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The Simon-Ehrlich bet: teaching relative vs. absolute scarcity.

I. Introduction

For undergraduate and graduate students, some with at best an introduction to economics course and/or coming from noneconomic disciplines, a common misunderstanding of economics has to do with relative versus absolute scarcity (for example, see Gowdy et al. 2010). The academic explanation of relative versus absolute scarcity is often perceived as insufficient as the physical limits of renewable and nonrenewable resources seem all too real. The definition of relative scarcity is built on the concept of alternative uses in the production and consumption of resources. An individual's choice of using a resource in a particular manner or at a particular time implies giving up its use in some other activity or substituting an alternative resource in its place (Pearce 1994). The definition of absolute scarcity is built on the concept of physical limits and the inability to substitute other resources for production or consumption. Therefore, it does not require any alternative use or opportunity cost and it is adequate to have a situation in which just a single use is greater than the available resource (Daoud 2010; Gowdy et al. 2010).

Historically, the conflict between absolute versus relative scarcity is illustrated by comparing Thomas Malthus (1826)--most students are familiar with Malthus--with his contemporary David Ricardo (1821)--most students are not familiar with Ricardo. (1) Malthusian scarcity is based on the physical limits associated with natural resources, while Ricardian scarcity is based on the idea that natural resources decrease in quality. That is, higher quality resources are used first while lower quality resources require using additional inputs, and there is the ability to substitute among alternative factors of production. Malthusian scarcity and a simple stock divided by flow model seems intuitively consistent with these students' economic worldview. Consequently, they are sure that the earth is running out of resources. However, they have not analyzed their conclusion critically.

Malthus and Ricardo set the historical context for this ongoing debate; a more contemporary illustration of this and the focus of this paper is "The Bet." This bet occurred between Paul Ehrlich (1968) and Julian Simon (1981) concerning changes in the real prices of five minerals between 1980 and 1990. Ehrlich, a neo-Malthusian, predicted the social and economic catastrophe that would result due to the physical limits of renewable and nonrenewable natural resources given an increasing population. Simon was less pessimistic; as the market price of natural resources increased, reflecting increased scarcity, individuals would find substitutes, increase production and consumption efficiencies, and recycling to mitigate these scarcities. Simon challenged Ehrlich to put his money where his mouth was. If market price is a measure of scarcity, then absolute scarcity and a stock divided by flow economic worldview would imply increasing prices for resources over time. The Ehrlich team (2) chose five metals--chromium, copper, nickel, tin, and tungsten--in 1980 predicting that their (real) prices would increase over a 10-year period reflecting increasing absolute scarcity. In fact, the real prices of all five metals went down in real terms: Ehrlich paid Simon $576.70 and went on to win a MacArthur Genius award.

As described by Joerding (2010), Brooks et al. (2010), and Hmelo-Silver (2004) there is considerable evidence that students who explain and defend their ideas obtain a deep and long-lasting understanding of new material. The key features of the pedagogy we describe are student derived problem statements (not a contrived problem), developing a hypothesis based on their problem statement, developing an analytical approach to test their hypothesis, gathering data, testing their hypothesis, and sharing and defending their conclusions with other students. In short, students have an incentive to take ownership of their learning.

Building on this structure, the following applied analytical approach--based on applied and problem learning pedagogies--can be used to allow students to "Bet" on their economic worldview. This approach is comprised of three components. The first is our Bet. We replicate the Simon-Ehrlich Bet with the students taking the Ehrlich position--the real prices of minerals has increased due to absolute scarcity that is consistent with their world economic view. (3) The Bet: we will buy one (1) carbon offset (1 metric ton of carbon) for every mineral that they show to be economically scarce, based on the indicators described in the assignment and up to a predefined budget. Over the counter carbon offsets can be purchased easily from http://www.terrapass.com/ retrieved on November 8, 2012 or http://www .nativeenergy.com/ retrieved on November 8, 2012. This bet requires the students to develop a testable cause and effect relationship--a hypothesis--based on their economic worldview.

