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Finding (,) is the utility maximization problem. If u is continuous and no commodities are free of charge, then x ( p , I ) {\displaystyle x(p,I)} exists, [ 4 ] but it is not necessarily unique. If the preferences of the consumer are complete, transitive and strictly convex then the demand of the consumer contains a unique maximiser for all ...
The social planner's problem is maximizing the social welfare function = (,) Assume that the economy is populated by identical immortal individuals with unchanging utility functions () (a representative agent), such that the total utility is: (,) = = The utility function is assumed to be strictly increasing (i.e., there is no bliss point) and ...
The problem of finding the optimal decision is a mathematical optimization problem. In practice, few people verify that their decisions are optimal, but instead use heuristics and rules of thumb to make decisions that are "good enough"—that is, they engage in satisficing.
The welfare maximization problem is an optimization problem studied in economics and computer science. Its goal is to partition a set of items among agents with different utility functions , such that the welfare – defined as the sum of the agents' utilities – is as high as possible.
The utilitarian rule is easy to interpret and implement when the functions u i represent some tangible, measurable form of utility. For example: [ 1 ] : 44 Consider a problem of allocating wood among builders.
The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Rational choice theory, a cornerstone of microeconomics, builds this postulate to model aggregate social ...
In some cases, there is a unique utility-maximizing bundle for each price and income situation; then, (,) is a function and it is called the Marshallian demand function. If the consumer has strictly convex preferences and the prices of all goods are strictly positive, then there is a unique utility-maximizing bundle.
Welfare maximization then consists of maximizing the welfare function subject to the possibility function as a constraint. The same welfare maximization conditions emerge as in Bergson's analysis. For a two-person society, there is a graphical depiction of such welfare maximization at the first figure of Bergson–Samuelson social welfare ...