A Budget Constraint represents the combinations of goods and services that a consumer can purchase given current prices and his income. Consumer theory uses the concepts of a budget constraint and a preference ordering to analyze consumer choices. Both concepts have a ready graphical representation in the two-good case.

Many goods

Suppose there are n\, goods called X_i\, for i=1,\dots,n.\, Let the price of good i\, be denoted by p_i.\, If \,W\, is the total amount that may be spent, then the budget constraint is:

\sum_{i=1}^np_ix_i\leq W.

If the consumer spends his income entirely, the budget constraint binds:

\sum_{i=1}^np_ix_i=W.

In this case, the consumer cannot obtain an additional unit of good i\, without giving up some other good. For example, he could purchase an additional unit of good i\, by giving up p_i/p_j\, units of good j.\,

See also

• Budget
• Constraint (mathematics)

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