The second component is a directed discussion that provides students with an applied analytical model to determine who wins the Bet, or to analyze critically their worldview hypothesis. The third component is an assignment requiring students to test their hypothesis by evaluating the scarcity of a specific mineral based on the applied analytical model in a written report, an oral presentation of their results, and critically reflecting on theirs and others' findings. Developing a testable cause and effect relationship based on their economic worldview then collecting empirical data to test their hypothesis is novel for these students. This applied analytical approach gives students the responsibility for their own learning and provides many avenues for them to develop and find answers to further questions: As relative scarcity is the reason for being of economics, does this imply that absolute scarcity can be ignored? Does this also imply that absolute scarcity is not reflected in the necessary condition describing the economically optimal allocation of resources or market price? What is the role of markets in determining market price? With these students, it is the testing of their economic worldview hypothesis, discovery, and critical reflections that are crucial.

II. Directed Discussion--Developing an analytical tool to determine who wins the Bet

The directed discussion is used to set up an applied analytical model that the students can use when thinking about absolute versus relative scarcity, testing their hypothesis, and, more importantly, determining who wins the Bet. The purpose of this discussion is not to build a detailed narrative, nor have us test their hypothesis for them using sophisticated economic models and econometric methods, nor have us explain the variation on observed market price and consumption overtime. Rather, we provide an outline that can be tailored to develop an appropriate narrative for the students so that they can test their hypothesis empirically. Our discussion here will use endnotes to highlight some areas that can be brought in to develop further narratives, depending on the students' interest and level of analytical sophistication.

We use copper to illustrate the applied analytical model. Copper is an example of a nonrenewable natural resource. It is used in building construction, power generation and transmission, electronic product manufacturing, and the production of industrial machinery and transportation vehicles. Copper wiring and plumbing are integral to appliances, heating and cooling systems, and telecommunications links used in homes and businesses. Copper is an essential component in motors, wiring, radiators, connectors, brakes, and bearings used in cars and trucks. Figure 1 gives price-quantity relationships for copper from 1900 to 2010 (http://minerals.usgs .gov/ds/2005/140/ retrieved on October 4, 2012). Examining Figure 1 shows that the axes are world copper production and real price of the extracted resource. This graph does not illustrate a market per se but a sequential series of market equilibrium prices and quantities through time.

Figure 2 illustrates the market equilibriums of two periods. The market equilibrium price in time t + 1 is the result of movements along and/or shifts in the supply and demand curves. What could have caused the supply curve to shift?--Increases in found reserves or changes in extraction technology. For example, the development of the solvent extraction-electrowinning method for refining copper ore reduces costs greatly by eliminating smelting and refining, and this allows the economical use of much lower grade copper ore, including material that was left behind by previous mining operations (Krautkraemer 2005).

What could have caused the demand curve to shift?--Recycling of and substitutes for copper. For example, copper can be continually recycled without any loss of quality (chemical or physical properties) which makes copper very recyclable. As the real market price of copper increases relative to several other minerals, firms will substitute for copper in production and consumption. Aluminum substitutes for copper in power cables, electrical equipment, automobile radiators, and cooling and refrigeration tube; titanium and steel are used in heat exchangers; plastics substitute for copper in water pipe, drain pipe, and plumbing fixtures; and fiber optics substitutes for copper in some telecommunications applications. For example, Goeller and Weinberg (1978) illustrated the importance of the availability of substitutes in their article entitled: "The Age of Substitutability." (4) This illustrates how markets and market price respond to changes in information. (5)

These movements along and/or shifts in the supply and demand curves are reflected in the market equilibrium prices and quantities illustrated in Figures 1 and 2. This draws directly from beginning microeconomics and the causes for movements and/or shifts in the supply and demand curves. However, the question remains: Is copper scarce? Given the economic definition of price, the real market price of copper reflects its relative scarcity. Copper is relatively scarce as the real market price of copper is positive (Figure 1). But, copper is also absolutely scarce and reserves are decreasing in quality. Does this market price (Figures 1 and 2) reflect physical scarcity and declining quality? Does its optimal use (Figures 1 and 2) reflect physical scarcity and declining quality? If the earth is running out of resources (absolute scarcity), then the real price of resources (e.g., copper) should be increasing as described by Malthus and Ehrlich. How can scarcity be modeled?

