All bundles a consumer can afford based on various conditions
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 prices of commodities available to the consumer and the consumer's income. Let the number of commodities available to the consumer in an economy be finite and equal to formula_1. Thus, for commodity amounts formula_2, also known as consumption plans which should not exceed the income, with associated prices formula_3 and consumer income formula_4, the budget set is defined as
formula_5,
where the consumption set is taken to be formula_6. It is typically assumed that formula_7 and formula_8, in which case formula_9 is also known as the Walrasian, or competitive, budget set.
The budget set is bounded above by a formula_1-dimensional budget hyperplane characterized by the equation formula_11, which in the two-good case corresponds to the budget line. Graphically, the budget set is the subset of formula_12 that contains all the consumption bundles that lie on or below the budget hyperplane.
Given the framework described above, Walrasian budget sets are convex and compact.
Other sources of wealth, including stocks, savings, 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 formula_13 is the set that the consumer chooses to go with based on the preferences from the budget set.
References.
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