In economics, a budget set, or the opportunity set facing a consumer, is the set of all possible consumption bundles that the consumer can afford taking as given the

price A price is the (usually not negative) quantity of payment or compensation given by one party to another in return for goods or services. In some situations, the price of production has a different name. If the product is a "good" in t ...

s of commodities available to the consumer and the consumer's

income Income is the consumption and saving opportunity gained by an entity within a specified timeframe, which is generally expressed in monetary terms. Income is difficult to define conceptually and the definition may be different across fields. F ...

. Let the number of commodities available to the consumer in an economy be finite and equal to

k

. Thus, for commodity amounts

\mathbf = \left x_, x_, \ldots, x_ \right /math>, also known as consumption plans which should not exceed the income, with associated prices \mathbf = \left p_, p_, \ldots, p_ \right /math> and consumer income m, the budget set is defined as
: B_ = \left\,
where the consumption set is taken to be X = \mathbb^_. It is typically assumed that \mathbf >> 0 and m \in \mathbb_, in which case B is also known as the Walrasian, or competitive, budget set.

The budget set is bounded above by a k -dimensional budget

hyperplane In geometry, a hyperplane is a subspace whose dimension is one less than that of its '' ambient space''. For example, if a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hype ...

characterized by the equation

\mathbf \mathbf = m

, which in the two-good case corresponds to the budget line. Graphically, the budget set is the subset of

\mathbb^_

that contains all the consumption bundles that lie on or below the budget hyperplane. Given the framework described above, it can be shown that Walrasian budget sets are

convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytop ...

and

compact Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to: * Interstate compact * Blood compact, an ancient ritual of the Philippines * Compact government, a type of colonial rule utilized in British ...

. Other sources of wealth, including

stocks Stocks are feet restraining devices that were used as a form of corporal punishment and public humiliation. The use of stocks is seen as early as Ancient Greece, where they are described as being in use in Solon's law code. The law describing ...

savings Wealth is the abundance of valuable financial assets or physical possessions which can be converted into a form that can be used for transactions. This includes the core meaning as held in the originating Old English word , which is from an ...

, pensions, profit shares, etc., are not included in the income described above. The income described above are also known as initial wealth. The demand set

\phi(p,m)

is the set that the consumer chooses to go with based on the

preferences In psychology, economics and philosophy, preference is a technical term usually used in relation to choosing between wikt:alternative, alternatives. For example, someone prefers A over B if they would rather choose A than B. Preferences are centra ...

from the budget set.

References

* Set Consumer theory {{Microeconomics-stub