In economics, abudget set, or the opportunity set facing a consumer, is the set of all possible consumption bundles that the consumer can afford taking as given theprices of commodities available to the consumer and the consumer'sincome. Let the number of commodities available to the consumer in an economy be finite and equal to${\displaystyle k}$. Thus, for commodity amounts${\displaystyle \mathbf{x}=\left[x_1,x_2,\dots ,x_k\right]}$, also known as consumption plans which should not exceed the income,^[1] with associated prices${\displaystyle \mathbf{p}=\left[p_1,p_2,\dots ,p_k\right]}$ and consumer income${\displaystyle m}$, the budget set is defined as

${\displaystyle B_{\mathbf{p},m}=\left\{\mathbf{x}\in X:\mathbf{p}\mathbf{x}\le m\right\}}$,

where the consumption set is taken to be${\displaystyle X={\mathbb{R}}_{+}^k}$. It is typically assumed that${\displaystyle \mathbf{p}\gg 0}$ and${\displaystyle m\in {\mathbb{R}}_{+}}$, in which case${\displaystyle B}$ is also known as theWalrasian, orcompetitive, budget set.

The budget set is bounded above by a${\displaystyle k}$-dimensional budgethyperplane characterized by the equation${\displaystyle \mathbf{p}\mathbf{x}=m}$, which in the two-good case corresponds to thebudget line. Graphically, the budget set is the subset of${\displaystyle {\mathbb{R}}_{+}^k}$ that contains all the consumption bundles that lie on or below the budget hyperplane.

Given the framework described above, Walrasian budget sets areconvex andcompact.

Other sources of wealth, includingstocks,savings,pensions, profit shares, etc., are not included in the income described above. The income described above are also known as initial wealth.^[1]

The demand set${\displaystyle \varphi (p,m)}$ is the set that the consumer chooses to go with based on thepreferences from the budget set.^[1]

• 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.

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