Marie Antoinette’s advice and eating cake. It may not be as cold as ice cream, but it’s just as sweet and enticing. And if chilled in the refrigerator, it may even provide some relief from the heat.

Both of these phenomena (satiation and switching to substitutes) point in the same direction. As prices go up, sales go down (and vice versa), because fewer people can afford the thing (whatever it may be), and many switch to cheaper substitutes. As the market supplies more, prices decrease because of satiation.

This “law of supply and demand” works for anything bought or sold, be it cars, oranges, rice, copper or oil. There is nothing controversial or “theoretical” about it. Economists, bankers, accountants and business people rely on it every day.

Elasticity of Demand

But not all commodities are equal. Some are more important than others. Taken clean, potable water, for instance. For human beings, it is the most important commodity of all. If you lack it, you’ll die in about a week. There are no substitutes, because everything that serves the same function (quenching thirst) contains water.

You might think that water is a bad example of a tradable commodity. Only recently has it been bought and sold on the market, with Evian and the bottled-water mania. For most of our history it has been supplied for free—or at nominal cost—by that most maligned of American institutions, government. The vast majority of Americans still gets the vast majority of its potable water from taps supplied by systems owned, run and maintained by local government.

Isn’t that interesting? The thing we need most, what we least can live without, government supplies, at low and uniform prices. How does that square with our American “Soviet period” economic religion, that government can do no right and markets can do no wrong? Why don’t we do the same with energy? It’s something to ponder.

But I digress. Bear with me. There’s more.

Let’s suppose for a moment that there were no government suppliers of water, only a private market. Let’s suppose also that clean, fresh water got scarce, so that available quantities on the market diminished rapidly. What would happen?

Well, first of all, prices would rise. Since water is essential and there are no substitutes, prices would rise dramatically, as buyers bid against each other to stay alive. Eventually, as the poor were priced out of the market, people would start to suffer thirst and die. That’s already happening in drought-stricken parts of the world that we Americans don’t like to read or hear about. Or people use inadequate substitutes, like tainted water; then they die from other causes like cholera or arsenic poisoning.

When a commodity is as important as water, economists call demand for it “inelastic.” That means the relationship between supply and demand is different than for other, nonessential commodities, like the ice cream and cake in our example above.

Not only is the demand curve steeper (i.e., price rises more quickly with increasing demand or decreasing supply). But demand is nonlinear. That is, demand is not just a straight line but can rise dramatically with varying conditions.

Again, think of water. If water is plentiful and cheap, people might use it to water their lawns, take long showers, and fill swimming pools. As it becomes scarcer, these “frivolous” uses cease, and people start conserving water for drinking. As more and more people do so—and only the very rich water their lawns, take showers, or have pools—water gets down to its most basic and important use: saving people from dying of thirst. Once that happens, the demand curve becomes very steep indeed, as people spend all they have on water to stay alive. Prices rise dramatically because life is at stake and there are no substitutes.

That’s where Marie Antoinette went wrong. You see, bread is usually cheaper than cake; it’s the basic commodity. Like water, it was essential for life in pre-revolutionary France. It had no ready substitute. So when Marie advised French peasants to switch from bread to cake, her advice wasn’t very practical. She lost her head, in part because of inelasticity of demand.

What’s Happening Now

There’s a good analogy between these bread and water parables and what we’re all experiencing now. Demand for most basic commodities today is relatively inelastic because there are no good substitutes.

Oil has virtually no substitutes, at least for transportation. There are virtually no flex-fuel vehicles outside of Brazil and virtually no electric vehicles anywhere. Most of the world has followed America’s lead in creating completely non-diversified transportation economies dependent on a single fuel. (Whether this situation has to remain so is another story entirely.) If you own a car built for gasoline, you can’t suddenly switch to running it on, say, cooking oil or even kerosene. Try that switch, and you’ll have to replace your engine.

Similarly, there aren’t many substitutes for steel, with its strength and longevity for construction. Ditto for copper, which has the best electrical conductivity of any commodity metal, and for aluminum, which is the lightest metal in widespread commercial use. (Lithium and magnesium are flammable in air, and beryllium is toxic.)

These commodities are not all getting scarcer. Except for oil (which may have already reached its peak in worldwide production), their supplies are growing slowly and steadily. But demand is growing much faster as the developing world develops.