Fisher (1979) states that the ideal measure of scarcity has "just one essential property: It should summarize the sacrifices, direct and indirect, made to obtain a unit of the resource." Given that individuals are wealth maximizers, economic theory presents the following result with respect to optimal resource use given a market described by competition: (6)

MR = P = MC (1a)

MRP = P x MP = MFC (1b)

where MR denotes marginal revenue, P denotes market price, MC denotes marginal cost (i.e., production costs with respect to output), MRP denotes marginal revenue product, MP denotes marginal product, and MFC denotes marginal factor cost (i.e., production costs with respect to input). (7) The optimal use rule consistent with market price (equations (1a) and (1b)) describes a resource with no physical limits and non-decreasing quality. However, an optimal use rule can be derived that is constrained by absolute scarcity and decreasing quality thus incorporating the students' Malthusian concerns. (8) As illustrated by Hall and Hall (1984), the optimal use rule taking into account absolute scarcity and decreasing quality given a market described by competition is a combination of (9)

* Production costs (MC)

* Stock Effect (SE)--accounting for the additional costs associated with extracting a resource of decreasing quality (10)

* Scarcity Rent (SR)--accounting for the additional costs of extracting an absolutely scarce resource (11)

P = MC + SE + SR (2)

Figures 3 through 6 illustrate graphically how to interpret the impact of the absolute scarcity and decreasing quality constraints resulting in equation (2). Let Figure 3 represent the physical amount of copper available currently (i.e., reserves). If we extract more copper now there will be less in situ copper in the future, due to its finite limit or absolute scarcity, so that the stock of the situ resource copper will be reduced. In addition, if the reserves are characterized by decreasing quality, then as the in situ resource is reduced so too is its quality. The physical effect on future conditions of natural resource availability caused by today's resource extraction is called Stock Effect. The increasing extraction costs in the future are due to decreasing quality combined with cumulative amount of the resource extracted relative to the existing reserves available. SE denotes the present value in perpetuity of the increase in extraction costs at time t multiplied by the amount extracted at time t. SE is illustrated by the movement to the dashed line in Figure 4. SE clearly connects the decisions made in one period with the production potentials of following periods: the more in situ resources used today ceteris paribus, the higher will be tomorrow's recovery costs (Howe 1979, Hall and Hall 1984).

Again, given absolute scarcity, extracting more copper now implies less in situ copper in the future; namely, the stock of the in situ resource will be reduced. What is the cost of extracting the additional unit, extensive margin, or the "just producible" marginal unit of copper today versus next year or in any of the following years? That unit of copper extracted today will simply not be available for use in future periods. Scarcity Rent is the opportunity cost of producing the last unit of a resource in this period and is the discounted value of that unit of the resource sold in the next and all future periods (Hotelling 1931, Howe 1979, Hall and Hall 1984). SR is illustrated by Figure 5 as the cost of the last or "just producible" unit being extracted at any time t and, under appropriate market conditions, the market value of the marginal in situ resource (Howe 1979, 79).

If P > MC on the marginal unit then SE + SR > 0 and the market price would reflect absolute scarcity and/or decreasing resource quality (Hall and Hall 1984). Thus, a resource's market price captures changes in the components in the right-hand side of equation (2). Figure 6 illustrates this graphically. In addition, Figure 6 also can be used to illustrate the impacts on market price of discovering new reserves, new extraction and production use technology, availability of substitutes, and recycling on stock effect and scarcity rent. For example, discovery of new reserves, availability of substitutes, and recycling would reduce the scarcity rent and more efficient extraction technology would reduce the stock effect. These are mimicked in shifts in and/or movements of the supply and demand curves and the resulting market price as given in Figures 1 and 2.

