# Budget set

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A budget set or opportunity set includes all possible consumption bundles that someone can afford given the prices of goods and the person's income level. The budget set is bounded above by the budget line. In set notation, for consumption goods $\mathbf {x} =\left[x_{1},x_{2},\ldots ,x_{k}\right]$ with associated prices $\mathbf {p} =\left[p_{1},p_{2},\ldots ,p_{k}\right]$ , the budget set is A price is the quantity of payment or compensation given by one party to another in return for one unit of goods or services.. A price is influenced by both production costs and demand for the product. A price may be determined by a monopolist or may be imposed on the firm by market conditions.

Income is the consumption and saving opportunity gained by an entity within a specified timeframe, which is generally expressed in monetary terms.

Sets are fundamental objects in mathematics. Intuitively, a set is merely a collection of elements or members. There are various conventions for textually denoting sets. In any particular situation, an author typically chooses from among these conventions depending on which properties of the set are most relevant to the immediate context or on which perspective is most useful.

$B=\left\{\mathbf {x} \in X:\mathbf {p} \mathbf {x} \leq m\right\}$ where $m$ is income, and the consumption set $X$ is assumed to be the nonnegative orthant in $\mathbb {R} ^{k}$ . In geometry, an orthant or hyperoctant is the analogue in n-dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions.

Graphically speaking, all the consumption bundles that lie inside the budget constraint and on the budget constraint form the budget set or opportunity set. In economics, a budget constraint represents all the combinations of goods and services that a consumer may purchase given current prices within his or her given income. Consumer theory uses the concepts of a budget constraint and a preference map to analyze consumer choices. Both concepts have a ready graphical representation in the two-good case.

By most definitions, budget sets must be compact and convex. In geometry, a convex set or a convex region is a subset of a Euclidean space, or more generally an affine space over the reals, that intersects every line into a line segment. Equivalently, this is a subset that is closed under convex combinations. For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex.

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• Mas-Colell, Andreu; Whinston, Michael D.; Green, Jerry R. (1995). Microeconomic Theory. New York: Oxford University Press. pp. 9–11. ISBN   0-19-507340-1. Andreu Mas-Colell is a Spanish economist, an expert in microeconomics and one of the world's leading mathematical economists. He is the founder of the Barcelona Graduate School of Economics and a professor in the department of economics at Pompeu Fabra University in Barcelona, Catalonia, Spain. He has also served several times in the cabinet of the Catalan government. Summarizing his and others' research in general equilibrium theory, his monograph gave a thorough exposition of research using differential topology. His textbook on microeconomics, co-authored with Michael Whinston and Jerry Green, is the most used graduate microeconomics textbook in the world.

Michael Whinston is an American economist and currently the Sloan Fellows Professor at Massachusetts Institute of Technology. Previously he was the Robert E. and Emily H. King Professor at Northwestern University and is also a Fellow to the American Academy of Arts and Sciences and Econometric Society. The International Standard Book Number (ISBN) is a numeric commercial book identifier which is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.