To estimate how much faster, do some simple arithmetic. It is well known that the United States has about five percent of the world’s population but consumes about a quarter of its resources. What would happen if the rest of the world came up to that same standard of living?

Well, every five percent of the other 95% of the world’s population would also have to consume one-quarter of what the world produces now. World production would have to increase 500%. In order to accommodate the rest of the world at an American standard of living, supplies of everything would have to increase fivefold.

We may be learning how to grow more crops and mine more copper and aluminum, but we’re not doing it at anywhere near that rate. Nor is there any indication that the Earth contains enough arable land or recoverable ore to do so.

So the next time you read a news story about “dramatic” increases in production of oil, steel, aluminum, copper, corn, or cotton, pay attention to the numbers. They are usually in the range of five or ten percent. Occasionally, an extraordinarily good year might produce an increase of 15%. That’s a long way, and many years, from 500 percent, even if natural reserves permitted such an increase.

So what is happening? As you might expect, the commodities in shortest supply, and the ones with the fewest substitutes, are experiencing the most rapid increases in price. Things like oil, copper, aluminum and iron lead the pack. Second come basic foodstuffs like wheat, corn and soybeans, whose production in our mechanized world depends heavily on another inelastic commodity: oil.

All this is in complete accordance with the law of supply and demand. As demand explodes, these commodities are moving rapidly up the demand curve, where prices get higher.

Increasing inelasticity of demand is also responsible for the rapid raise in prices. As developing countries modernize, they become dependent on these commodities. Where once stone, wood or mud brick were good enough for housing, now modern buildings require steel and copper. Airplanes require aluminum. Wheat, corn and soybeans have substitutes, but their demand has become more inelastic as billions of people have abandoned their traditional diets and come to depend upon them. Who wants to eat cassava and millet when you can eat bread, soy products, and cake? There is no going back.

It’s even worse for oil. Hundreds of millions of people just entering the middle class are making the biggest investments of their lives in oil-powered cars. Every one of those cars, and every production or assembly plant to make them, is an irreversible commitment of human and societal resources making demand for oil more inelastic. The more the world invests in gas-guzzling cars with no flex-fuel capability, plus the plants to make them and the infrastructure to supply them, the more inelastic demand for oil becomes.

All this may seem like so much abstract theory. But inelasticity of demand for oil is an established historical fact. Over the last twenty-five years, while the price of gasoline has risen steadily, demand for it in our own country has increased by 40%. The first sign of a decrease in demand came in the first quarter of 2008, when demand decreased 1.3% from the previous year.

So as the price of gas inside the United States increased 100% from roughly $ 2 to $ 4 per gallon (which it did as oil rose from $65 to $130 per gallon, from mid-2005 to mid-2008), demand at first rose, and then fell only 1.3%. That relationship—a 100% price increase and a 1.3% decrease in usage—reflects extraordinary inelasticity of demand for oil in the United States.

Just how extraordinary? Well, imagine that the price of chocolate cake or tickets to movie theaters increased by 100%, so that a good chocolate cake cost $50 and entrance to a movie theater cost $25 per person ($50 per couple), or more in big cities. Now imagine further that the cost of substitutes, such as ice cream, sponge cake, DVDs and home video, didn’t increase at all. Do you think that chocolate-cake consumption or movie attendance would decrease by only 1.3%? Not on your life.

Prices for gas and other essential commodities are rising because of extraordinary demand and its extraordinary inelasticity. The result is nonlinear. When an increase of 100 % in price can produce a decrease of only 1.3% in demand, the reverse is also true. Increases of only a few percent in demand can produce a doubling or tripling in price. There are no demons, only the inexorable mathematical laws of nonlinear economics.

In the case of food, there are some additional short-term phenomena. Some countries now are hoarding and/or refusing to export food to protect their populations from famine and themselves from political instability. But national hoarding is a temporary, sporadic phenomenon. What’s driving hoarding is same economic forces driving worldwide price increases: steadily and rapidly increasing demand, a high baseline of inelasticity, and increasing inelasticity as billions of people become dependent, for the first time, on “modern” levels of consumption of “modern” commodities. (For a depressing review of some of the short-term phenomena affecting the oil market, concluding that none can change the long-term trends discussed above, see this post.)

How long can this phenomenon continue? Well, consider the world’s population. Two of the most rapidly developing nations on Earth are India and China. Together they have about 2.4 billion people, more than one-third of humanity. So far, only a few hundred million of them have achieved anything like a Western, middle-class standard of living.

