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VOTING PARADOX: The observation that voting by a relatively small group of people might generate a intransitive or inconsistent ranking of three or more alternatives, creating a paradox of rankings. The preferences of rational individuals are generally assumed to transitive and consistent, that is, if a person prefers A to B and B to C, then the person also prefers A to C. However, the preferences of group of voters might not be consistent. That is, as a group, voters might prefer A to B and B to C, but then prefer C to A. This is not only paradoxical and confusing, it also can be inefficient.
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                           TOTAL-MARGINAL RELATION: A mathematical connection between a marginal value and the corresponding total value stating that the marginal IS the slope of the total curve. This mathematical relation between total and marginal surfaces throughout the study of economics, especially utility (total utility and marginal utility), production (total product and marginal product), cost (total cost and marginal cost), and revenue (total revenue and marginal revenue). A related mathematical relation exists between a marginal value and the corresponding average value. The mathematical relation between total and marginal means that the slope of a total curve is the marginal value. If the total curve has a positive slope (that is, is upward sloping), then the marginal is positive. If the total curve has a negative slope (downward sloping), then the marginal is negative. If the total curve has a zero slope (horizontal), then marginal is zero. Moreover, if the total curve has an increasing slope (becoming steeper), then the marginal is rising. If the total curve has a decreasing slope (becoming flatter), then the marginal is falling.To see the connection between a marginal and the slope of a given total, consider this general formula for calculating a marginal from a total: | marginal | = | change in total
change in quantity |
Now consider the general forum for calculating the slope of a total curve. | slope | = | rise
run | = | change in total
change in quantity |
Is this an illusion, or are these two formulas the same? A quick check with an optometrist and psychiatrist suggests a firm grip on reality. The only possible conclusion is that these two formulas are, in fact, the same. And this means that the slope of a total is, in fact, the corresponding marginal. To put this another way, the term "marginal" is really just another way of saying "slope." The two are really one and the same. The only conceivable difference is that slope is used when an actual graph is under discussion, whereas marginal is used when attention is turned to a mathematical equation. But, the underlying concept is the same, whether it is presented in the form of a graph or a mathematical equation--marginal is slope. This total-marginal relation surfaces throughout the study of economics. Four of the more important total-marginal relations encountered are total utility and marginal utility, total product and marginal product, total cost and marginal cost, and total revenue and marginal revenue.
Recommended Citation:TOTAL-MARGINAL RELATION, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2023. [Accessed: May 29, 2023].
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Lewis Carroll, the author of Alice in Wonderland, was the pseudonym of Charles Dodgson, an accomplished mathematician and economist.
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