Budget constraint

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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.

[edit] 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 $j.\,$