FREC 324 -- What happens when we run out?

The traditional "big questions" in resource economics are about the future of the earth: How long can a growing human population continue to enjoy rising standards of living with finite natural resource reserves? What will happen to society when we run out of reserves?

We begin with a more in-depth discussion of the two contradictory visions of the future: pessimistic forecasts of economic and social collapse, versus optimistic forecasts of sustained improvements in standards of living.

The pessimist models

The traditional pessimist model derives from Rev. Thomas Malthus's Essay on the Principle of Population (1798). Malthus observed that population tends to grow exponentially (due to unbridled human lust!) while the food production capacity of the land base is fixed, so it is only a matter of time before the human population outgrows the carrying capacity of the Earth. At that point, humans will be reduced to bare subsistence living. (Malthus cited population figures from America to prove his point, but overlooked the fact that much of the American population increase was due to immigration rather than births.)

Any exponential growth trend can be extrapolated to ridiculous magnitudes.  For example, a population of E. coli bacteria can double every 20 minutes, so if you start with only 1 μg of E. coli under your fingernails, you could have 4 grams of it after 4 hours, 16Kg after 8 hours, and 68 metric tons of it after 12 hours.  Within 24 hours it would cover the entire Earth about 2 miles deep.  This is why you should wash your hands.

The Malthusian model is widely believed because it is simple and logical, and its predictions are clear and dramatic--just do the math! There are numerous modern variants of it:

In 1968 the biologist Paul Erlich published The Population Bomb, which really ramped up the hysteria: "The battle to feed humanity is over. In the 1970s, the world will undergo famines. Hundreds of millions of people are going to starve to death in spite of any crash programs embarked upon now...Population control is the only answer." Erlich later admitted his predictions had been premature, but never gave up his strident calls for strict government controls on human reproduction. When economists pointed out that rising per-capita incomes reduce population growth, and that economic growth might solve the global population problem, Erlich countered: "We've already had too much economic growth in the United States. Economic growth in rich countries like ours is the disease, not the cure." (1990)

Garrett Hardin's article "The Tragedy of the Commons" (Science, 162:1243-1248) was published the same year. It discusses the problem of a pasture on which anyone may graze his or her sheep. Since no one owns the common, and it is open to all, every herder has an incentive to enlarge his or her own flock even though it reduces grazing for everyone else's flocks. Unless all its users can agree among themselves to maintain the productivity of the common by limiting the size of their flocks, the common will be overgrazed and ruined. (We will analyze problems of property rights and negative spill-over effects such as these later on in the course.) By analogy, the Earth is a common at risk of ruin from the freedom to pollute or have as many children as we want. Hardin argued that long-term survival requires progressive elimination of freedoms--including government restrictions on reproductive rights--and growing reliance on "mutual coercion."

Hardin confused a "common property" resource with an "open-access" resource. Grazing commons such as Hardin described actually persisted for centuries in medieval Europe because the users developed ad hoc institutions to manage them. Villagers would exclude outsiders and agree on mutually beneficial size limits on herds, or informal allocations of the common. And some common-property resources are managed the same way today. For example, lobster harvesting in Maine is managed by "lobster gangs" that have divided a nominally "common property" fishery into de facto private fishing grounds for specific lobster boats. (See James Acheson's book The Lobster Gangs of Maine)


Check out my swanky Powerpoint slide below.  It shows a couple of mathematical projections that I ran in Excel based on current world population growth rates.  With population increasing 15% per decade, we'll reach 12 billion people by 2050 and 24 billion people by 2100.  Three out of five experts agree that 12 billion people is about the maximum carrying capacity of the Earth, so one forecast assumes this is a hard ceiling, with resources at maximum utilization from 2050 onward, humans reduced to subsistence living, and periodic global famines to keep things interesting.

Now this is a pretty naive forecast, because it doesn't really account for resource depletion and gradual degradation of the Earth's carrying capacity.  So I introduced a simple positive feedback mechanism into the model:  as overpopulation destroys the Earth's carrying capacity, the sustainable population falls to zero.  This more "logical" forecast predicts human extinction around the end of this century.  I included the image of the melting Earth to add a little salience.

Back in 1972, unencumbered by humility or self-doubt, Dennis and Donella Meadows and Jay Forrester started calling themselves the "Club of Rome" and published The Limits to Growth, a mathematical forecasting model based on similar positive feedback mechanisms represented in simple differential equations.  Their extrapolations of exponential growth in resource use, population and pollution, all culminate in sudden collapses of industrial output and food production.  Their models predicted worldwide famine and population collapse occurring in the next 30 to 100 years.  The book was a best-seller.

