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 map to analyze consumer choices. Both concepts have a ready graphical representation in the two-good case.

Uses

Individual choice

An individual consumer will choose to consume goods at the point where the most preferred available indifference curve on their preference map is tangent to their budget constraint.

International economics

A production-possibility frontiers is a budget constraint presented by the limitation of available factors of production. Under autarky this is also the limitation of consumption by individuals in the country. However, the benefits of international trade are generally demonstrated through allowance of a shift in the consumption-possibility frontiers of each trade partner which allows access to a more appealing indifference curve.

Many goods

While low level demonstrations of budget constraints are often limited to two good situations which provide easy graphical representation, it is possible to demonstrate the relationship between multiple goods through a budget constraint.

In such a case, assuming there are $n,$ goods, called $x\_i,$ for $i=1,dots,n.,$, and that the price of good $x\_i,$ is denoted by $p\_i.,$, if $,W,$ is the total amount that may be spent, then the budget constraint is:

$sum\_\{i=1\}^np\_ix\_ileq\; W.$

Further, 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 $x\_i,$ without giving up some other good. For example, he could purchase an additional unit of good $x\_i,$ by giving up $p\_i/p\_j,$ units of good $x\_j.,$