HOTELLING'S LAW: IS IT USEFUL OR WASTEFUL? Julian L. Simon INTRODUCTION In their fifty-year retrospective, Devarajan and Fisher (1981) noted that Hotelling's famous 1931 article on exhaustible resources is unusual in being the sole origin of an entire formal "field" of economics. And after half a century, the literature it spawned appears at an ever more rapid pace (e. g. Farzin, 1984; Miller and Upton; Romer and Sasaki, 1985). It is even more notable that such a body of work exists at all, however, let alone flourishes. Hotelling's analysis has no descriptive or prescriptive power, because it is founded on a contrary-to-fact assumption -- that the price of the supposedly- exhaustible resource will rise secularly (p. 140). The fact that all natural resources have fallen rather than risen in price throughout history is inconsistent with Hotelling's starting- point assumption - that the "indefinite maintenance of a steady rate of production is a physical impossibility". Hence that proposition is out of place even if it is not without meaning. (In Simon, 1981, Chapter 1, I argue that it is indeed without meaning.) Hotelling's Rule is not merely irrelevant for decision- making and for the understanding of decision-making; if that were so, it could be appreciated for its charm, and an attack upon it might decently be dismissed as bad form or lack of an aesthetic sense. But to the extent that it affects decision-makers, Hotelling's Rule is perverse, and imposes a cost because it is misleading. Furthermore, Hotelling's Rule wastes the time of economists who could be devoting themselves to more profitable activities, because it focuses them upon an analysis which leads to wrong conclusions for all known situations. If valid, this is no small criticism, I trust. I belabor the point because of a tendency to justify formal analyses if they are "interesting" even if they are without reference to any conceivable actual situation.1 Hotelling's Rule may help illuminate a very different sort of situation than that about which he was writing, embargoed goods whether or not of an "exhaustible" natural resource, e. g. Bergstrom, Loury, and Persson (1985, and references therein), who arrive at solutions that may be viewed as special cases of Hotelling's Rule. But if such solutions might just as well be arrived at without reference to Hotelling's analysis, these studies of embargoes would seem to be scant justification for continued interest in Hotelling's Rule. Everything said here has been noted by others, but in passing. What is new is a blunt rejection of Hotelling's Rule, and complete dismissal of the body of work built on it. (That there is not general agreement with this assessment is shown by the continued appearance of articles based upon Hotelling's Rule, despite Barnett and Morse's great book [1963] which should have laid Hotelling's rule in its grave. That book is not even cited in the mainstream Devarajan-Fisher review.) HOTELLING'S NON-PROBLEM The flaw in Hotelling's analysis begins (and can end) with the title of his article, which refers to a "resource" that is "exhaustible". It is crucial to be clear on what we are talking about; to rush on to technical matters without such classification and agreement dooms the discussion. We must first agree, I believe, that the appropriate definition of "exhaustible" must be an "operational" or "working" definition along the lines of Einstein's definition of time, rather than a "property" definition along the lines of pre-Einsteinian definitions of time. (A discussion of these types of definitions may be found in many places. My own view may be found in Simon and Burstein, 1985, Chapter 2, or in Simon, 1970). Exhaustible resources are frequently classified into "renewable" and "non-renewable". The latter type -- the subject of Hotelling's paper, and of the present discussion -- is defined by him as "an industry in which the indefinite maintenance of a steady rate of production is a physical impossibility, and which is therefore bound to decline" (p. 139). The term "exhaustible" has at least two different defini- tions in this context, one for a well owner and another for society. For the oil-well owner who was the subject of Hotelling's formal analysis -- though not the original source of his interest, which was (in his opening sentence) "the world's disappearing supplies of...exhaustible assets" - Hotelling's definition in the paragraph above is quite appropriate. In the context of the well owner, the term "exhaustible" means that if pumping continues at a constant rate per period, there will come a time when (with the technology that is assumed fixed) no more oil will appear at the surface, or that it will appear in sufficiently small quantities that the value will be below the cost of production. (Oil is the strongest case for Hotelling because, unlike such resources as copper, oil is burned up and energy cannot be completely recycled.) The physical (in contrast to economic) nature of this definition causes no difficulty here