This is their model schematic (above), scanned at 400 DPI from the Signet paperback 2nd edition.  It's not even legible without magnification, but that's okay; it's obviously so complex that we wouldn't understand it anyway.  We can't question the underlying equations because they didn't publish them.  We are expected to take these intellectual giants at their word: without Draconian controls on population growth and resource use, civilization will collapse.  The "standard" forecast derived from the model is shown below.

This figure commingles a bunch of scary-looking trendlines, but there's no vertical scale, and no definition of the units by which resources, services, pollution, etc. are measured.  "Births" and "deaths" (are these numbers or rates?) both exceed total population?  Pollution (do they mean the cumulative build-up of pollutants, or annual emissions?) increased five-fold between 1950 and 2000???

This is a brilliant piece of obfuscatory eyewash, a work of Powerpoint genius created 20 years before Powerpoint was even invented!

Critics who questioned the economic assumptions of the Limits to Growth model quickly discovered that the model doesn't incorporate any economics at all.  There are no markets.  There are no market prices to signal increasing scarcity and moderate consumption.  The model assumes consumption will just keep accelerating until current reserves suddenly run out.  There are no incentives for conservation, no resource substitution, and no convertibility of resources into capital.  There will be no new reserves discovered or developed from new technologies.  This model was designed to crash and burn.


Malthus was not the first writer to worry about unrestrained population growth. Jonathan Swift's famous essay "A Modest Proposal" (1729) explains the demographic problems of early 18th-century Ireland before introducing his tongue-in-cheek population control strategy: "I have been assured by a very knowing American of my acquaintance in London, that a young healthy child well nursed is at a year old a most delicious, nourishing, and wholesome food, whether stewed, roasted, baked, or boiled; and I make no doubt that it will equally serve in a fricassee or a ragout."

The optimist models

The popular Malthusian crash-and-burn models developed over the last 200 years have salience and superficial plausibility, but their predictions of resource exhaustion and collapse have been consistently wrong--at least so far!  There is a solid body of economic theory to explain why:

In 1931 Harold Hotelling formalized the standard economic model of exhaustible resource depletion, explaining why profit-maximizing behavior in competitive resource markets causes efficient allocations of resources through time. This is the fundamental principle behind the exhaustible resource depletion theory taught in this course.

Hotelling explains that competitive resource owners all compare the discounted resource rents they could expect to receive in different time periods, and try to sell their resource stocks in the time period(s) when the discounted rents are maximized. If resource owners expect that resource rents will rise faster than the rate of discount, they withhold the resource from the market (viewing them as high-return investments), and the current price of the resource immediately rises to a level from which rents then grow at the rate of discount. If resource owners expect that resource rents will rise slower than the rate of discount, they sell off their resources (as low-return investments), and the current price of the resource immediately falls to a level from which rents will grow at the rate of discount. So market consensus expectations about future rents are reflected in current resource prices. Resource markets exhibit foresight! They anticipate future scarcity, and reflect it (discounted) in today's prices. Over the long term, marginal rents from an exhaustible resource will rise at the rate of discount through time. We will revisit these concepts in detail over the next few weeks.

Robert Solow's 1974 article "The Economics of Resources or the Resources of Economics" (American Economic Review) expands on Hotellling's hypotheses and provides a good explanation of how rising resources prices signal scarcity, stimulate conservation, new discoveries, new recovery technologies, development of substitute resources, etc. Solow's growth models demonstrate that we can have limitless economic growth with a limited physical resource base as long as we maintain adequate capital investment.

Alfred Kahn's The Next 200 Years is another rebuttal of the Limits to Growth model, and projects that technology will keep food production ahead of population growth. As long as the economy continues to develop technological efficiencies and substitute capital for raw materials, we will be fine.

Julian Simon's The Ultimate Resource (1981) takes the most contrarian, optimistic view of the future. Simon's "ultimate resource" is people, and the imaginations and ever-increasing stock of knowledge they possess. He argues that per-capita incomes and living standards have been rising pretty steadily in line with population for 500 years and will likely continue to do so indefinitely. Efficient markets naturally signal impending scarcities with rising prices. But long-term prices for most resources have declined. It's not the quantity of reserves we have left that indicates resource scarcity, but the real (inflation-adjusted) prices of resources.

(Simon had some high-profile debates with Paul Erlich over resource scarcity, and in 1980 they made a bet. Erlich would track the inflation-adjusted value of a $1,000 portfolio of five metals for ten years (Erlich chose copper, chrome, nickel, tin and tungsten, $200 of each at 1980 prices). If the real value of the portfolio had increased by 1990, indicating rising economic scarcity, Simon would pay Erlich the increase in value. If the real value of the portfolio had fallen, indicating reduced economic scarcity, Erlich would pay Simon the decrease in value. Simon won the bet handily. By 1990 the inflation-adjusted value of the metals portfolio had fallen by more than half, and Erlich sent Simon a check for $576.07.)

