A demand set is a model of the most-preferred bundle of goods an agent can afford. The set is a function of the preference relation for this agent, the prices of goods, and the agent's endowment.
Assuming the agent cannot have a negative quantity of any good, the demand set can be characterized this way:
Define 
as the number of goods the agent might receive an allocation of. An allocation to the agent is an element of the space 
; that is, the space of nonnegative real vectors of dimension .
Define 
as a weak preference relation over goods; that is, 
states that the allocation vector 
is weakly preferred to 
.
Let 
be a vector representing the quantities of the agent's endowment of each possible good, and 
be a vector of prices for those goods. Let 
denote the demand set. Then:
.
In economics, utility is a measure of the satisfaction that a certain person has from a certain state of the world. Over time, the term has been used in two different meanings.
In economics, an indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is indifferent. That is, any combinations of two products indicated by the curve will provide the consumer 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 can also refer to each point on the indifference curve as rendering the same level of utility (satisfaction) for the consumer. In other words, an indifference curve is the locus of various points showing different combinations of two goods providing equal utility to the consumer. Utility is then a device to represent preferences rather than something from which preferences come. The main use of indifference curves is in the representation of potentially observable demand patterns for individual consumers over commodity bundles.
The theory of consumer choice is the branch of microeconomics that relates preferences to consumption expenditures and to consumer demand curves. It analyzes how consumers maximize the desirability of their consumption, by maximizing utility subject to a consumer budget constraint. Factors influencing consumers' evaluation of the utility of goods include: income level, cultural factors, product information and physio-psychological factors.
In mathematics, especially in order theory, a maximal element of a subset of some preordered set is an element of that is not smaller than any other element in . A minimal element of a subset of some preordered set is defined dually as an element of that is not greater than any other element in .
Utility maximization was first developed by utilitarian philosophers Jeremy Bentham and John Stuart Mill. 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 goods and their preferences.
In mathematical economics, the Arrow–Debreu model is a theoretical general equilibrium model. It posits that under certain economic assumptions there must be a set of prices such that aggregate supplies will equal aggregate demands for every commodity in the economy.
There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information, and in perfect competition, will be Pareto optimal. The requirements for perfect competition are these:
- There are no externalities and each actor has perfect information.
- Firms and consumers take prices as given.
Revealed preference theory, pioneered by economist Paul Anthony Samuelson in 1938, is a method of analyzing choices made by individuals, mostly used for comparing the influence of policies on consumer behavior. Revealed preference models assume that the preferences of consumers can be revealed by their purchasing habits.
In economics, convex preferences are an individual's ordering of various outcomes, typically with regard to the amounts of various goods consumed, with the property that, roughly speaking, "averages are better than the extremes". The concept roughly corresponds to the concept of diminishing marginal utility without requiring utility functions.
Competitive equilibrium is a concept of economic equilibrium, introduced by Kenneth Arrow and Gérard Debreu in 1951, appropriate for the analysis of commodity markets with flexible prices and many traders, and serving as the benchmark of efficiency in economic analysis. It relies crucially on the assumption of a competitive environment where each trader decides upon a quantity that is so small compared to the total quantity traded in the market that their individual transactions have no influence on the prices. Competitive markets are an ideal standard by which other market structures are evaluated.
In economics, and in other social sciences, preference refers to an order by which an agent, while in search of an "optimal choice", ranks alternatives based on their respective utility. Preferences are evaluations that concern matters of value, in relation to practical reasoning. Individual preferences are determined by taste, need, ..., as opposed to price, availability or personal income. Classical economics assumes that people act in their best (rational) interest. In this context, rationality would dictate that, when given a choice, an individual will select an option that maximizes their self-interest. But preferences are not always transitive, both because real humans are far from always being rational and because in some situations preferences can form cycles, in which case there exists no well-defined optimal choice. An example of this is Efron dice.
The Shapley–Folkman lemma is a result in convex geometry that describes the Minkowski addition of sets in a vector space. It is named after mathematicians Lloyd Shapley and Jon Folkman, but was first published by the economist Ross M. Starr.
Some branches of economics and game theory deal with indivisible goods, discrete items that can be traded only as a whole. For example, in combinatorial auctions there is a finite set of items, and every agent can buy a subset of the items, but an item cannot be divided among two or more agents.
In economics, the Debreu's theorems are preference representation theorems—statements about the representation of a preference ordering by a real-valued utility function. The theorems were proved by Gerard Debreu during the 1950s.
In economics and consumer theory, a linear utility function is a function of the form:
Efficiency and fairness are two major goals of welfare economics. Given a set of resources and a set of agents, the goal is to divide the resources among the agents in a way that is both Pareto efficient (PE) and envy-free (EF). The goal was first defined by David Schmeidler and Menahem Yaari. Later, the existence of such allocations has been proved under various conditions.
Fisher market is an economic model attributed to Irving Fisher. It has the following ingredients:
Egalitarian equivalence (EE) is a criterion of fair division. In an egalitarian-equivalent division, there exists a certain "reference bundle" such that each agent feels that his/her share is equivalent to .
In theoretical economics, an abstract economy is a model that generalizes both the standard model of an exchange economy in microeconomics, and the standard model of a game in game theory. An equilibrium in an abstract economy generalizes both a Walrasian equilibrium in microeconomics, and a Nash equilibrium in game-theory.
Market equilibrium computation is a computational problem in the intersection of economics and computer science. The input to this problem is a market, consisting of a set of resources and a set of agents. There are various kinds of markets, such as Fisher market and Arrow–Debreu market, with divisible or indivisible resources. The required output is a competitive equilibrium, consisting of a price-vector, and an allocation, such that each agent gets the best bundle possible given the budget, and the market clears.