# Utility Function

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 Utility FunctionA way of assigning a number to every possible consumption bundle such that more preferred bundles are assigned bigger numbers than less preferred bundles.(Benjamin, Dwayne. Class Lecture.  PPG 1002H Microeconomics for Policy Analysis, University of Toronto School of Public Policy and Governance.)---------------------------------There are several different types of utility functions. Some of the most important ones are:1)       Perfect Substitutes:  If a consumer is willing to substitute one good for another at a constant rate, those two goods are perfect substitutes for one another. The indifference curve for perfect substitutes has a constant slope.2)       Perfect Complements: Goods that are always consumed together in fixed proportions. For example, left shoes and right shoes are perfect complements; perfect complements are represented by utility function in the form u (x1,x2) = min (x1,x2)3)       Quasi-Linear: This means partly linear utility because the utility function is linear in one good but non-linear in the other. 4)       Cobb-Douglas: The utility function is in the form u (x1,x2) = x1cx2d  whereby c and d are positive numbers describing the preferences of the consumer. A monotonic transformation of a Cobb-Douglas utility function will represent exactly the same preferences. For the overwhelming majority of utility functions, the only important property of utility assignment is how the bundles are ordered. The numerical magnitude of the utility difference between any two consumption bundles does not matter. Because these sorts of utlity functions emphasize the ordering of bundles of goods, they are referred to as ordinal utility functions.
Utility Function

A way of assigning a number to every possible consumption bundle such that more preferred bundles are assigned bigger numbers than less preferred bundles.

(Benjamin, Dwayne. Class Lecture.  PPG 1002H Microeconomics for Policy Analysis, University of Toronto School of Public Policy and Governance.)

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There are several different types of utility functions. Some of the most important ones are:

1)       Perfect Substitutes:  If a consumer is willing to substitute one good for another at a constant rate, those two goods are perfect substitutes for one another. The indifference curve for perfect substitutes has a constant slope.

2)       Perfect Complements: Goods that are always consumed together in fixed proportions. For example, left shoes and right shoes are perfect complements; perfect complements are represented by utility function in the form u (x1,x2) = min (x1,x2)

3)       Quasi-Linear: This means partly linear utility because the utility function is linear in one good but non-linear in the other.

4)       Cobb-Douglas: The utility function is in the form u (x1,x2) = x1cx2d  whereby c and d are positive numbers describing the preferences of the consumer. A monotonic transformation of a Cobb-Douglas utility function will represent exactly the same preferences.

For the overwhelming majority of utility functions, the only important property of utility assignment is how the bundles are ordered. The numerical magnitude of the utility difference between any two consumption bundles does not matter. Because these sorts of utlity functions emphasize the ordering of bundles of goods, they are referred to as ordinal utility functions.

 Approved for glossaryposting by Ben Eisen on March 20, 2011

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