Technologies continue to enhance the productive efficiencies of finite resources. The quantity of farmland is pretty stable, but technologies have increased yields per acre dramatically and food prices keep falling. Today's cars get about twice as many miles per gallon as cars built in 1970 got.

Pollution has actually declined as population and per-capita incomes increased. The US has significantly cleaner air and water today than it had 30 years ago. This demonstrates that environmental quality is a luxury good, which simply means that its income elasticity is greater than one. In other words, as incomes increase, demand for environmental quality increases proportionately more. Note that the term "luxury good" does not imply the good is frivolous or high-priced or just for rich people. Other "luxury" goods include safe water, sanitation, education, health care and even longevity.

Most modern economists would argue that the pessimist models are gross over-simplifications--mechanistic and myopic, because they ignore the capacities of people and markets to adapt to changing resource endowments. The pessimist models generally assume that the carrying capacity of our environment is fixed, that people will keep reproducing at the same constant rate, and that there will be no market adjustments to resource scarcity; so resource depletion will be sudden and catastrophic. There is no differentiation of land qualities, or human abilities, no capital or wealth accumulation, no technological improvements in resource use efficiency--in short, no economics! The pessimist models yield clear predictions, but they turn out to be wrong.

The optimist models are somewhat more technical, and their predictions are less specific. They recognize that the world is more complex, and human societies (market democracies, at least) are more responsive and adaptable to change than the pessimist models allow.

In general, the pessimist models imply that the free market system will ultimately fail or betray us. The implication is that markets and behaviors must be controlled to insure society's survival. We may need to restrict peoples' reproductive rights (as Hardin suggested and China has done), ration their consumption, control their choices, etc.

In contrast, the optimist models argue that the free market system generally does allocate resources efficiently. Market interventions are only necessary to correct identifiable market failures such as externalities or undersupply of public goods. Government failure leading to the imposition of unnecessary market distortions may represent a more significant risk to our future welfare than market failure.

Although economics has been termed "the Dismal Science," economists are typically optimistic about the abilities of efficient markets to protect us from "overshoot and collapse" scenarios in the future. Unfortunately, public confidence in market efficiencies is not so strong. Public mistrust of markets can easily foster wasteful and even counter-productive government policies to correct perceived economic problems.

In the policy realm, the resource economist's primary mission is to distinguish truly inefficient resource markets from efficient markets, and argue for limiting policy interventions to inefficient markets only. Please keep in mind that political processes are not necessarily more efficient than market processes. Government interventions in markets often create bigger problems than they solve. That is why this course includes a large amount of political economy theory to complement the standard resource economics theory.


The population crisis itself seems to be abating.  Over the past few decades a clear link has emerged between incomes and fertility rates.  As GDP per capita rises across the world, the average number of births per female falls.  Children are inferior goods! 

This graph shows the relative populations of the 60 most populous counties in the world, representing more than 90% of the world's population.  The trendline traces the overall relationship between the natural logarithm of GDP per capita and the natural logarithm of fertility rate (average births per female). The trendline equation indicates that the income elasticity of global demand for children is about -0.28.  As per-capita GDP rises, fertility rates decline.

A sustained fertility rate of about 2.1 births per female (ln[2.1] = 0.74) yields a steady-state population over the long run.  About 44% of the world's population now lives in countries with fertility rates at or below this level.  If global economic growth continues, we can expect the world's population to stabilize within two generations. (Click on the graph for a larger version.)


Here are a few resource depletion stories that show how pessimism is not always warranted. (Jared Diamond's book Collapse explores a number of other resource depletion crises at length, some with tragic outcomes, some with happy outcomes.)

In the 19th century many households used whale oil lamps for lighting, but as the US whaling industry expanded and the technological efficiency of whaling improved, whale stocks were seriously depleted, and whale oil prices rose sharply. But rather than sit home in the dark, people switched to gas and electric lighting and the whaling industry faded into obsolescence. There was no crisis. Some little old lady went down to the corner store and bought the last pint of whale oil, and the story didn't even make the local paper. Then she bought an electric lamp.

In 1908 Teddy Roosevelt shared widespread concern that the US was rapidly running out of trees: "If the present rate of forest destruction is allowed to continue, a timber famine is obviously inevitable. Fire, wasteful and destructive forms of lumbering, and legitimate use are together destroying our forest resources far more rapidly than they are being replaced.... Unless the forests can be made ready to meet the vast demands which...growth will inevitably bring, commercial disaster is inevitable." This didn't happen, obviously. Instead, the US timber industry developed more efficient growth management, harvesting and processing technologies, and the nation switched from wood to coal, and then to other fuels, for energy.

