Budget constraint

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

Budget

A budget is generally a list of all planned expenses and revenues. It is a plan for saving and spending. A budget is an important concept in microeconomics, which uses a budget line to illustrate the trade-offs between two or more goods...

 constraint

Constraint (mathematics)

In mathematics, a constraint is a condition that a solution to an optimization problem must satisfy. There are two types of constraints: equality constraints and inequality constraints...

 and a preference map to analyze consumer choices. Both concepts have a ready graphical representation

Consumer theory

Consumer theory is a theory of microeconomics that relates preferences to consumer demand curves. The link between personal preferences, consumption, and the demand curve is one of the most complex relations in economics...

 in the two-good case.

An individual consumer

Consumer

Consumer is a broad label for any individuals or households that use goods and services generated within the economy. The concept of a consumer is used in different contexts, so that the usage and significance of the term may vary....

 will choose to consume goods at the point where the most preferred available indifference curve

Indifference curve

In microeconomic theory, an indifference curve is a graph showing different bundles of goods, each measured as to quantity, between which a consumer is indifferent. That is, at each point on the curve, the consumer has no preference for one bundle over another. In other words, they are all equally...

 on their preference map is tangent

Tangent

In geometry, the tangent line to a curve at a given point is the straight line that "just touches" the curve at that point...

 to their budget constraint.

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

Budget

A budget is generally a list of all planned expenses and revenues. It is a plan for saving and spending. A budget is an important concept in microeconomics, which uses a budget line to illustrate the trade-offs between two or more goods...

 constraint

Constraint (mathematics)

In mathematics, a constraint is a condition that a solution to an optimization problem must satisfy. There are two types of constraints: equality constraints and inequality constraints...

 and a preference map to analyze consumer choices. Both concepts have a ready graphical representation

Consumer theory

Consumer theory is a theory of microeconomics that relates preferences to consumer demand curves. The link between personal preferences, consumption, and the demand curve is one of the most complex relations in economics...

 in the two-good case.

Individual choice

An individual consumer

Consumer

Consumer is a broad label for any individuals or households that use goods and services generated within the economy. The concept of a consumer is used in different contexts, so that the usage and significance of the term may vary....

 will choose to consume goods at the point where the most preferred available indifference curve

Indifference curve

In microeconomic theory, an indifference curve is a graph showing different bundles of goods, each measured as to quantity, between which a consumer is indifferent. That is, at each point on the curve, the consumer has no preference for one bundle over another. In other words, they are all equally...

 on their preference map is tangent

Tangent

In geometry, the tangent line to a curve at a given point is the straight line that "just touches" the curve at that point...

 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

Factors of production

In economics, factors of production are the resources employed to produce goods and services. They facilitate production but do not become part of the product or are significantly transformed by the production process...

. Under autarky

Autarky

Autarky is the quality of being self-sufficient. Usually the term is applied to political states or their economic policies. Autarky exists whenever an entity can survive or continue its activities without external assistance. Autarky is not necessarily economic. For example, a military autarky...

 this is also the limitation of consumption by individuals in the country. However, the benefits of international trade

International trade

International trade is exchange of capital, goods, and services across international borders or territories. In most countries, it represents a significant share of gross domestic product . While international trade has been present throughout much of history , its economic, social, and political...

 are generally demonstrated through allowance of a shift in the consumption-possibility frontier

Consumption-possibility frontier

The CPF, or consumption-possibility frontier, is the budget constraint where participants in international trade can consume. Under autarky this constraint is identical to the production-possibility frontier....

s 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