because the depletion discussed in the definition is within the well owner's control and is reasonably knowable with standard geological-engineering techniques. For a society, however, or for humanity taken together, a physical definition of "exhaustible" is not helpful because there is no generic commodity -- including oil -- that demonstrably cannot be produced at a constant or increasing rate indefinitely. Oil -- that is, a commodity that is viscous and burns -- can be produced by growing plants, and hence is proximately limited only by the life of the sun. Georgescu-Roegen (and following him, Daly, and much of the environmental movement's writings) would like us to allocate our energy resources taking into account that eventual demise of the sun, and in their review, Peterson and Fisher (1977) say "The physical concept of entropy, as described by Nicholas Georgescu-Roegen 1971) is relevant here" (p. 692). But I hope that the reader will agree that such matters as the sun's lifetime, the possibility of other suns, whether or not the cosmos is or is not expanding, and so on, are not part of reasonable thinking here. If one agrees that a physical definition of "exhaustible" will not serve, it is reasonable (and it probably would be preferable even if a satisfactory physical definition were available) to turn to an economic definition. An appropriate working definition would seem to be: a natural resource whose cost or price3 will rise with time as increments of the resource are used. The question whether cost (price) will indeed rise is crucial in both a) the context of society at large, because it defines "exhaustible", and b) in the private firm's context, because expected price is the fundamental datum in the well owner's decision-making. THE TREND OF NATURAL RESOURCE PRICES Hotelling is very clear that he bases his analysis on the assumption that price will rise. "[I]t is not unreasonable to expect that the price p will be a function of time of the form p=poegt" (p. 140). But given all historical evidence price should be expected to fall, not rise. Let us briefly review the evidence showing that the long term course of raw materials is indeed downwards. The basic source is Barnett and Morse (1963) together with the Resources for the Future series covering 1870-1957 which they analyzed. Their work, together with my analysis of individual resource prices in the United States from 1800 to 1976 (the period covered by Historical Statistics of the United States), plus scraps of evidence covering various commodities such as copper back to 1800 B. C., shows that over the entire span of recorded history, the prices of all exhaustible raw materials (excluding industrial diamonds, for which I have not found data, and excluding also those resources such as gold which are used as stores of value) have been constant or have declined relative to consumer goods, as shown in the typical Figure 1.2 A vivid demonstration of the disastrous outcome of following Hotelling's Rule is given by Anders, Gramm, Maurice, and Smithson (1980, Table 10.2), where they compare the actual prices of various "depletable resources" in 1975 to the implied prices if the resources had been bought in 1900 and the buyers had received a reasonable return on their investments (considering a wide variety of rates of return). It is very clear that holding stocks of minerals starting in 1900 (or in 1800 or any other year) would have been an atrocious investment under any conceivable assumptions. Figure 1 There has recently been discussion of alternative measures of natural resource scarcity (e. g. Brown and Field, 1978) and Halvorsen and Smith (1984), but no proposed measure alters the basic conclusion that the trend in prices is downward. From the standpoint of human welfare as well as economic development, the trend in resource prices relative to the price of the most important good -- human time -- is even more important than relative to consumer goods. And the downward trend in resource prices relative to wages is even more marked than relative to consumer prices, especially in the advanced countries but also in poorer countries, as typical Figure 2 shows. Figure 2 The question may be raised whether a price rise for some period of years or decades -- and there frequently are periods of increasing prices -- may not constitute grounds for the application of Hotelling's analysis even if the secular trend is down. Work by Smith (1979), Halvorsen and Smith (1984) covering the years 1956 to 1974 for the Canadian metal mining industry, and Miller and Upton (1985) covering U. S. oil and gas companies from the end of 1979 to the middle of 1981, illustrates analysis of trends using periods shorter -- in some cases, much shorter -- than the longest series available. This raises the difficult philosophical-statistical question about the appropriate length of series to use; one must balance a greater volume of information versus (typically) less accuracy as one proceeds further back in history. This seems clear: The number of incorrect forecasts based on too-short time series surely is much larger than the number of incorrect forecasts based on too-long time series or due to insufficient attention being paid to the most recent period. For the very shortest periods, the literature on random walks in security-price behavior would suggest that trend analysis of such periods is doomed to fail. And for the longest periods in the past, a forecast from one randomly-chosen date to another randomly-chosen date that price would fall would have had a far better-than-chance accuracy, which would seem to suggest that the longest secular trend should be the basis of a forecast, as long as that trend is monotonic (as resource prices are). This does not deal with the issue of whether there may be temporary trend reversals, a matter that calls for investigation of autocollinearity of adjusted series for raw materials. But even if one could predict upward price movements for a while based on past price movements, this would hardly seem a solid basis for one's thinking about Hotelling's Rule as a general matter, especially when such upward price movements may be expected to turn around sometime, based on the long secular trend. A related issue is whether the analysis is useful if the future may be expected to be different than the past, to wit, that past trends do not forecast future trends; as Peterson and Fisher put it: "[W]e have no guarantee that the behaviour of extractive resource costs and prices will be the same over the next hundred years as it has been over the last hundred -- indeed the work of Smith suggests that it may not" (p. 706). It is always logically possible that a long secular trend will change direction; The sun may not come up tomorrow. But if so, an explicit forecast of the change in direction is required. And if the forecast is other than the sort of environment assumed by Hotelling, which would lead to a smooth price rise of a particular form -- a forecast requiring much stronger assumptions than even a change in historical direction -- then the Hotelling analysis would not be useful; indicated instead would be a straightforward present-value analysis as with any other kind of investment or manufacturing operation. IMPLICATIONS FOR DECISION-MAKERS Hotelling's analysis has two implications, one for managerial decision-making and the other for forecasting the prices of raw materials. The form of the future price curve, which is the heart of the forecast, is of interest to us here only as input to the decision-making, to which we address ourselves. Consider the situation to which Hotelling first applied his analysis: the owner of a single mine in "free competition", i. e. a mine owner whose sales are assumed to be too small to have an effect upon market price; this is the appropriate assumption in every conceivable case. If the market price is expected to fall or even to remain constant, the owner obviously would have no use for Hotelling's Rule or even for dynamic programming; s/he would sell as much output as possible just as soon as possible, subject only to the qualification of increasing production cost in the short run due to heavier use of facilities. Next, consider a mine owner who has sufficient monopoly power so that his/her sales affect the market price; Saudi Arabia as a whole might be such a case. If price is on a long-term decline which may be expected to continue in the future no matter what the owner's output decisions, then the optimizing decision is to set each year's output independently of future output decisions, as a first approximation. Or as a second approximation, a dynamic program embodying the effects of current sales on future price would yield an optimum set of price decisions for future periods. But in neither case would Hotelling's Rule be appropriate, given that prices are expected to fall. THEORETICAL EXPLANATION One reason that Hotelling's Rule has reigned so supreme may be the absence up to now of a well-developed competing theory of resource prices. "No viable alternative paradigm exists," say Miller and Upton (1985, p. 24). But though a well-developed formal theory may not be available, the core ideas necessary for such a theory are at hand, and some formal analysis has begun to appear. There is every economic reason to expect an actual or impending increase in price to trigger additional search for new sources (e. g. new oil fields) and new substitutes (e. g. oil from coal), as Nef (1977), Barnett and Morse (1963), and Rosenberg (1973) have described. And given the difficulty of the discoverer capturing a large portion of the returns to the discovery, and given the long-livedness of knowledge, prices will reflect the new knowledge. Romer and Sasaki (1985) have set a model of endogenous technical advance in resource production into a competitive market situation, and shown that a competitive equilibrium exists. Here the resource is implicitly not finite in supply. Simon and Steinmann (forthcoming) have built a very-long-run model, using