III. The Student Assignment--Settling the Bet

The Bet tests whether the real price of minerals has increased due to absolute scarcity, which is consistent with the students' world economic view. Is this view of absolute scarcity consistent with market data? Alternatively, do these data better reflect Simon's optimism about markets? The students are required to examine the scarcity of one of the following resources:

Antimony      Bauxite      Clay        Helium
Cement        Chromium     Graphite    Manganese
Copper        Gold         Lithium     Silicon
Iron Ore      Lead         Platinum    Tin
Molybdenum    Nickel       Sulfur
Silver        Strontium    Cadmium
Vermiculite   Zinc         Cobalt


They each write a two-page, single-spaced typed report presenting and evaluating evidence indicating whether or not the resource has become "economically" scarcer worldwide over time. They do this by considering the following indicators, based on the components of the optimal use rule given by equation (2) and illustrated in Figure 6:

* Average world (real) price and factors affecting price

* World proven and estimated reserves

* World stocks of recycled material, if applicable

* World consumption (utilization)

* Existence and availability of substitutes

plus any other considerations they believe to be relevant. They must assess a time-period long enough to distinguish long run trends; at least from 1960 (if not earlier) to the present. (12) The assessment should include evidence which the student finds most compelling and why, plus any evidence that contradicts their assessment. Graphs and accompanying interpretations of real price vs. time, real price vs. world production or consumption over time, world production or consumption vs. time, and, if possible, stocks vs. time must be part of the report and presentation, although not part of the two pages of discussion.

The following sources provide much of the relevant data

* Mineral Commodity Summaries (http://minerals .usgs.gov/minerals/pubs/mcs/)

* Minerals Yearbook (http://minerals.usgs.gov/ minerals/pubs/myb.html)

* Metals prices 1998 (http://minerals.usgs.gov/ minerals/pubs/metal_prices/)

* Historical Statistics for Mineral and Material Commodities in the United States (http://minerals .usgs.gov/ds/2005/140/)

In addition to the report, students give a 3 to 5 minute presentation with accompanying PowerPoint slides evaluating whether their resource is indeed "scarce." In this way, they are able to evaluate the implications of a whole range of factors and resources.

IV. Learning Outcomes--Who wins the Bet

There are four learning outcomes. First, students test their world economic view hypothesis and determine who wins the Bet by examining what has happened to the real price of their selected resource. The sophistication of the test depends on the student and can range from a simple comparison of starting and ending prices to various types of econometric models. Our role is not to do the analysis for them but to provide guidance. With a few exceptions, the general conclusion that the class reaches is that these resources do not reflect scarcity as described by Malthus and Ehrlich. (13) Based on United States Geological Survey data, the real price of most of the minerals have not increased over time and for those that did world production also increased. In the end, we still buy carbon credits for the class.

Second, markets matter. By incorporating the availability of substitutes, changes in technology, recycling, current flows from existing reserves, and discovery of new reserves into equilibrium market price and quantity, prices have moderated over time. It is not displaying or mathematically deriving the optimal use rule given by equation (2), nor using simple to complex econometric models that show this. Rather, having the students interpret equation (2) economically (as illustrated by the conceptual model given in Figure 6 and the price-quantity relationships given in Figures 1 and 2) with respect to their chosen resource that is a primary outcome of this pedagogical example. This interpretation is a crucial part of determining who wins the Bet--testing their hypothesis--and is included in their written report and oral presentations.

Third, market prices rise and fall in the short term, but it is the long term that illustrates how markets respond to changes in substitutes, recycling, technology, and discovery. As illustrated by Figure I, if Ehrlich and Simon had picked a different decade the outcome of their Bet could have been different, as could the outcome of our students' Bet. For more sophisticated students, these dramatic price variations make for interesting econometric modeling questions. However, it is each student interpreting how markets reflect perceived scarcity relative to the conceptual model that is important in testing their hypothesis and settling who wins the Bet. This is a critical part of the written report and presentation.

Fourth, students reflect critically on the conclusions reached through the process of formulating their hypotheses; developing analytical models; gathering data and testing their hypotheses; and interpreting and presenting their results. This critical reflection begins with summarizing their major findings and the commonalities in terms of their analysis and conclusions; namely, the impact of substitutes, recycling, and changes in technology on markets and the resulting equilibrium price and quantity. The students now think differently about the role of markets, how markets respond to changes in information, and that physical measures and models of scarcity (e.g., Hubbert 1956, Ehrlich 1968, Meadows et al. 1972, and Gowdy et al. 2010) do not adequately reflect the perceived scarcity of resources. Purely physical measures of output ignore the fact that individuals assign values to outputs. The students not only think about scarcity and their perception of scarcity differently but also are more critical of their and others Malthusian economic worldview for a variety of reasons. In addition, they also have a systematic approach to analyzing similar issues.

