The cake of oil

I will buy your gas tomorrow


Our world and society have changed in the two last centuries more than in the two last millennia. The innovations born at the Industrial Revolution have modified our way of living probably only comparable to the Neolithic Revolution, when humans leaved their nomads lives to settle in cozier places thanks to agriculture.

The turning point that motivated Industrial Revolution was to learn how to dominate heat for generating power and how to use this power. Moreover, the prior changes on the structure of the civil society allowed the raise of innovation and scientific research. The last four or five generations of humans have understood and modified the world more than the hundred generations before. The changes have been so profuse and fast that today we are still catching up.

Nevertheless, probably these changes would not have taken place so quickly without the tremendous energy provided by fossil fuels. As it is known, fossil fuels were formed by natural processes such as anaerobic decomposition of buried dead organisms. Millions of years ago, those organisms processed CO2 and water to create high-energy chemical compounds, through the mechanism of photosynthesis. Those compounds evolved over geological time till what they are today, sometimes exceeding 650 million years. In other words, they are sun energy stored and chemically processed long time ago.

Unfortunately, burning fossil fuels is not free. They have condemned our society to two big issues which are getting worse every day, little by little, and that will probably drive to catastrophic consequences. The first problem is that fossil fuels are not infinite. Despite reserves of fossil fuels are expanding along with new exploration and techniques, some day they will end. Forecasts say that we will have oil for one or two centuries but coal will last three or four centuries more, under current consumption. The second big problem is related to a combustion product, the CO2 (burning is actually reversing the formula that created fuels). That gas is probed to be responsible for the global warming effect. The consequences of the generalized increase of earth temperature are unknown and under discussion, but there is consensus in that it is not prudent to modify a complex system as a planet ecology. This problem is closer in time and there is great literature and possible solutions (sequestration, cap-and-trade, quotas, CDMs…) to avoid or mitigate it, despite no one of the solutions have achieved to be effective enough to solve the problem.

This paper is focused on the first problem, especially oil which is used mainly for transportation. The common response to the issue is related to fuels substitutes. As oil becomes scarce, its price will rise, and today expensive substitutes will be profitable then, addressing to a smooth transition (Simon, 1996). Despite that could be probably true, there are some authors (Meadows, 1972; Barbier, 2005) who warn that this transition can slow down economic growth and cause a miserable crisis for a long time. Nevertheless, our bad decisions today are definitely creating challenging issues for future generations. There is an important intergenerational externality here, which is causing sub-optimal economic decisions from a broad time point of view. There is not only a moral o ethic problem here; I believe that this is an economic problem that should be faced by any responsible social planner.

Our current human generation should not be the only owner of the earth gratitude in terms of resource availability. Similar to a free rider in a public bus, we are taking advantage of the world endowment of energy. In thermodynamic terms, out rate of entropy generation (that is order or energy degradation) is greater than the system order creation (mainly by the sun supply), addressing to a non-sustainable equilibrium.

In this paper, I will try to address this economic problem and pose solutions or elements to take into account to solve it. The ideal conclusion would be to answer the question How much I owe you for using oil today, so avoiding you from using tomorrow?

Intergenerational externalities as a particular case of the Tragedy of the Commons

From my point of view, the biggest problem of capitalism is that the system confuses value with price. The dogma is that the value of the goods is the price that any consumer is willing to pay for it. In other words, for things that does not have price or its price is zero, they have no value or they are useless. For instance, nobody would pay a penny for a can of pure air or for knowing that there is an animal similar to the elephant with a horn in the face. However, nobody would say that clean air or black rhinoceros (an animal about to extinct) are worthless. Worthless means that your utility (or satisfaction) is the same having or not the good. Obviously nobody can be equally happy with clean air than with contaminated, as well as, nobody could say that watching a rhinoceros in a zoo or TV cannot cause someone else´s satisfaction.

Nevertheless, under our current economic and social scheme, these things have not price, or it is very difficult to determine, because, actually, there is not a market for them. That end in economic problems, like depletion, abusing, scarcity or injustice. That is what is known in economics as externalities. The common definition for externalities is a cost or benefit that is not transmitted through prices in that it is incurred by a party who was not involved as either a buyer or seller of the goods or services causing the cost or benefit. Quantify externalities is the hard part and the challenge for our current economic model.

As it has been said, the root of the problem is to set the price for those goods that are not traded in a market. One common resulting issue is what is known as the Tragedy of the Commons, that can be summarized in the depletion of a shared resource by individuals, acting independently and rationally according to each one’s self-interest, despite their understanding that depleting the common resource is contrary to the group’s long-term best interests.

