Utility maximization problem

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.

Not only used in Microeconomics, it often used to explain human propensity or human behavior in terms of evolutionary psychology. Human has been known as "fitness maximizers" or "utility maximizers", which means that people tend to strive to obtain the greatest amount of profit and value possible when individuals invest on something. According to this theory, people would not behave irrationally or make any reckless decision that might hurt or devalue their property. However, situations in modern international relations are different from ancestors and adaptations to such environment might shape human behavior. Since Homo Sapiens evolved in small groups, not nation-states, people now would not always behave as "utility maximizes" but rather as "adaptation executors". This is related to human evolutionary psychology and contradicted to rational utility maximization model. Therefore, this idea of human adaptation can also be applied to the study of politics and international security.

Suppose the consumer's consumption set, or the enumeration of all possible consumption bundles that could be selected if there were no budget constraint, has L commodities and is limited to positive amounts of consumption of each commodity. Let x be the vector x={x_i;i=1,...L} containing the amounts of each commodity; then

Suppose also that the price vector (p) of the L commodities is positive,

and that the consumer's income is ${\displaystyle I}$; then the set of all affordable packages, the budget set, is

where ${\displaystyle \langle p,x\rangle }$ is the dot product of p and x, or the total cost of consuming x of the products at price level p:

...
Wikipedia