review_ch4 - Chapter 4 Review Utility A utility function is...

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Chapter 4 Review: Utility A utility function is a way of assigning a number to every possible con- sumption bundle such that more-preferred bundles get assigned larger num- bers than less-preferred bundles.Tht is, ( x 1 , x 2 ) ´ ( y 1 , y 2 ) if and only if u ( x 1 , x 2 ) > u ( y 1 , y 2 ). The only property of a utility assignment that is important is how it it orders or ranks the bundles of goods; the actual size of the utility difference between any tow consumption bundles doesn’t matter. This kind of utility is known as ordinal utility . A monotonic transformation is way of transforming one set of num- bers into another set of numbers in a way that preserves the order of the numbers. Examples of (positive) monotonic transformation are multiplica- tion by some positive number (e.g., f ( u ) = 3 u ), adding a constant (e.g., f ( u ) = u + 15), raising u to an odd power ( f ( u ) = u 3 ), etc. The rate of change of f ( u ) as u changes can be measured by looking at the change in f between two values of u , divided by the change in u : 4 f 4 u = f ( u 2 ) - f ( u 1 ) u 2 - u 1 For a monotonic transformation,
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