![]() This point becomes clear from the indifference map shown in Fig. An example of this is X > Y > Z > A.Ī utility function, is a way to label the indifference curves such that large numbers are assigned to higher indifference curves. It may be noted at the outset that intransitive preferences cannot be represented by a utility function. In other words, the labelling will represent the same preferences. Since a larger label is put on indifference curves containing more-preferred bundles than those containing less-preferred bundles, the labelling does not alter the preferences. Since utility is a way to label indifference curves a monotonic transformation is just a relabeling of them.Ī related point may also be noted in this context. In short, a monotonic transformation of a utility function is one that represents the same preferences as the original utility function. Part (b) illustrates a function that is not monotonic, since it sometimes increases and sometimes decreases. A monotonic function is one that is always increasing. The graph of a monotonic function will always have a positive slope, as shown in Fig 5.1 (a). Mathematically speaking, there is no fundamental difference between a monotonic transformation and a monotonic function. A monotonic transformation is a way of transforming one set of numbers into another in such a way that the order of the numbers is not disturbed.Ī monotonic transformation of a function f(u) occurs when each number u is transformed into some other number f(u) such that u 1 > u 2 which implies that f(u 1) > f(u 2). If, for example, m(x 1, x 2) represents a way to assign utility numbers to the bundle (x 1, x 2), then multiplying u(x 1, x 2) by 2 (or any positive number) is an example of a monotonic transformation. ![]()
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