ⓘ Utility functions on divisible goods
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: w x log x + w y log y {\displaystyle w_{x}\log {x}+w_{y}\log {y}}. 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, x {\displaystyle x} and y {\displaystyle y}. p x {\displaystyle p_{x}} and p y {\displaystyle p_{y}} are their prices. w x {\displaystyle w_{x}} and w y {\displaystyle w_{y}} are constant positive parameters and r {\displaystyle r} is another constant parameter. u y {\displaystyle u_{y}} is a utility function of a single commodity y {\displaystyle y}. I {\displaystyle I} is the total income wealth of the consumer.
 individual utility functions are additive, then the following is true for the aggregate functions Utility functions on divisible goods Gul, F. Stacchetti
 utility is the satisfaction or benefit derived by consuming a product thus the marginal utility of a goods or service is the change in the utility from
 with equal levels of utility and the consumer has no preference for one combination or bundle of goods over a different combination on the same curve. One
 standard assumption of neoclassical economics that goods and services are continuously divisible the marginal rates of substitution will be the same
 service. Assuming that goods and services are continuously divisible the only way that it is possible that the marginal expenditure on one good or service
 money, which is divisible The agents have quasilinear utility functions their utility is the amount of money they have plus the utility from the bundle
 John von Neumann and Oskar Morgenstern expected utility functions Fearon finds the expected utility for war for states A and B, which are PA  CA and
 and budget, in order to maximize his utility Consider an economy with two types of homogeneous divisible goods traditionally called X and Y. The consumption
 indivisible heterogeneous goods e.g., rooms in an apartment and simultaneously a homogeneous divisible bad the rent on the apartment Fair river
 explain the discrepancy in the value of goods and services by reference to their secondary, or marginal, utility The reason why the price of diamonds is
 the three fundamental functions of money in mainstream economics. It is a widely accepted token which can be exchanged for goods and services. Because
 calculates an equitable, envy  free and efficient division of a set of divisible goods between two partners. Jones, M. A. 2002 Equitable, Envy  Free, and
Dichotomous preferences 

Exponential utility 
Fractionally subadditive 
Gorman polar form 
Gross substitutes (indivisible items) 
Homothetic preferences 
Indirect utility function 

Isoelastic utility 
King–Plosser–Rebelo preferences 
Leontief utilities 
Linear utility 
Responsive set extension 
Stone–Geary utility function 

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