There are many examples of this problem. In the figure below, some examples have been plotted considering the time to suffer the issue and the time required to solve the issue, with the current technology and knowledge, approximately. Note that the scale is logarithmic and that some issues do not have possible solution (or the time to solve them is infinite).

Sustainability issues, time to solve vs time to occur

Moreover, two lines have been projected, marking the area of influence of each human generation, which, for developed countries, could be considered for simplicity around a century. The area between axis and dotted lines (<100 years) is the temporal limit when the acts of a generation can be seen and can be solved within itself. That is to say, issues in that area could be, in theory, easy to solve or avoid for rational consumers, since they personally can see the results of their actions.

That happens in real world. There are successful mechanisms and examples that have solved these issues. For instance, the Montreal Protocol for protect the ozone layer, the cap-and-trade program of EPA for SO2 emissions that provoke acid rain, or toll highways for reduce traffic. In general, problems that can be solved (or regenerated) in less than a century (under horizontal dotted line), can be solved setting up a quota. However, a quota is almost useless for nuclear waste or oil consumption, since the problem will occur sooner or later.

Another important factor is that the time to problem was under the limit when the current generation can suffer the issue or think that they are in charge to solve it (on the left of the vertical dotted line). In this case, it is feasible that different governments achieve an agreement to put a limit in the shared good or, at least, everyone agrees in that the problem does exist. There are still many advocates that doubt about the climate change or even the depletion of fossil fuels (for instance, John Skvarla, secretary of the Department of Environment and Natural Resources in North Carolina), as new reserves or methods (as fracking) are emerging. The common response is to rely on future innovation to get rid of the issue. It seems risky to trust in scientists that are not born yet, for clearing up problems that we have not been able to solve.

There is an ancient implicit psychological factor in all of this. Despite we usually take care of our children, it is very difficult to make decisions thinking in more than two or three generations. The uncertainty of our lives, tend to overvalue the present to the future, and that can represent a failure from the complete timeline view. Our capitalist economy follows this principle, and the rate is the inflation. Money today values more than tomorrow, or translating in goods, a gallon of gas today values more than tomorrow, so, for us, it is worthier to burn it today. But maybe, the demand and human needs of tomorrow are greater than today, so, actually, a gallon of gas could value much more in future than today. This is what happens with exhaustible resources. However, it can be difficult to ask an oil producer to not sell oil today and leave it to his great grandchildren to use it for making more profit.

This type of issues are called intergenerational externalities, that is, cost or benefits that are not transmitted through current prices and are assumed by future consumers. They are, in fact, a Tragedy of the Commons case when more than one human generation is involved.

Current and future generations have limited opportunities for trade or coordinate polices, and, moreover, it would be an asymmetrical negotiation, when the current generation has an advantageous position over the future ones. So, traditional solutions as Coase’s theorem, quotas or prohibitions are ineffective methods, as it can be seen in real world, where the problems on the upper-right corner remain unresolved.

The economics of exhaustible resources

The first economist who studied these issues in depth was Hotelling in 1931. As he stated in the first lines of his article, contemplation of the world’s disappearing supplies of minerals, forest and other exhaustible assets has led to demands for regulation of their exploitation. The feeling that these products are now too cheap for the good of future generations, that they are being selfishly exploited at too rapid rate, and that in consequence of their excessive cheapness they are being produced and consumed wastefully has given rise to the conservation movement. He studied the case from the producer point of view in different market cases as competition, monopoly or oligopoly. The concern, at that time, was to find the appropriate rate of extraction that maximize the ‘total utility’, since restricted exploitation could raise prices over benefiting producers, but excessive production could sink the prices and bankrupt producers. His conclusion is called the Hotelling’ rule: the most socially and economically profitable extraction path of a non-renewable resource is one along which the price of the resource, determined by the marginal net revenue from the sale of the resource, increases at the rate of interest. His work laid the foundation for further research in the field of non-renewable resource economics, and derived from the classic model called cake-eating economy.

Before the 1970s, serious attention was not given to Hotelling’s views regarding economics of exhaustible resources. Great Depression and World Wars recoveries were more impending issues. However, the oil crisis on 70s, and the work of Meadows and the Club of Rome, set off another period of intense public concern for natural resources.