In 1920, US consumption of petroleum was a half-billion barrels/year, and the USGS estimated total reserves to be 7 billion barrels--about 15 more years of petroleum left even if consumption didn't increase! But 15 years later, although consumption had increased dramatically, total reserves were up to 12 billion barrels--enough to last about 15 more years. Today the US consumes over 7 billion barrels/year, about 40% of this is produced domestically, and current US petroleum reserves are estimated to be about 22 billion barrels--enough to last about 9 years without any imports-- but that's not the whole story. In 2008, world oil consumption was about 64 billion barrels/year from global reserves now estimated to be about 1.2 trillion barrels--enough to last over 50 years.


The total volume of oil deposits in the earth--what we will call the "total resource base"--is certainly finite. The USGS defines "reserves" as the portion of the natural resource base that is currently identified and economical to extract

Suppose the rectangle below represents the total quantity of some non-renewable natural resource. The various stocks of this resource are sorted left to right by degree of certainty, and top to bottom by cost of extraction. Since we aren't necessarily certain about the total quantity that would be available at very high prices or that would be found after every part of the Earth is thoroughly explored, the right and bottom boundaries of this rectangle are fuzzy.



As consumption reduces reserves, the price of the resource increases, converting some sub-economic resources into reserves by definition.  The price increase also motivates exploration (shifting the reserves boundary to the right), R&D into lower-cost extraction technologies (shifting the reserves boundary downward), demand-side conservation and substitution of alternative resources. Over time, oil companies discover more deposits, and develop more efficient extraction technologies that make previously sub-economic deposits profitable to extract. For most of the past 100 years global oil reserves have been increasing on the production end at least as fast as they were being depleted on the consumption end.

The naive static reserve index, which is calculated by dividing current reserves by annual consumption, is very misleading, since it confuses reserves with the overall resource base, and it doesn't account for price responses (motivating conservation, substitution, R&D and new exploration) to increasing reserve scarcity.


The concept of resource rents

During the 19th century various economists refined and elaborated on the theories of Malthus. David Ricardo (1772-1823) observed that some farmland is more productive than other farmland, but the owners of the more productive farmland can hire workers for the same wages that owners of less productive farmland pay their workers. Thus a resource "rent" accrues to the owners of high-quality farmland. As population grows, the excess supply of labor drives wages lower, and successively poorer quality land is brought into production. As the relative scarcity of land increases, rents on higher quality land rise. Ricardo's theory implies that society will become polarized into two classes: a large population of landless, impoverished workers scraping out a bare living on rented land and a small landowner elite who collect the rents. Unrestrained population growth will keep wages at subsistence level, and the peasant population will be fully exploited by the capitalists who capture all of the economy's economic surplus.

The Ricardian model troubled many 19th century economists, because the concentration of wealth in fewer and fewer hands seemed to imply eventual "secular stagnation," an inadequate aggregate demand leading to economic collapse: how much consumption can a dwindling number of super-rich capitalists maintain? Who will buy all the stuff their farms and factories produce? This logic convinced Karl Marx (1818-1883) that capitalism would necessarily fail. The proletariat (workers) would finally overthrow their capitalist masters, seize the means of production and establish a socialist state in which everything is communally owned.

Marx's vision of a utopian "workers' paradise" inspired a series of communist revolutions in the 20th century. Unfortunately, the conversion of farmland and factories to communal ownership and the imposition of central planning in place of free markets involved huge social costs. In China, about 40 million people were killed or starved to death during Mao Zedong's "Great Leap Forward" and "Cultural Revolution." In the Soviet Union, Stalin's political purges, engineered famines, forced migrations and labor camps cost about 30 million lives. These guys rank #1 and #2 as the 20th century's top mass murderers; Hitler ranks #3. In Cambodia, Pol Pot killed about 21% of his fellow citizens between 1976 and 1979 with his "agrarian socialism" program. These are the human costs of the failed ideas of "some defunct economist."

The Ricardian concept of a resource rent is fundamental to the economic models we will study that predict how competitive markets allocate resources through time. The marginal rent earned on a unit of resource is the difference between its market price and the marginal cost of getting it to market. Since the market price reflects the scarcity of the resource, the marginal rent does too. In fact resource rents are sometimes called "scarcity rents." The marginal resource rent is equivalent to a marginal profit or resource investment value. As the resource gets scarcer, marginal rent rises in line with price, which is what investment values are supposed to do.

The flip-side equivalent of marginal rent is the marginal opportunity cost of not using the resource in its next-best use or in the next-best time period. This is why resource rents are sometimes referred to as "marginal user costs."