land as the resource example, showing how the price of the service (actually, the food that is produced) triggers a rise in the price of the resource, which then induces new discovery. The upshot of the model is that the price is lower in the long run if population growth or other pressure causes a run- up in the price in the short run, compared to no change in pressure ever being exerted upon demand. Even if the resource is considered finite, a more difficult scenario than the one offered here, a discovery process could lead to a long-run fall in price. Baumol (1986) has observed that the effect of a given change in knowledge depends upon the "stock" of the resource that is augmented by a change in knowledge. (The appropriate concept of resource stock need not be troublesome in a discussion as abstract as this one.) He then sketches such a system numerically and concludes that a drop in price indefinitely is feasible even if the stock asymptotically approaches zero. This notion could be a building block in a discovery-based formal theory of resource prices in which the outcome of the process will be a cost lower than if the scarcity had not increased or threatened. Perhaps when the process of problem-induced solutions is understood in more detail, and then formalized, the field will drift in that direction and away from Hotelling's Rule as the "canonical model for modern theorists to build on" (Devarajan and Fisher, 1981, p. 71). The analysis is much the same if it is intended for a country, even a dominant producer such as Saudi Arabia, or even a cartel with monopoly power such as OPEC. True, in the 1970's some countries planned (or at least they said they planned) their oil production on the assumption that price would rise high enough in the future so that it would be a good investment to hold some oil in the ground; if that really took place, the behavior probably was motivated by the same ill-informed forecasts of rising prices that emanated from the doomsayers and such agencies as the U. S. Department of Energy. But now the behavior of all oil-producing countries, and of OPEC as a whole, clearly fits the model of sellers who do not assume that price will be rising enough in the future to make it worthwhile to withhold any output, or even that it will rise at all. SUMMARY AND CONCLUSIONS Hotelling devised a theory for "the Economics of Exhaustible Resources". By "exhaustible" he meant a resource (say oil) whose "rate of production...is bound to decline" (1931, p.139) He therefore assumed that price will increase as production declines. He offered rational methods for both a well owner and for a public monopolist to proceed in the face of price increase. Throughout history, however, the prices of even supposedly- exhaustible natural resources have declined rather than increased. And there is meaningful theory which explains this phenomenon and suggests that this trend need not reverse. Hence it is not inevitable that there is such a thing as a resource whose rate of production is "bound to decline", the entity whose existence Hotelling had to assume; we need not even inquire into the existence of such an entity, because there is no case of a natural resource whose price has increased secularly. If price is not expected to increase, there is no need for a theory of how to handle price increase. Therefore Hotelling's theory, though fascinating and stimulating to much additional writing, is damaging for decision-makers and a costly waste of economists' time. By its very existence and prominence, moreover, it encourages countries and individuals to produce more slowly than would be most profitable for the resource owners as well as for the public at large; the OPEC cartel cited this idea as part of their planning in the 1970s. An individual well owner must plan for either a diminishing rate of production, or an increasing cost of extraction per unit, or both. The appropriate production plan will depend upon the dynamic cost function appropriate in the given situation. The particulars of such planning are beyond the scope of this paper, however, since they will not involve Hotelling's theory, whose fundamental assumption is an increased market price. One might conceivably translate Hotelling's theory into such a plan, but this would be only a tortuous device to resuscitate an exhausted idea. 5-42a natresources article0 9-13-0 page 1/article0 natresou/September 6, 1990 References Anders, Gerhard, W. Philip Gramm, S. Charles Maurice, and Charles W. Smithson, The Economics of Mineral Extraction (New York: Praeger, 1980). Barnett, Harold and Chandler Morse, Scarcity and Growth (Baltimore: Johns Hopkins, 1963). Baumol, William J., "On the Possibility of Continuing Expansion of Finite Resources", Kyklos, 39, Fasc. 2, 1986, 167- 179 Bergstrom, Clas, Glenn C. Loury, and Mats Persson, "Embargo Threats and the Management of Emergency Reserves", The Journal of Political Economy, 93, February, 1985, 26-42 Brown, Gardner M., Jr. and Barry C. Field, "Implications of