Given an allocation of two goods, the budget line through that allocation is the set of all other allocations of the two goods that someone in a market could arrive at by selling one of the goods for the other.

For instance, if I have four dogs and two horses, and each horse is worth two dogs, then the budget line through my present allocation includes the following other allocations:

• eight dogs
• six dogs and one horse
• two dogs and three horses
• four horses

It is often useful to plot budget lines in conjunction with indifference curves. Budget lines are the same throughout a market, but indifference curves are personal. A budget line tangent to Bob's indifference curve represents an allocation from which Bob cannot trade without reaching a less valuable (to Bob) allocation. At any other allocation, Bob will trade.