期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1972
卷号：69
期号：5
页码：1230-1233
DOI：10.1073/pnas.69.5.1230
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：It is well known that successful speculation can be a boon to society, whether or not the successful speculator is ruled to be the legitimate appropriator of his profits. It is also understood that unsuccessful speculation can naturally impose losses on the unsuccessful speculator himself. Little, however, is known about the effect of the unsuccessful speculator on the rest of society: one view is that the others gain what he loses, so that in a sense he is their benefactor and only his own enemy; a more plausible view is that his loss must in some sense exceed the gain splashed on others. Nothing seems to have been proved in a rigorous way in this matter. Here, the problem is subjected to mathematical analysis. It is shown that others do definitely gain from an act of unsuccessful speculation, thus providing rigorous proof of what has long been surmised. But it is also shown that their gain is necessarily less, in an objective sense, than the loss to the speculator himself. Indeed, in the model of unnecessary positive carryover of grain into the future, the gain to the nonspeculators is proved to be actually of a second-order of smallness of infinitesimals compared to the speculator's loss.
关键词：mathematical analysis ; unnecessary positive carryover model
