Editing Budget constraint (section)

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

There are 2 requirements for this case. The first one is that the constraint is not affected if the prices are multiplied by any positive scalar. The second one is that all commodities are desirable and the constraint will always be binding.  

In such a case, assuming there are <math>n\,</math> goods, called <math>x_i\,</math> for <math>i=1,\dots,n\,</math>, that the price of good <math>x_i\,</math> is denoted by <math>p_i\,</math>, and if <math>\,W\,</math> is the total amount that may be spent, then the budget constraint is:
:<math>\sum_{i=1}^np_ix_i\leq W.</math>

Further, if the consumer spends his income entirely, the budget constraint binds:
:<math>\sum_{i=1}^np_ix_i=W.</math>
In this case, the consumer cannot obtain an additional unit of good <math>x_i\,</math> without giving up some other good. For example, he could purchase an additional unit of good <math>x_i\,</math> by giving up <math>p_i/p_j\,</math> units of good <math>x_j.\,</math>