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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?" Microeconomics is a branch of economics that studies how individuals, households, and firms make decisions to allocate limited resources,[1] typically in markets where goods or services are being bought and sold. ...
In economics, consumers are individuals or households that consume goods and services generated within the economy. ...
This article needs additional references or sources to facilitate its verification. ...
In economics, utility is a measure of the relative happiness or satisfaction (gratification) gained. ...
Suppose their consumption set In economics, utility is a measure of the relative happiness or satisfaction (gratification) gained. ...
 has L commodities. If the prices of the L commodities are  and the consumer's wealth is w, then the set of all affordable packages, the budget set, is A budget set includes all possible consumption bundles that someone can afford given the prices of goods and the persons income level. ...
 . The consumer would like to buy the best package of commodities it can afford. If  is the consumer's utility function, then the consumer's optimal choices x(p, w) are  . Finding x(p, w) is the utility maximization problem.
The solution x(p, w) need not be unique. If u is continuous and no commodities are free of charge, then x(p, w) is nonempty. Proof: B(p, w) is a compact space. So if u is continuous, then the Weierstrass theorem implies that u(B(p, w)) is a compact subset of  . By the Heine-Borel theorem, every compact set contains its maximum, so we can conclude that u(B(p, w)) has a maximum and hence there must be a package in B(p, w) that maps to this maximum. In mathematics, a subset of Euclidean space Rn is called compact if it is closed and bounded. ...
In mathematics, a continuous function is a function for which, intuitively, small changes in the input result in small changes in the output. ...
Karl Theodor Wilhelm Weierstrass (Weierstraß) (October 31, 1815 – February 19, 1897) was a German mathematician who is often cited as the father of modern analysis. He was born in Ostenfelde, Westphalia (today Germany) and died in Berlin, Germany. ...
In mathematical analysis, the Heine-Borel theorem, named after Eduard Heine and Émile Borel, states: A subset of the real numbers R is compact iff it is closed and bounded. ...
If a consumer always picks an optimal package as defined above, then x(p, w) is called the Marshallian demand correspondence. If there is always a unique maximizer, then it is called the Marshallian demand function. The relationship between the utility function and Marshallian demand in the Utility Maximization Problem mirrors the relationship between the expenditure function and Hicksian demand in the Expenditure Minimization Problem. In microeconomics, a consumers Marshallian demand function specifies what the consumer would buy in each price and wealth situation, assuming it perfectly solves the Utility Maximization Problem. ...
In microeconomics, a consumers Marshallian demand function specifies what the consumer would buy in each price and wealth situation, assuming it perfectly solves the Utility Maximization Problem. ...
This article is about utility in economics and in game theory. ...
In microeconomics, a consumers Marshallian demand function specifies what the consumer would buy in each price and wealth situation, assuming it perfectly solves the Utility Maximization Problem. ...
In microeconomics, a consumers expenditure function describes how much money a consumer needs to be happy. ...
In microeconomics, a consumers Hicksian demand function gives the cheapest bundle under a price level for which the consumer derives a utility level of at least . ...
In microeconomics, the Expenditure Minimization Problem is the dual problem to the Utility Maximization Problem: how much money do I need to be happy?. This question comes in two parts. ...
In practice, a consumer may not always pick an optimal package. For example, it may require too much thought. Bounded rationality is a theory that explains this behaviour with satisficing - picking packages that are suboptimal but good enough. Many models of human behavior in the social sciences assume that humans can be reasonably approximated or described as rational entities, especially as conceived by rational choice theory. ...
// Economics In economics, satisficing is a behaviour which attempts to achieve at least some minimum level of a particular variable, but which does not strive to achieve its maximum possible value. ...
See also
This article is about utility in economics and in game theory. ...
In microeconomics, the Expenditure Minimization Problem is the dual problem to the Utility Maximization Problem: how much money do I need to be happy?. This question comes in two parts. ...
References - Mas-Colell, Andreu; Whinston, Michael; & Green, Jerry (1995). Microeconomic Theory. Oxford: Oxford University Press. ISBN 0-19-507340-1
- Consumer Theory: The Neoclassical Model and Its Opposite Alternative, by Valentino Piana.
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