This page compares the properties of several typical utility functions of divisible goods. These functions are commonly used as examples in consumer theory.
The functions are ordinal utility functions, which means that their properties are invariant under positive monotone transformation. For example, the Cobb–Douglas function could also be written as: formula_1. Such functions only become interesting when there are two or more goods (with a single good, all monotonically increasing functions are ordinally equivalent).
The utility functions are exemplified for two goods, formula_2 and formula_3. formula_4 and formula_5 are their prices. formula_6 and formula_7 are constant positive parameters and formula_8 is another constant parameter. formula_9 is a utility function of a single commodity (formula_3). formula_11 is the total income (wealth) of the consumer.
Acknowledgements.
This page has been greatly improved thanks to comments and answers in Economics StackExchange.