So we’ve assimilated a few hundred million people and have about two billion more, give or take, waiting impatiently to enter the middle class. That’s about three times the combined populations of North America, Europe and Japan. And that’s in China and India alone! What about South America, Africa, and the many populous portions of the Islamic world? The demand pig is less than one-tenth through the development snake.

If you think on these things, you’ll have some vague idea of what we’re up against. It’s not speculators. It’s not evil spirits. It’s something much more simple, more important and more profound. We humans are coming up against the mathematical limits of our Earth’s ability to support all of us in the manner to which we would like to become accustomed.

Conclusion: Malthus and the Great Accommodation

Remember Malthus? That’s Thomas Robert Malthus, the late eighteenth-century English thinker who predicted mass starvation, mainly of the “lower classes,” as the world’s growing population ran out of space and resources for agriculture.

Malthus was wrong about many things. He had no crystal ball, and he was apparently unaware how big the world really is. So his prediction was off by about two centuries in timing.

Malthus couldn’t predict how worldwide dispersion of the human population would find new land and produce new resources. He couldn’t know that the rise of Reason, and its handmaidens science and technology, would produce means for vastly increasing the productivity of agriculture and staving off the crash. He couldn’t know that the same science and technology eventually would produce rapid global transportation and communication, make nation-states commercially obsolete, and create a smoothly functioning global marketplace. And he certainly couldn’t know that, because of all this, when the crunch time came that same global marketplace would warn us with the clearest signal of classical economics: dramatic and steady price increases.

But Malthus nevertheless was fundamentally right. He just got his numbers, his timing and his commodities wrong. It’s all happening centuries later than he predicted; and energy, not food, is the first commodity to go. But his basic point of an infinitely expanding human population (with an infinitely expanding thirst for a better standard of living) bumping up against a finite planet was essentially correct.

As we are finally becoming painfully aware, our Earth’s resources are not infinite. We live on a finite planet with a rather delicate ecosystem that took billions of years to evolve. We are part of that ecosystem, and we have to live within its mathematical limitations unless we can find some other suitable planet or planets to live on.

Don’t hold your breath. We still have a least a decade to go before we set foot even on Mars, a planet whose climate is less hospitable to life than the Gobi desert with a North Polar climate.

For a while, we could indulge our illusion that we are above the world that gave us birth and could bend it to our will. We could delay the inevitable collision with reality by using science and technology to create a “green revolution.”

But that revolution took energy and chemicals, including organic chemicals derived from oil. Now we are running out of both energy and the oil we use to make chemicals, let alone more space to plant. As we burn more oil to run about and more rain forest to create more space for planting, we are destroying the delicate carbon balance that keeps our climate stable. We are also extinguishing millions of unknown and possibly priceless species of plants and animals, which could help protect us against an ecological catastrophe.

Price increases are just one of the many ways in which we each are just beginning to encounter this phenomenon personally. In Tom Friedman’s “flat world,” we have a global marketplace for almost everything that matters. When you fill up your tank, you are bidding against the Chinese entrepreneur who just bought his first Mercedes and the Indian woman who answers your telephone calls to your bank or software supplier and just bought her first subcompact. You are also bidding against all the car owners in Europe, the ANZUS nations and Japan, who are just as rich and just as tied to their cars as you. And most of their governments, like ours, made no provision for the coming scarcity or for a diversified transportation economy.

As you put the nozzle in your tank, the price you pay depends, in essence, on a bidding war with these folks in foreign lands. All of them want the good life too. The newer entrants in developing countries are hungrier and maybe more ambitious than you and willing to work just as hard or harder. But there is only so much oil to go around, so you have to bid against all of them to fill your tank. The laws of market economics favor no one. All are equal in scarcity.

So rant all you want. Seek out speculators and other evil spirits to scapegoat and exorcise. Pillory them if it makes you feel good. Hang them in the public square if it pleases you.

But don’t delude yourself that doing so will change a thing.

The inexorable laws of economics don’t give a damn about your pain or the supposed divine right of American workers. They respect only the mathematics of demand and inelasticity. They reflect the yearning of the rest of the world’s 6 billion people for a life just as good as yours, and their striving to get it, which is just as energetic as yours.

