## Figure 10

## Figure 11

Table 4 lists some of the more important mineral and fuel resources, the vital raw materials for today’s major industrial processes. The number following each resource in column 3 is the static reserve index, or the number of years present known reserves of that resource (listed in column 2) will last at the *current *rate of usage. This static index is the measure normally used to express future resource availability. Underlying the static index are several assumptions, one of which is that the usage rate will remain constant.

But column 4 in table 4 shows that the world usage rate of every natural resource is growing exponentially. For many resources the usage rate is growing even faster than the population, indicating both that more people are consuming resources each year and also that the average consumption per person is increasing each year. In other words, the exponential growth curve of resource consumption is driven by both the positive feedback loops of population growth and of capital growth.

We have already seen in figure 10 that an exponential increase in land use can very quickly run up against the fixed amount of land available. An exponential increase in resource consumption can rapidly diminish a fixed store of resources in the same way. Figure 11, which is similar to figure 10, illustrates the effect of exponentially increasing consumption of a given initial amount of a nonrenewable resource. The example in this case is chromium ore, chosen because it has one of the longest static reserve indices of all the resources listed in table 4. We could draw a similar graph for each of the resources listed in the table. The time scales for the resources would vary, but the general shape of the curves would be the same.

The world’s known reserves of chromium are about 775 million metric tons, of which about 1.85 million metric tons are mined annually at present. Thus, at the current rate of use, the known reserves would last about 420 years. The dashed line in figure 11 illustrates the linear depletion of chromium reserves that would be expected under the assumption of constant use. The actual world consumption of chromium is increasing, however, at the rate of 2.6 percent annually. The curved solid lines in figure 11 show how that growth rate, if it continues, will deplete the resource stock, not in 420 years, as the linear assumption indicates, but in just 95 years. If we suppose that reserves yet undiscovered could increase present known reserves by a factor of five, as shown by the dotted line, this fivefold increase would extend the lifetime of the reserves only from 95 to 154 years. Even if it were possible from 1970 onward to recycle 100 percent of the chromium (the horizontal line) so that none of the initial reserves were lost, the demand would exceed the supply in 235 years.

Figure 11 shows that under conditions of exponential growth in resource consumption, the static reserve index (420 years for chromium) is a rather misleading measure of resource availability. We might define a new index, an “exponential reserve index,” which gives the probable lifetime of each resource, assuming that the current growth rate in consumption will continue. We have included this index in column 5 of table 4. We have also calculated an exponential index on the assumption that our present known reserves of each resource can be expanded fivefold by new discoveries. This index is shown in column 6. The effect of exponential growth is to reduce the probable period of availability of aluminum, for example, from 100 years to 31 years (55 years with a fivefold increase in reserves). Copper, with a 36-year lifetime at the present usage rate, would actually last only 21 years at the present rate of growth, and 48 years if reserves are multiplied by five. It is clear that the present exponentially growing usage rates greatly diminish the length of time that wide-scale economic growth can be based on these raw materials.

Of course the actual nonrenewable resource availability in the next few decades will be determined by factors much more complicated than can be expressed by either the simple static reserve index or the exponential reserve index. We have studied this problem with a detailed model that takes into account the many interrelationships among such factors as varying grades of ore, production costs, new mining technology, the elasticity of consumer demand, and substitution of other resources. [pp. 55-65]