Budget constraint

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A Budget constraint represents the combinations of goods and services that a consumer can purchase given current prices with his or her 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. All two dimensional budget constraints are generalized into the equation:

((Px)(X))+((Py)(Y))=m

m= money income allocated to consumption (after saving and borrowing)

Px= the price of a specific good

Py= the price of all other goods

x= amount purchased of a specific good

y= amount purchased of all other goods

The equation can be rearraged to represent the shape of the curve on a graph:

y= (I/Py)-(Px/Py), where I/Py is the y-intercept and -Px/Py is the slope, representing a downward sloping budget line.

The factors that can shift the budget line are a change in income (I), a change in the price of a specific good (Px), or a change in the price of all other goods (Py).

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 goods, called for , and that the price of good is denoted by , if is the total amount that may be spent, then the budget constraint is:

Further, if the consumer spends his income entirely, the budget constraint binds:

In this case, the consumer cannot obtain an additional unit of good without giving up some other good. For example, he could purchase an additional unit of good by giving up units of good