If you want to make things better for yourself and your children, you are going to have to do more than exorcise evil spirits and find scapegoats. You are going to have to join the Great Accommodation—of the human race with its small, fragile planet.

You are going to have to learn to do more with less. You are going to have to develop substitutes for things like oil, which already may have seen their most abundant days. You are going to have to accept new technologies like nuclear energy and help make them safe and reliable with intelligent policy, not irrational fear. You are going to have to depend much more on renewable substitutes, like wind and solar energy.

You are going to have to exploit the factor-of-fourteen difference in transportation energy prices between electricity and oil—a factor that will continue to grow until we begin to exploit that difference. And you are going to have to make sure that your elected representatives are no longer so innumerate that they neglect factors of fourteen (or four) that could work to our benefit in the cost-energy-commodity balance.

Finally, you are going to have to demand, not just support, rational public policies toward these ends. Every one of us is responsible for our current lamentable condition. Every one of us bought the oil industry’s assurances of inexhaustible cheap energy. Every one of us is now buying the coal industry’s lies about “clean coal.”

There are no happy alternatives to playing energy and commodities by the numbers, conserving them and developing real substitutes as necessary. There are only want, suffering, famine and war—humankind’s historical answers to scarcity. Or, in the case of coal, there is a Faustian bargain: exchanging a century or so of cheap energy for a blasted, polluted planet on which no one who has seen any of our world’s few remaining pristine areas would ever want to live.

Life is unfair. But as anthropologists know, it is most acutely unfair to societies that prefer witchcraft and scapegoating to Reason, science and math. So we had all better learn to think by the numbers, while we still have an economy and a planet worth saving.


Site Meter


  • At Thursday, July 3, 2008 at 2:26:00 AM EDT, Blogger cjcalgirl said…

    Dear Jay, This essay is one of your very best! You set out the problems and their causes in the simplest terms, yet with a depth of consideration and information that is inspiring and reassuring.(That there are people like you thinking deeply about our growing dilemmas). Every other national and international issue pales against the reality of the illness and eminent death of the current life on this planet. I remember a childhood full of bees, butterflies, finches and blackbirds, Beaches upon which I could only find the natural detritus(sp?) washed up ashore. I fear that most governments will react too slowly to galvanize people to make the changes necessary and the poorest will not be able to at all. When has Govt. EVER moved quickly? Even WWII went along quite a while without us. Yes?

  • At Saturday, July 5, 2008 at 3:13:00 AM EDT, Blogger Jay Dratler, Jr., Ph.D., J.D. said…

    Dear Carol,

    Your comment encapsulates our predicament well. There still are places on Earth that appear as nature made them, but they are getting rarer and rarer.

    My wife and I are traveling in Southern Europe, and everywhere we have gone there has been visible coal pollution, sometimes starkly visible. People call it “haze,” but it’s easily distinguishable from water vapor by its brown or orange color. The entire Aegean Sea is full of it.

    Unfortunately, the pollution is increasing so gradually that people are largely unaware of it. I feel sorry for kids born today, especially in urban areas, who may never know what a clear, blue sky looks like or see the Milky Way at night. As pollution increases, so will respiratory diseases and general bad health. Then will come horrendous global warming.

    If people have a choice between an energy-rich life style and a clean planet, they will always take the easy route. Entrenched industries, such as coal and oil, will take the profits out until the last gram of fuel is gone and the most remote parts of Earth polluted.

    What is so tragic is that there are good alternatives. Nuclear energy can avoid air pollution and global warming. Wind and solar---which we have just begun to exploit---have virtually no undesirable effects. Exploiting these clean sources of power will create good, honorable manufacturing jobs that cannot be outsourced.

    All we need is political will and vision. That’s why this presidential election is so important. We Americans have to arrest our national decline and regain our leadership in saving our planet.

    As Tom Friedman wrote recently, nothing else matters.


  • At Wednesday, September 14, 2011 at 9:10:00 AM EDT, Blogger Janet Camp said…

    Hello Jay,

    Your writing is clear and concise, but unless you "come out" and use your real name, it's just more words and cannot make much difference. Your NYT post today was excellent as well, but again, what does "Old Curmudgeon" tell us? It helps that you got the #1 slot, and I will visit this blog again, but I truly wish more bloggers would be more public about their backgrounds.

  • At Wednesday, September 14, 2011 at 4:37:00 PM EDT, Blogger Ormond Otvos said…

    Well, Jay, you manage a good description of what overpopulation does to us without ever mentioning the need for an end to population growth.