The students' presentations of their conclusions and the short question and answer period following their presentations plus a debriefing done at the completion of all the presentations allow us to address three common oversights students make. The first common oversight is that while the "Bet" focuses on price, students often forget to think about the quantity responses to these changing prices. The second is the importance of identifying and highlighting the role of substitutes, recycling, and changes in production/consumption technology have on the market equilibriums. The final is the impact of governmental interventions on the market equilibrium prices through regulations and creating artificial scarcities.

V. Conclusions

We described a pedagogical model--applied analytical approach--using "The Bet" between Paul Ehrlich and Julian Simon as its focus to discuss absolute versus relative scarcity. The model includes a "Bet"--the students taking the Ehrlich position; a directed discussion providing students with an approach to determine who wins the Bet; and a written assignment and oral presentations. The learning outcomes are: 1) students examine their Malthusian beliefs through developing hypotheses, analyzing and testing them, and writing and presenting their conclusions orally; 2) that market's incorporate changes in substitutes, technology, recycling, and discovery; 3) that market prices rise and fall in the short term but it is the long term that illustrates how markets respond to changes in information; and 4) students reflect critically on their initial absolute scarcity assertion.

Following his loss of The Bet, Ehrlich proposed a second bet that he felt would be more appropriate to get at the impact of scarcity. The metrics that comprised the second bet were those that defined the human condition, not those related to markets (i.e., the real prices of the five minerals) of the prior bet. These metrics included

* The three years 2002-2004 will on average be warmer than 1992-1994.

* There will be more carbon dioxide in the atmosphere in 2004 than in 1994.

* There will be more nitrous oxide in the atmosphere in 2004 than 1994.

* The concentration of ozone in the lower atmosphere (the troposphere) will be greater than in 1994.

* Emissions of the air pollutant sulfur dioxide in Asia will be significantly greater in 2004 than in 1994.

* There will be less fertile cropland per person in 2004 than in 1994.

* There will be less agricultural soil per person in 2004 than 1994.

* There will be on average less rice and wheat grown per person in 2002-2004 than in 1992-1994.

* In developing nations there will be less firewood available per person in 2004 than in 1994.

* The remaining area of virgin tropical moist forests will be significantly smaller in 2004 than in 1994.

* The oceanic fisheries harvest per person will continue its downward trend and thus in 2004 will be smaller than in 1994.

* There will be fewer plant and animal species still extant in 2004 than in 1994.

* More people will die of AIDS in 2004 than in 1994.

* Between 1994 and 2004, sperm cell counts of human males will continue to decline and reproductive disorders will continue to increase.

* The gap in wealth between the richest 10% of humanity and the poorest 10% will be greater in 2004 than in 1994.

Market prices are a measure of relative scarcity for market goods and respond to changes in perceived scarcity of that good, ceteris paribus. The non-market metrics as those described by the second bet have neither corresponding markets nor market prices to illustrate perceived scarcity or resource allocation changes to perceived scarcity. For these reasons, Simon did not take this bet nor do we make a similar Bet.

References

Barnett, H. 1979. Scarcity and Growth Revisited. In V. Kerry Smith, ed., Scarcity and Growth Reconsidered. Baltimore, MD: The Johns Hopkins University Press for Resources for the Future.

Barnett, H. and C. Morse. 1963. Scarcity and Growth: The Economics of Natural Resource Availability. Baltimore, MD: Johns Hopkins University Press for Resources for the Future.

Baumgartner, S., C. Becker, M. Faber, and R. Manstetten. 2006. Relative and Absolute Scarcity of Nature. Assessing the Roles of Economics and Ecology for Biodiversity Conservation. Ecological Economics. 59:487-198.

Brooks, E., C.R. Harris, and P.H. Clayton. 2010. Deepening Applied Learning: An Enhanced Case Study Approach Using Critical Reflection. Journal of Applied Learning in Higher Education. 2:55-76.

