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In microeconomics, the utility maximization problem is the problem consumers face: "How should I spend my money in order to maximize my utility?" It is a type of optimal decision problem . It consists of choosing how much of each available good or service to consume, taking into account a constraint on total spending (income), the prices of the ...
In decision theory, the von Neumann–Morgenstern (VNM) utility theorem demonstrates that rational choice under uncertainty involves making decisions that take the form of maximizing the expected value of some cardinal utility function. This function is known as the von Neumann–Morgenstern utility function.
In economics, utility is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings. In a normative context, utility refers to a goal or objective that we wish to maximize, i.e., an objective function.
Standard utility functions represent ordinal preferences. The expected utility hypothesis imposes limitations on the utility function and makes utility cardinal (though still not comparable across individuals). Although the expected utility hypothesis is standard in economic modelling, it has been found to be violated in psychological experiments.
A consumer's indirect utility (,) can be computed from their utility function (), defined over vectors of quantities of consumable goods, by first computing the most preferred affordable bundle, represented by the vector (,) by solving the utility maximization problem, and second, computing the utility ((,)) the consumer derives from that ...
Leontief utility functions represent complementary goods. For example: For example: Suppose x 1 {\displaystyle x_{1}} is the number of left shoes and x 2 {\displaystyle x_{2}} the number of right shoes.
In microeconomics, the expenditure function gives the minimum amount of money an individual needs to spend to achieve some level of utility, given a utility function and the prices of the available goods. Formally, if there is a utility function that describes preferences over n commodities, the expenditure function
The sign of the second derivative of a differentiable utility function that is cardinal, is the same for all the numerical representations of a particular preference structure. Given that this is usually a negative sign, there is room for a law of diminishing marginal utility in cardinal utility theory.