Information about Western Hemisphere Hemisferio Occidental

14 How to Warrant a Sufficient Level of Energy Supply to Future Generations

Jacob Frenkel, and Morris Goldstein
Published Date:
September 1991
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Information about Western Hemisphere Hemisferio Occidental
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Jan Tinbergen

I. The Problem and Its Core

One of the hobbies that my long-time friend Jacques Polak, whom the Dutch call Koos, and I enjoy the most is building models. He has built some real beauties as we all know.1 I hope he likes the one I dedicate to him on the occasion of his seventy-fifth birthday.

The problem dealt with in this essay is whether, and if so how, nonrenewable natural resources may be distributed between current and future generations. Since future generations are the children, grandchildren, and so on, of today’s generation, it is natural to think that sharing the known reserves of natural resources poses a problem of equal sharing. In order to understand the most essential features of this problem, we simplify it to what we shall call its core. We assume that world population is stable and that the goal is to keep the standard of living of future generations equal to ours. The core question to be answered then is whether the infinity of future generations can be offered our standard of life (a quantity of goods and services) with the finite quantity of natural resources. The goods and services mentioned, although meant for consumption as well as for investment, will be called consumer goods.

The answer to the core question is in the affirmative provided there is technological development. This means improvements in the production technology so that the quantity of resources needed to produce a unit of consumer goods diminishes over time. We choose the simplest assumption—albeit one not far from reality—that the quantity of resources needed decreases at a constant rate per annum, p < 1. If the quantity needed in year t = 1 is q, then the quantity needed in year 2 is qp, and in year t, qpt-1. For all future years, a quantity Q is needed and

If the known reserves of natural resources are

it follows that the standard of life that can be warranted, q*, as measured by the amount of natural resources used to produce a unit of consumer goods each period, is

II. Permissible Consumption and “Optimum Moment”

The quantity q* depends on the technology, characterized by p, and the resource reserves R. If actual consumption c rises at an observed rate of growth, we can calculate the time x it takes to make c equal to q*. If c < q*, x will be positive and the point where c = q* will be reached in the future. There are good reasons to call that point an optimum moment. It is the point of the highest value of c that warrants future generations our standard of life. These characteristics suggest a scenario starting with “underconsumption,” reaching the optimum moment, and then entering a phase of overconsumption. The optimal policy is to attain the optimal point and to stay there. The optimal point is not constant: it changes with—mostly rising—reserves R and possible changes in technology p.

III. Some Interesting Computations

In this essay, two components (coal and natural gas) of the natural resource energy will be studied with the aid of data published by British Petroleum in its Statistical Review of World Energy and by the World Bank. The same set of computations was made for coal and natural gas. First, efficiency changes per annum in producing consumer goods were estimated by dividing the annual rate of increase of consumer goods production (proxied by the annual rate of increase of gross national product (GNP)) by the annual rate of growth in the consumption of the energy type considered. This yields 1/p. From it, q* = R(1- p) is obtained. The time x needed to make c = q* is calculated with the aid of the annual growth of consumption c. The relation used is

which is solved for

For each type of energy, six alternative computations were made. Two alternative figures are used for the rate of growth in GNP, using data for the periods 1965-80 and 1980-87 obtained from the World Bank’s World Development Report, 1989.2 In addition, three alternative values for the rate of growth of energy consumption were used: the (geometrical) average of the period 1979-89 and those for the subperiods 1979-84 and 1984-89. These figures, as well as the reserves R at the end of 1989, are published in British Petroleum’s Statistical Review of World Energy. In Sections IV and V, coal and natural gas will be considered.

Given the simplicity of the model and since all figures used may have random components, some of the results obtained seem very unlikely, particularly in cases where technological development appears to be absent. Of the two types of energy, coal seemed the least susceptible to this problem and provides therefore the clearest example of the scenario mentioned at the end of Section I. Natural gas was more susceptible to the impact of random forces. For these reasons, the discussion starts with the results for coal, followed by those for natural gas. The data used are shown in Annex I.

IV. Coal

Consumption In 1989, permissible consumption, and time needed to attain permissible consumption are shown in Table 1.

Table 1.Coal: Consumption In 1989, Permissible Consumption, and the Time Needed to Attain It(In years)
Alternative Computations
Time needed79368227151110
Memo item:
Actual 1989
consumption, 2,231

The main feature of these results is that in each alternative computation, the permissible consumption is larger than consumption in 1989, and accordingly a positive time period is needed to attain the “optimum moment.” In terms of development policy, this means that a policy of expansion of world production of consumer goods may go on for at least 27 years, that is, during the next few decades, without the threat of a coal shortage.

V. Natural Gas

For natural gas, the results are shown in Table 2. Here we find a different situation. In two out of the six alternative scenarios, a situation without technological development is found (i.e., p≥1), where the possibility of warranting to future generations our standard of life does not exist. Of the four remaining alternatives, permissible consumption is lower than actual consumption in three cases and, accordingly, the optimal moment has been passed. In one case, short time is available before actual consumption reaches permissible consumption; otherwise, a shortage of natural gas may well develop, or the interests of future generations will be damaged.

Table 2.Natural Gas: Consumption In 1989, Permissible Consumption, and the Time Needed to Attain It(In years)
Altamative Compuations
Time needed-26+6-38-53
Memo item:
Actual 1989
consumption, 1,707

VI. Conclusion

Summarizing our findings, the calculations from this simple model suggest that a further expansion of world production of consumer goods is not assured without damaging the interests of future generations. Coal would be available in sufficient quantities, but here the environmental consequences—too high an expulsion of carbon dioxide—may constitute a limit. This remains a topic of future research.

ANNEX I Basic Data Used
Table 3.Consumption and Reserves
ConsumptionReserves, End of 1989
(106 tons oil equivalent)(106 tons oil
197919841989equivalent)(Other units)
Coal1,819.51,973.62,231.3722.2671,083,403million tons
Natural gas1,271.01,412.21,707.4101,700113.01012 m3

Take, for instance, J. J. Polak, An International Economic System (Chicago: University of Chicago Press, 1953; London: Allen & Unwin, 1954).


World Bank, World Development Report, 1989 (New York: Oxford University Press, 1989).

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