The reality is not so simple as the Hotelling model, since, there are capital and/or technical change that can compensate for the decrease of the resource. That has been deeply studied by economist as Solow (1974), Stiglitz (1974) or Dasgupta and Heal (1974, 1979), who have cared about how to maintain growth in an economy based on exhaustible resources. Under different hypothesis, they conclude that an optimal path of extraction with a positive consumption exists if the discount rate is high enough. Then, the declining use of the resource is compensated for by capital accumulations. In simple words, if the yields of the capital investment (and technology development) are high enough to compensate the lost of the resource, then exhaust the resource would not badly affect the economy. Similar conclusions are posed using the maximum criterion or Rawls’s criterion: if the elasticity of output with respect to capital is greater than that of the resource used, then a sustainable positive level of consumption exists. That introduces the concept of efficiency, meaning that it could be sustainable if what you obtain by using a resource (for instance, a car moving) is greater than the value of that resource (oil) used.

Nevertheless, it is not clear what should be the sustainable discount rate in the case of oil, or what is the actual value obtained for using oil. So the solutions go from not using the resource at all (total conservationism or ‘dictatorship of the future’) to using it at a certain rate (‘dictatorship of the present’).

Moreover, these economic models do not cope with intergenerational equity or altruism questions; and they do not take into account the fact described in previous paragraphs, about the discrepancies between the today decision maker and the future affected. For that reason, the overlapping generations (OLG) framework have been used recently to address the problem. Different models and assumptions have been studied by Howarth (1991) o Gutierrez et al. (2003).

Another interesting example of sub-optimal economic allocation due to intergenerational externalities has been recently studied by Lazkano (2012), using the OLG model and regarding the positive externality of research and development in clean energies. In her work, it is demonstrated that as consumers do not care about the effect of capital accumulation on future pollution, their demand for clean technologies is not sufficiently high to offset the negative effect on the environment. Moreover, the economy’s transition from dirty to clean technologies, […], might not occur because of the insufficient demand for clean technologies. And as a result, when agents care little about the environment, environmental quality not only deteriorates but economic growth can be negative.

That represents a market failure. In the same way, not compensate future generations for consuming an exhaustible resource implies that the current demand of oil can be greater than the optimal and the oil price lower than the optimal. That price probably is not high enough to encourage investigation and investment in substitutes as renewable sources. That results in an inferior rate of substitution and a delay in the transition, letting some future generation to assume these costs and facing lower economic growth.

All of the previously commented models try to find the optimal solution or the best extraction path. Another approach has been currently studied by other economists as Martinet et al. (2006), focusing on feasible solutions, that is, viable development paths that can be or not the optimal. With that, they lower the requisites for achieving a sustainable economy and find interesting conclusions.

Trying to calculate a figure to add to the current price of oil can be hard and it will need more time and effort than the scope of this paper, but, however, I will try to contribute with some ideas with a simple example, in the next section. That quantity should be a tax on the consumption of oil specifically designated to investigate in oil substitutes (increasing technology development) or a ‘green’ fund for future generations (increasing capital accumulation).

The cake of oil

Let’s imagine a simpler and graphical example of what we are discussing here. Imagine a cake that is sliced in 20 pieces. Imagine that there is a cue of 20 people waiting for eat one piece everyone. Each person can take as many as pieces he or she wants and are on the plate at that turn, and they cannot discuss between them, only with the next or two next persons on the cue. They would be happy just eating one piece (1/20), but if they take more, it is ok.

The first person in the line can perfectly take all of the cake, eat one piece and throw away the rest, but he does not so because the second person is watching out and he does not want to be a bully. However, he takes two pieces (2/20), one more just in case he gets hungry again. The second person does the same, and so the third and the rest ones (maybe the ninth and tenth would take only one regarding the almost empty plate, but it doesn’t matter). The problem arises with the eleventh and following, because there is not more cake on the plate. So ten people are more than happy but other ten are very disappointed because they eat nothing; and moreover, the first tenth have already left the fiesta¡

If you have gone to any party, you know that this is possible to happen. Now, just substitute the cake for an exhaustible resource as oil, and each person in the line for a complete generation, and you have our oil-based economy. It is obviously much more complicated in reality, because that cake can produce other outputs, there are substitutes for it, and the price fluctuates pushed by momentary offer and demand. All of these assumptions are considered and studied in the articles mentioned before.

Looking at the historical prices of oil, plot below (inflation adjusted, red line), it can be seen a great stability in prices until the oil crisis, that seems a steady and pace cake-eating model. It reminds me to the first lucky tenth. From the 70’s the prices started to fluctuate, due to the decisions of some of the people to keep some of the cake for rising prices (let’s call them party-poppers?) and the crazy new game called ‘trade the cake’ where the party animals play to exchange pieces of cake betting some money.

