V. On the Use and Misuse of Mathematics in Presenting Economic Theory

Abstract

Articles on economic theory are usually intended to explain to the reader what results may be expected to follow various policies or disturbances in given circumstances. The task of explanation is made difficult by the varying capacities and demands of the readers. If the theory is to be realistic, the given circumstances must reflect a great many of the complications of a real-world situation: an exhaustive account of these, whilst necessary for logical completeness, would be intolerably lengthy and boring for the reader who is well informed about the situation to which the theory is intended to apply. He can supply for himself, as obvious, many of the underlying assumptions about institutions and psychology which justify the reasoning in good non-mathematical articles on economic theory. But some readers will lack the experience or the docility to do this, and will either attempt to apply the theory to inappropriate circumstances, or will attack the writer for not giving an exhaustive account of his assumptions. Since proof is not always the most effective method of explanation, many writers are content to sketch their ideas in a manner which will enlighten sympathetic readers without attempting to convey complete conviction to anybody. The cautious economic theorist, whose overriding ambition is never to appear wrong and yet to appear in print at all, has little scope beyond the discussion of economic models. These are shadows of the real situations so drastically simplified that they can be completely described and many of their workings exactly portrayed within the compass of a single article. The logic leading from the assumptions about the model to the conclusions about how it will behave can now be made rigorous and independent of the reader's knowledge of the real world. Such models serve the useful purpose of making it possible to reach complete agreement within reasonable time: occasionally a study of them will reveal that earlier disagreements have been entirely due to a difference of intuitive assumptions about the real world. Unfortunately for the cautious theorist, his economic models will be judged according to the degree in which they appear to be relevant to the real world; so that in avoiding the appearance of being wrong, he may yet appear silly by publishing a long article whose relevance to any practical issue seems to be superficial. This danger of manufacturing mere toys is especially great since the assumptions which are most convenient for modelbuilding are seldom those which are most appropriate to the real world. Many would regard as the best and most important articles on economic theory those which reveal keen observation and judgment in choosing assumptions which accord well with facts and which are yet able to demonstrate fairly convincingly powerful conclusions of a simple nature, which suggest important analogues in the real world. They would regard the rigor of the logic and the exactness of the descriptions of the assumptions as secondary matters relating to their style rather than to their importance. The ability to judge the relevance of an economic theory and its conclusions to the real world is but rarely associated with the ability to understand advanced mathematics. An important article on economic theory is therefore likely to be wasted unless it can be set out in prose supported by the most elementary mathematics. It is obvious that there is no room in economics for long trains of deductive reasoning, 4 so that those economic models which are realistic and yet sufficiently simple to allow