The "bell-shaped" production curve of a non-recyclable mineral resource was described first by M. King Hubbert in 1956, and was used to correctly predict that the production of crude oil in the United States (Lower-48) would peak in 1970. It is reasonable to suppose that the worldwide production of crude oil will also follow a similar bell-curve, with much of the present debate focusing on when the peak will occur. It is anticipated that it will generate an epochal change deriving from a steep rise in prices.

The rise in prices at the peak is expected because of the switch from a market driven by production to one driven by supply. The Hubbert model, however, does not itself provide quantitative information on prices, and it is not possile to draw conclusions from individual country peaks because oil prices are set globally.

In order to obtain historical evidence for price trends, one needs to examine a case where a non-recyclable resource went through a complete Hubbert cycle worldwide. There are no previous examples of a mineral resource that has done so. In fact, crude oil may turn out to be the first, which incidentally may be one of the reasons why the concept of "peak oil" is so difficult for many people to grasp.

A resource does not need to be a mineral one to show a Hubbert curve. A biological resource which is produced (or "extracted") much faster than it is replaced may also follow a bell-curve. Historically, there have been several cases of terminally depleted biological resources. The whaling industry of the 19th Century is a good example, as already noted by Coleman (Non Renewable Resources, Oxford University Press, 4(1995) 273). The present note re-examines the whaling example with the specific objective of determining how the production peak affects prices, confirming that prices should rise after peak production.

Two species of whale: the Sperm whale and the Right whale, were hunted in the 19th Century, mainly for the oil obtainable from their fat, which was used as fuel for lamps. Whales were also hunted for so-called Whale Bone (or baleen), which was used for stiffening clothing.

The following figure summarizes the production and price data extracted from Starbuck's 1878 book (A. Starbuck, History of the American whale fishery, Seacaucus, N.J. 1878, reprinted 1989). Here, oil production is shown as the sum of the production of Sperm and Right whale oil. The indicated prices are the weighted average production of the two types of oil, corrected for inflation and translated into 2003 values, according to data by R. Sahr oregonstate.edu/dept/pol_sci/fac/sahr/sahr.htm)

From the figure, it is evident that the production of whale oil followed a bell-curve according to Hubbert's theory, modelled with a simple Gaussian curve, albeit showing strong oscillations. These data are in excellent agreement with the report on Right Whale abundance by Baker and Clapham (Trends in Ecology and Evolution Vol.19 No.7 July 2004), indicating that the fall in production after the peak was caused by depletion and not by the switching to different fuels. Indeed, "Rock oil" (or "coal oil") began to replace whale oil only in the 1860s, after the invention of the kerosene lamp by Michael Dietz in 1859. Despite the availability of kerosene, whale hunting continued well into the 1870s and 1880s, driving Sperm and Right whales to near extinction.

Turning attention to the price data, we may note first how expensive whale oil was in comparison with the crude oil that replaced it. Even at its lowest historical prices, in the 1820s, the least expensive type of oil (whale oil) was priced at more than $200 (2003$) a barrel (42 gallons). At its highest price level (1855) Sperm Whale oil sold at more than $35 (2003$) a gallon, namely almost $1500 (2003$) a barrel (!). This tells us something about how difficult it may be to substitute fossil fuels with "biofuels" (bio-ethanol, bio-diesel, or other). Without the support of fertilizers, irrigation, transportation, and agricultural machinery, which all depend on fossil fuels, biofuels would probably cost as much today as whale oil did in the 19th Century. It also shows what an incredible bonanza crude oil has been. When kerosene became first available in the 1860s, a barrel of crude oil sold for some $90 a barrel in to-day's money (data from www.wtrg.com). In the 1870-80s it had already fallen to values in the order of $20 (2003$) a barrel, comparable with modern prices. If hydrogen were to substitute gasoline today at the same price differential, it would have to cost no more than a few cents for the equivalent of a gallon. Needless to say, we aren't getting there any time soon.

Finally, we can derive insight into crude oil price trends from the figure. Whale oil prices started to increase approximately at the inflection point of the curve well and before the production peak,. An upward spike in prices took place a few years after the peak, being also detectable in the non-inflation corrected price data (see Coleman, ibid.). A somewhat surprising result is that the inflation corrected prices remained approximately constant after the peak despite the progressive depletion of whales.

In the case of crude oil, we can recognize an initial phase (up to 1971) of nearly constant prices. This phase was followed by an epoch of rising oscillation. If, as often claimed, we are close to the peak, and if the analogy with oil production holds, we may expect a further sharp increase in prices in the coming years, a trend that may, actually, have already started in 1999.

In his 1878 book, Alexander Starbuck cited several factors for the decline of production of the whale fisheries in times that for him were recent. He seems to have believed that it was not the extermination of the whales that caused the decline but, rather, the increase of the human population which led to "an increase in consumption beyond the power of the fishery to supply." But it was also clear to him that the cost and the length of voyages had increased beyond reasonable limits. He did cite "the scarcity and shyness of whales" as a problem, but he stops short of saying that the whale stock was depleted beyond recovery. Most likely, the concept of "extinction" was alien to him, as it was to most of his contemporaries.

Our perception problem with crude oil is equivalent to that of Starbuck, and indeed it is perhaps more severe. The concept of the terminal depletion of a mineral resource is alien to us, since there have been no worldwide precedents. In addition, we are apparently just near the midpoint on the production curve, so we still have to experience the peak, the associated price rise, and the decline. What the future has in store is uncertain: perhaps an energy equivalent of the "rock oil" of Starbuck's times will materialize in the near future. But if it does not materialise we will have to live with depletion and before long begin to see lamps going out.