puted for only three stockpile sizes and zero stockpile.

e. Optimal Stockpile Size.-The net benefit curve in figure V-3 can be used to indicate the probable optimal stockpile size, where the curve appears to be at a maximum positive value (or minimum negative value). Although this can only be taken as an indication of the area of an optimal quantity, it illustrates the desired value of the stockpile size for the values of the input variables chosen.

The calculations resulted in an optimal stockpile size of 250-500 million barrels accumulated over a 1-year period. The economic net benefits expected for this stockpile will be approximately $19 billion. It should be emphasized that the estimates apply only to

the specific materials examined and within the scenario assumptions described, and should therefore not be taken to indicate that precise quantities of specific materials should or should not be stockpiled. Nevertheless, the nature and magnitude of the estimates are sufficient to indicate that an economic stockpile should be given detailed consideration as one component of a more comprehensive national materials policy and that measuring the benefits or costs of a supply disruption in terms of the probability, rather than the certainty, of a disruption will significantly reduce the quantity of material to be stockpiled.

As a measure of scale for the results of these calculations, two current stockpiling proposals can be examined. The first proposal, Title II of

the Adminsitration's Energy Independence Act (IEP)-the National Strategic Petroleum Reserve (Civilian) Act of 1975-proposes the establishment of a strategic petroleum reserve of 1 billion barrels' reserve for the military. The second proposal is part of the requirements for allocation rights under the International Energy Agency which stipulates that each participating country maintain emergency oil reserves sufficient to sustain consumption for 60 days with no net imports. For the United States, which presently is importing 5.5 million barrels per day, satisfaction of this obligation would require a stockpile of 330 million barrels. The IEP also calls for demand curtailment measures which would reduce consumption by 7 percent in the event of an embargo or 67 1/2 million barrels over a 60day period.

In this example, the optimal stockpile size of 250-500 million barrels was based on the probability of four distinct cartel/unilateral actions and the damages which would result from each action (i.e., a 6-month, 50-percent import interruption; and a 3-month, 25-percent import interruption; a 3-month, 50-percent interruption; and a 3-month, 25-percent import interruption). At the lower end of the scale this stockpile size falls short of the IEP requirement by a minimum of 10 percent and is approximately 25 percent the size of the NSPR act's proposed stockpile. It is interesting to note that both the IEP requirement and that calculated with the Decision Criteria for SP-1 are approximately one-third of the possible total petroleum import interruption of 1 billion barrels for a 6-month period.

In summary, the example calculations for SP-1 indicate that the stockpile size should be based upon the expected economic net benefits of the stockpile. The example calculations also show that a stockpile based upon the probability of an interruption is significantly smaller than one based on the certainty of total interruption.

These calculations also illustrate the role of the risk aversion factor. It should be noted, for example, that the difference in economic net benefits for stockpile sizes of 250 and 500 million barrels is relatively small ($140 million). Yet the protection provided by the larger stockpile in the event of a cartel action is substantially greater. The risk aversion factor has been treated as an unknown, and the value of r which equates the economic net benefits for the two stockpile sizes has been solved. The resulting small value of 1.007 suggests that implementation of the larger stockpile should be given serious consideration. If the value for r were equal to say, 3.5, such a high-risk aversion would most likely be questioned.

f. Sensitivity Analysis for SP-1.-This section is a discussion of the particular sensitivity analysis of SP-1. An examination of table V-4 indicates the economic net benefits to be fairly insensitive to any input variable per