Orthogonal Time in Euclidean 3-space
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This paper begins by asking a simple question: can a farmer own and fully utilize precisely five tractors and precisely six tractors at the same time? Of course not. He can own five or he can own six – but he cannot own five and six at the same. The answer to this simple question eventually led this author to Alfred Marshall’s historically-ignored, linguistically-depicted ‘cardboard model’ where my goal was to construct a picture based on his written words. More precisely, in this paper our overall goal is to convert Marshall’s (‘three-dimensional’) words into a three-dimensional picture so that the full import of his insight can be appreciated by all readers.
After a brief digression necessary to introduce the reader to the intricacies of Euclidean 3-space, plus a brief digression to illustrate the pictorial problem with extant theory, the paper turns to Marshall’s historically-ignored words. Specifically, it slowly constructs a visual depiction of Marshall’s ‘cardboard model’. Unfortunately (for all purveyors of extant economic theory), this visual depiction suddenly opens the door to all manner of Copernican heresy. For example, it suddenly becomes obvious that we can join the lowest points on a firm’s series of SRAC curves and thereby form its LRAC curve; it suddenly becomes obvious that the firm’s series of SRAC curves only appear to intersect because mainstream theory has naively forced our three-dimensional economic reality into a two-dimensional economic sketch; and it suddenly becomes obvious that a two-dimensional sketch is analytically useless because the ‘short run’ (SR) never turns into the ‘long run’ (LR) – no matter how long we wait.