Alternative Measures of Natural Resource Scarcity", The Journal of Political Economy, 86, no. 2 part 1, April, 1978, 229-243. Devarajan, Shantayan, and Anthony C. Fisher, "Hotelling's `Economics of Exhaustible Resources' Fifty Years Later", Journal of Economic Literature, XIX, March, 1981, 65-73. Farzin, Y. Hossein, "The Effect of the Discount Rate on Depletion of Exhaustible Natural Resources", The Journal of Political Economy, 92, October, 1984, pp. 841-851 Halvorsen, Robert and Tim R. Smith, "On Measuring Natural Resource Scarcity", The Journal of Political Economy, 92, October, 1984, 954-964. Hotelling, Harold, "the Economics of Exhaustible Resources", The Journal of Political Economy, 39, April, 1931, 137-175. Miller, Merton H., and Charles W. Upton, "A Test of the Hotelling Valuation Principle", The Journal of Political Economy, 93, February, 1985,pp. 1-25 Nef, John V., "An Early Energy Crisis and Its Consequences," Scientific American, May, 1977, pp. 140-151. Peterson, Frederic M. and Anthony C. Fisher, "The Exploitation of Extractive Resources: A Survey", The Economic Journal, 87, December, 1977, 687-721. Rosenberg, Nathan, "Innovative Responses to Materials Shortages," American Economic Review, 63, May 1973, pp. 111- 118. Romer, Paul M. and Hiroo Sasaki, "Monotonically Decreasing Natural Resource Prices Under Perfect Foresight", xerox, U. of Rochester, February, 1985 Simon, Julian L., "The Concept of Causality in Economics", Kyklos, Vol 23, Fasc. 2, 1970, 226-254. -----, The Ultimate Resource (Princeton: PUP, 1981). _____ and Paul Burstein, Basic Research Methods in Social Science , 3rd edition (New York: Random House, 1985). ----- and Gunter Steinmann, "Population Growth, Natural Resources, and the Long-run Standard of Living", in Julian L. Simon, The Economic Effects of Population Growth in LDCs (Princeton: PUP, 1990, forthcoming). Skidelsky, Robert, John Maynard Keynes: Hopes Betrayed 1883-1920 (New York: Viking, 1983). Smith, V. Kerry, ed., Scarcity and Growth Reconsidered (Baltimore: Johns Hopkins, 1979) page 2/article0 natresou/September 6, 1990 Footnotes 1Marshall admonished us that "we are not a liberty to...exercise ourselves on subtleties which lead nowhere" (quoted by Skidelsky, 1983, p. 40. 2The statement is also true for all important "renewable" natural resources such as food grains. The sole exception of lumber is explained by its transition from its early status as a nuisance to be gotten rid of by farm builders, to being an agricultural commodity. 3We may leave aside the specifics of which price or cost concept is relevant except to note that it is a real price deflated relative to consumer prices to yield a "business price" of the sort that would be relevant for business calculations. This is unlike a "welfare price" which would properly be considered relative to the price of human time. page 3/article0 natresou/September 6, 1990 HOTELLING'S RULE: A USELESS AND WASTEFUL IDEA Julian L. Simon Abstract Hotelling devised a theory for "the Economics of Exhaustible Resources". By "exhaustible" he meant a resource (say oil) whose "rate of production...is bound to decline" (1931, p.139) He therefore assumed that price will increase as production declines. He offered rational methods for both a well owner and for a public monopolist to proceed in the face of price increase. Throughout history, however, the prices of even supposedly- exhaustible natural resources have declined rather than increased. And there is meaningful theory which explains this phenomenon and suggests that this trend need not reverse. Hence it is not inevitable that there is such a thing as a resource whose rate of production is "bound to decline", the entity whose existence Hotelling had to assume; we need not even inquire into the existence of such an entity, because there is no case of a natural resource whose price has increased secularly. If price is not expected to increase, there is no need for a theory of how to handle price increase. Therefore Hotelling's theory, though fascinating and stimulating to much additional writing, is damaging for decision-makers and a costly waste of economists' time. By its very existence and prominence, moreover, it encourages countries and individuals to produce more slowly than would be most profitable for the resource owners as well as for the public at large; the OPEC cartel cited this idea as part of their planning in the 1970s. An individual well owner must plan for either a diminishing rate of production, or an increasing cost of extraction per unit, or both. The appropriate production plan will depend upon the dynamic cost function appropriate in the given situation. The particulars of such planning are beyond the scope of this paper, however, since they will not involve Hotelling's theory, whose fundamental assumption is an increased market price. One might conceivably translate Hotelling's theory into such a plan, but this would be only a tortuous device to resuscitate an exhausted idea. page 4/article0 natresou/September 6, 1990