Daoud, A. 2010. Robbins and Malthus on Scarcity, Abundance, and Sufficiency: The Missing Sociocultural Element. American Journal of Economics and Sociology. 69(4): 1206-1229.

Ehrlich, P.R. 1968. The Population Bomb. New York, NY: Ballantine Books.

Fisher, A.C. 1979. Measures of natural resource scarcity. In V. K. Smith, ed. Scarcity and Growth Reconsidered. Baltimore, MD: Johns Hopkins Univ. Press.

Foreman, E.A. 1987. Absolute versus Relative Worth. Mathematical Modelling. 9(3-5): 195-202.

Goeller, H.E. and A.M. Weinberg. 1978. The Age of Substitutability. The American Economic Review. 68(6): 1-11.

Gowdy, J., C. Hall, K. Klitgaard, and L. Krall. 2010. What Every Conservation Biologist Should Know about Economic Theory. Conservation Biology. 24(6): 1440-1447.

Hall, D.C. and J.V. Hall. 1984. Concepts and Measures of Natural Resource Scarcity with a Summary of Recent Trends. Journal of Environmental Economics and Management. 11:363-379.

Hmelo-Silver, C.E. 2004. Problem-Based Learning: What and How Do Students Learn? Educational Psychology Review. 16(3):235-266.

Hotelling, H. 1931. The Economics of Exhaustible Resources. Journal of Political Economy. 39(2): 137-175.

Howe, C.H. 1979. Natural Resource Economics: issues, Analysis, and Policy. New York, NY: John Wiley & Sons.

Hubbert, M.K. 1956. Nuclear Energy and the Fossil Fuels. A paper presented before the Spring Meeting of the Southern District, American Petroleum Institute, Plaza Hotel, San Antonio, Texas, March 7-9, 1956. Retrieved on June 21, 2011 (http://www.hubbertpeak.com/hubbert/ 1956/1956.pdf).

Joerding, W. 2010. Teaching and Learning with Individually Unique Exercises. Journal of Economic Education. 41(2): 125-135.

Krautkraemer, J.A. 2005. Economics of Natural Resource Scarcity: The State of the Debate. Resources For the Future Discussion Paper 05-14. Retrieved on June 22, 2011 (http://www.rff.org/ documents/RFF-DP-05- 14.pdf).

Malthus, T.R. 1826. An Essay on the Principle of Population, or a View of Its Past and Present Effects on Human Happiness; with an Inquiry into Our Prospects Respecting the Future Removal or Mitigation of the Evils Which It Occasions. London, England: John Murray.

McKenzie, R.B., and Lee, D.R. 2006. Microeconomics for MBAs: The Economic Way of Thinking for Managers. New York, NY: Cambridge University Press.

Pearce, D.W., ed. 1994. The MIT Dictionary of Modern Economics, 4th ed. Cambridge, MA: The MIT Press,

Raiklin, E. and B. Uyar. 1996. On the relativity of the concepts of needs, wants, scarcity and opportunity cost. International Journal of Social Economics. 23(7):49-56.

Ricardo, D. 1821. On the Principles of Political Economy and Taxation, 3rd ed. London, England: John Murray. Retrieved on June 20, 2011 (http:// www.econlib.org/library/Ricardo/ricPCover.html).

Simon, J. 1981. The Ultimate Resource. Princeton, NY: Princeton University Press. Retrieved on October 18, 2011 (http://www.juliansimon.com/ writings/Ultimate_Resource/)

Simpson, R.D, M.A. Toman and R.U. Ayres. 2004. Scarcity and Growth in the New Millennium: Summary. Resources for the Future Discussion Paper 04-01. Retrieved on June 20, 2011 (http:// www.rff.org/rff/Documents/RFF-DP-04-01 .pdf).

Smith, V.K. ed., 1979. Scarcity and Growth Reconsidered. Baltimore, MD: The Johns Hopkins University Press for Resources for the Future.

Meadows, D.H., D.L. Meadows, J. Randers, and W.W. Behrens III. 1972. The Limits to Growth. A report for the Club of Rome's Project on the Predicament of Mankind. New York, NY: Universe Books.