History of oil prices without inflation

Maybe, the simple cake example could be solved just by imposing a quota (a sign with ‘please one piece by person’), but imagine an infinite cue with people with bigger or lower necessities. That bring to us to what has been posed in previous paragraphs, how to define an extra price or define the externality for consuming today an exhaustible resource on future generations? How create a market where consumers do not exist yet? It would be difficult to get this number but one thing it is clear, it has to be something.

This type of economic and social justice problems considering generation’s distribution have been addressed by some oil-producers countries and regions. Some countries and regions have established the so-called permanent funds, which are sovereign investment funds where the royalties for resource exploitation are saved and re-invested, letting future generations to enjoy the benefits of the resource endowment. Some examples are the Alaska Permanent Fund, the Alberta Heritage Savings Trust Fund, the State Oil Fund of Azerbaijan, the Future Generations Fund of the State of Kuwait or probably the largest one, the Government Pension Fund of Norway, previously known as The Petroleum Fund of Norway. These funds were not actually created with the objective to allocate benefits among generations; despite it is a consequent benefit. They were created to avoid the problems known as the Resource Curse, Paradox of plenty or Dutch Disease, which refer to the paradox that countries and regions with an abundance of natural resources, tend to have less economic growth and worse development outcomes than countries with fewer natural resources. This is hypothesized to happen for many different reasons, including a decline in the competitiveness of other economic sectors (caused by appreciation of the real exchange rate as resource revenues enter an economy), volatility of revenues from the natural resource sector due to exposure to global commodity market swings, government mismanagement of resources, or weak, ineffectual, unstable or corrupt institutions. That is probably happening nowadays in North Dakota, where the boom of the exploitation of shale oil is creating a great inflation in costs (outsize prices in rents, salaries, etc) that are drowning other non-oil related business. (Dobb, 2013).

The royalties are dedicated to the fund, which give it back to citizens as a yearly dividend (in some cases like Norway, that amount is determined by the Constitution). That resolves partially the inflation effect through sterilization and providing a stable revenue stream. As a consequence, allocate the benefits of exploitation among time, compensating future generations of the country for emptying the resource endowment. Nevertheless, that is not being done in a worldwide basis, creating a future problem of injustice.


In this paper, some relevant problems and ideas related with exhaustible resource exploitation have been posed. It is clear that allocating benefits and cost between different generations drives to economic issues than are not totally resolved. As many other current problems of our society, solutions and decisions should be taken considering the whole world and next generations.

Probably the existing system of resource extraction and consumption is not the best solution and is creating a problem that must be dealt by future generations. How to find the best answers is now under debate by economists. Nevertheless, there are some solutions running as the permanent funds, which should be adopted and considered as a regular basis. Moreover, I think that the investment policy of these funds should be oriented to projects that achieve reduce or eliminate the dependency on the resources that feed them. Otherwise, the future is probably compromised.

So, if we would want to buy the gas of our great grandchildren, we should start to save money now, since, they are actually paying part of our gas today.


  • Barbier Edward B., Natural resources and economic development, Cambridge University Press, Cambridge, 2005
  • Dasgupta, P., Heal, G., The optimal depletion of exhaustible resources, Poceedings of the Symposium on the Economics of Exhaustible Resources, 1974
  • Dasgupta, P., Heal, G., Economic Theory and Exhaustible Resources. Cambridge University Press, 1979
  • Dobb, E., The New Oil Landscape. National Geographic, 2013
  • Gutierrez, M.J., Agnani, B., Iza, A., Growth in overlapping generation economies with non-renewable resources, Journal of Environmental Economics and Management, 2003
  • Hotelling H., The Economics of Exhaustible Resources, The Journal of Political Economy, 1931
  • Howarth, R.B., Intertemporal equilibria and exhaustible resources: an overlapping generations approach, Ecological Economics 4, 1991
  • Meadows Dennis L., The limits to Growth, Pan Books Ltd, 1972
  • Lazkano I., Intergenerational Externalities and Sustainable Growth, 2012
  • Schilling M., Chiang L., The Depletion of Non-renewable Resources for Non-sustainable Externalities as an Economic Development Policy, CPSA Annual Conference, 2009
  • Simon Julian L., The Ultimate Resource, Princeton University Press, Princeton, 1996
  • Solow, R.M., Intergenerational equity and exhaustible resources, review of economic studies, Proceedings of the Symposium on the Economics of Exhaustible Resources, 1974
  • Stiglitz, J., Growth with exhaustible natural resources: efficient and optimal growth paths, Proceedings of the Symposium on the Economics of Exhaustible Resources, 1974

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>