Budget constraint
A budget constraint represents all the combinations of goods and services that a consumer may purchase given current prices within his or her given 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.
Consumer behaviour is a maximisation problem. It means making the most of our limited resources to maximise our utility. As consumers are insatiable, and utility functions grow with quantity, the only thing that limits our consumption is our own budget.
An individual consumer should choose to consume goods at the point where the most preferred available indifference curve on his preference map is tangent to his budget constraint. That is, the indifference curve tangent to the budget constraint represents the maximum utility obtained utilizing the entire budget of the consumer. The tangent point (the xy coordinate) represents the amount of goods x and y the consumer should purchase to fully utilize their budget to obtain maximum utility. A line connecting all points of tangency between the indifference curve and the budget constraint is called the expansion path.
All two dimensional budget constraints are generalized into the equation:
Where:
The equation can be rearranged to represent the shape of the curve on a graph:
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