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Utility function U(X,Y), in economics, measures the welfare or satisfactions of a consumer as a function of consumption of real goods. In other words, the utility function assigns a number to each basket so that the more preferred baskets get a higher number than less preferred baskets. The numerical number assigned to each basket is called its total utility. To postulate the utility function, some assumptions are made about preferences that they are: complete, transitive, monotonic and averages are preferred to extremes. Here are some common utility functions that might be used to represent consumer preferences (the other one is perfect complements) :
Cobb-Douglas Utility Function: U(X,Y) = XαYβ where α and β are parameter values which are given. The family of Cobb-Douglas utility functions is widely used in Economics because it yields the nice convex indifference curves that we typically observe in consumer behaviour.
Perfect Substitutes: U(X,Y) = αX + βY where α and β are parameter values which are given. This type of utility function will yield indifference curves which are straight lines. The slope of the indifference curve will depend on the values of α and β.