Notes

(1.) The on-going discussion of relative vs. absolute scarcity is illustrated by the interactions between Thomas Malthus (1826) and David Ricardo (1821) and more recently by the works of Hubbert (1956), Barnett and Morse (1963), Ehrlich (1968), Meadows et al. (1972), Barnett (1979), Smith (1979), Simon (1981), Hall and Hall (1984), Foreman (1987), Raiklin and Uyar (1996), Simpson et al. (2004), Krautkraemer (2005), Baumgartner et al. (2006), Daoud (2010), and Gowdy et al. (2010). This is not meant to be an encompassing literature review, but an illustrative select sample.

(2.) Along with John Holdren and John Harte.

(3.) While we do not require the students to take the Ehrlich position, this is the usual Bet. In terms of the applied analytical approach pedagogy, which position the student takes does not matter, as they have to explain and defend their conclusions.

(4.) This article first appeared in Science in 1976 and was reprinted in 1978 in The American Economic Review. Interestingly, this article was first published four years before the Simon-Ehrlich bet. Goeller and Weinberg (1978) also included a discussion of an energy caveat in their analysis. However further development of this topic is beyond the purpose of this pedagogical example, it does however, illustrate how this narrative can be modified to lead into a discussion of the economics of energy.

(5.) The erroneous conclusion reached by Gowdy et al. (2010) is that the perceived inability to substitute among inputs at some point far into the future extensive margin implies an inability to substitute at any point in time and that production systems are static not dynamic. This provides an additional discussion point.

(6.) Due to space limitations we have omitted a discussion of developing the optimal allocation rule given in equations (1a) and (1b) and the misunderstood concept of rational behavior (see Gowdy et al. (2010) for an illustration of this misunderstanding and McKenzie and Lee (2006:108-109) for a concise discussion of rational behavior).

(7.) The optimal use rule described in equations (1a) and (1b) and subsequently in equation (2) is derived from perfect competition. Different market structures (i.e., monopoly) will provide a different optimal use rule. A more detailed description of these implications provides an avenue for further discussion depending on the students.

(8.) The students' backgrounds will dictate how the mathematics of present value calculations, constrained optimization, and the calculus of variations are described.

(9.) The model has been also described as P = MC + UC where UC denotes user cost (Krautkraemer 2005)

(10.) Mathematically, stock effect is the result of a total available resource stock constraint and the increasing average cost of extraction depends on the rate of extraction (Hall and Hall 1984). The stock effect is the present value of these increased extraction costs. Howe (1979) identifies the increasing extraction costs as the opportunity cost of extraction that also includes the loss of environmental services. This provides another avenue for discussion depending on the students.

(11.) Mathematically, scarcity rent is the shadow price of the physical stock constraint given that a market equilibrium is defined as maximizing the sum of producer and consumer surplus. Scarcity Rent is a specific type of user cost; namely, the opportunity cost of producing the last unit of a resource in this period is the discounted value of the resource sold in the next and all future periods. This result is called the Hotelling Rule (Hotelling 1931). A user cost is the present value of all future sacrifices (including foregone use, higher extraction costs, and increased environmental costs) associated with the use of a particular unit of an in situ resource. It also includes any contribution of the resource stock itself to the net benefit of extraction--for example, a more abundant resource stock may decrease extraction or harvest cost (Krautkraemer 2005:12-13).

(12.) Prices do fluctuate in the short term as illustrated by Figure 1. Thus the period selected must be long enough to not be biased by any single short-term variation.

(13.) One exception is Helium. Again, this provides another avenue for discussing the impacts of various political and institutional forces on markets.

by John E. Wagner * and David H. Newman **

* State University of New York--College of Environmental Science and Forestry, 1 Forestry Drive, Syracuse, NY 13210, E-mail: jewagner@esf.edu

** State University of New York--College of Environmental Science and Forestry, 1 Forestry Drive, Syracuse, NY 13210, E-mail: dnewman@esf.edu
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Author:Wagner, John E.; Newman, David H.
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Date:Mar 22, 2013
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