    And traveling around the world to observe in person what's so easily learned on the internet is just the kind of self-serving convenience you rant about.

    What gives? Where's the rant on the mad sexual urge to procreate (or more accurately, engage in sex acts)?

  • At Wednesday, September 14, 2011 at 11:17:00 PM EDT, Blogger Jay Dratler, Jr., Ph.D., J.D. said…

    Dear Janet,

    Thank you for your comment and for your toughness.

    I had already decided to “come out” (of anonymity), but your comment confirmed my decision. You can see all the reasons pro and con in a post entitled “Coming Out!” that will appear on the home page in the next day or two.

    The day I reveal who I am will be Thanksgiving, so I hope you'll be patient!



    P.S. Since this post is an old one, I’m taking the liberty of transcribing your comment to that post.

  • At Thursday, September 15, 2011 at 12:03:00 AM EDT, Blogger Jay Dratler, Jr., Ph.D., J.D. said…

    Dear Ormond,

    Are you post-pubertal and healthy? If so, I wouldn’t think you would have to inquire about the sexual urge. It’s built into most of us.

    As for population control, I haven’t tackled that topic yet because it is a big and controversial one and I want to get my first essay right. Suffice it to say for now that I admire the Chinese with some reservations, and that many of our other problems will prove intractable unless we control population growth first.

    As for your middle paragraph, I’m at a loss for two reasons. First, you apparently haven’t learned yet not to assume things about people you don’t know. Part of my reason for traveling was to support my wife, who is caring for her aging parents (over 90!) in a foreign country.

    Second, if you believe you can learn all you need to know about the world through the Internet, you know little about the world. There are so many things you must experience directly even to know, let alone to understand, that I can't even begin to name them all. Among the few that come most readily to mind are food, culture, the native language as it's used in-country, relationships with natives in the homes and businesses, and the sights, sounds and smells of the streets, towns and buildings. Like the sexual urge, you have to experience these things to understand them.

    I surmise from your comments that you are young. Live, learn, experience, and withhold judgment until you do. The worst thing any serious mind can do is leap to erroneous conclusions on insufficient evidence.


  • At Thursday, September 15, 2011 at 10:26:00 PM EDT, Anonymous Anonymous said…


    This was a great essay. Here's someone else who is onto the same problem... Dr. Albert Bartlett. He has a series on YouTube that would interest you. It is NOT well titled - "The Most Important Video You'll Ever See", but the content is excellent. It covers our inability to understand exponential functions and fossil fuel availability. Hope you get a chance to see them.
    BTW, any chance you are Jay - Ottawa on the Sardonicky blog?
    I'll check back later in the hope that you'll reply. Thanks again for the great essay.

  • At Thursday, September 15, 2011 at 10:41:00 PM EDT, Anonymous Anonymous said…


    Just finished the comments. I see Janet Camp has the same idea. I'm afraid you're outed! As I recall your comments over at Sardonicky, you've grown more fiesty. I'm not sure I've always agreed with you over there, but this essay certainly enhances your reputation.

    At least for today, I feel like I'm done with fighting the political wars. Our political future seems grim - your essay and Dr. Bartlett only confirm a very bad (and short)"future".

  • At Saturday, September 17, 2011 at 1:47:00 PM EDT, Blogger Jay Dratler, Jr., Ph.D., J.D. said…

    Dear Anonymous (taking both your comments at once),

    I’m sorry to disappoint you, but I’m not the “Jay” at “Sardonicky.” I don’t even know what Sardonicky is.

    If you read Janet Camp’s comment carefully, you’ll see that she (correctly) identifies me as “Old Curmudgeon” in online comments to the New York Times. But “Old Curmudgeon” is also anonymous, as Janet notes. (The NYT allows screen names.)

    So no, I’m not outed yet. You’ll have to wait until Thanksgiving to find out.

    As for “The Most Important Video You’ll Ever See,” that’s precisely the sort of over-the-top self-promotion that people like Sarah Palin blithely spout but that I am constitutionally incapable of making. It’s just not accurate. (You can see why I have more than a little sympathy with the President’s habit of understatement.)

    Anyway, I will take a look at the video, and thank you for your comment. But you and most readers will probably be surprised (and maybe disappointed) when you actually find out who I am. Stay tuned.



Post a Comment

<< Home