# Budget Line

Budget line (also known as budget constraint) is a schedule or a graph that shows a series of various combinations of two products that can be consumed at a given income and prices.

Budget line is to consumers what a production possibilities curve is to producers. It is a useful tool in understanding consumer behavior and choices. Budget line depicts the consumer choices between two products. Number of units of one product are displayed along horizontal axis while those of the other along vertical axes. Each possible combination of the two products is then plotted to obtain a budget constraint curve.

A budget line is a constraint in that it limits the total potential consumption of a consumer. Only such combination of two goods is attainable which falls within or on the budget line. Any combination of two goods which falls outside the budget line is unattainable.

Together with a consumer’s indifference curves, which shows different combinations of two products which give the consumer the same utility, we can arrive at a combination of two goods which is optimal for the consumer i.e. which gives the consumer maximum attainable satisfaction.

## Budget Constraint Equation

Total spending on any combination of goods on the budget line is equal to consumer income. It can be expressed mathematically as follows:

$$ \text{Q} _ \text{A} \text{P} _ \text{A}+\text{Q} _ \text{B} \text{P} _ \text{B}=\text{I} $$

Where Q_{A} and Q_{B} are the units of good A and good B, P_{A} and P_{B} are their corresponding prices and I is total income of the consumer.

Let’s assume Product A is on y-axis and Product B is on x-axis. We can write the budget constraint in the standard format of the straight-line equation:

$$ \text{Q} _ \text{A}=\frac{\text{I}}{\text{P} _ \text{A}}-\frac{\text{P} _ \text{A}}{\text{P} _ \text{B}}\times \text{Q} _ \text{B} $$

It shows that the slope of the budget line equals the negative of the ratio of price of the good on x-axis on the price of the good on y-axis.

The budget line shifts when a consumer income changes: it shifts inwards when income decreases and shifts outwards when income increases. But when there is a change in price of only one good, the budget line rotates i.e. it shifts but not parallelly.

## Example

Assume you have received a $50 app store gift card from your friend. You are considering buying video games and songs for your smartphone. The price of a game is $5 and that of a song is $1. You can either spend the whole amount on games, in which case the games purchased would be 10 [=$50/5]. Or you can spend the whole amount on music, in which case the number of songs purchased would 50.

Let us say the number of songs are represented along horizontal axis X and those of games along vertical axis Y. We now have two points on budget line (0,10) and (50,0).

The above combinations will rarely be purchased by a typical consumer. You are mostly likely to buy both games and songs in some quantity above zero. Let’s say you buy 6 games. That would be $30 [=4×5]. The remaining amount can buy you 20 songs. We now have another point on the graph (20,6).

If we plot the above points and any other possible combinations you might choose, we obtain a straight budget line as shown below:

## Graph

Attainable combination is any combination of two products which may be purchased using the given income. All points on or below the budget line are attainable, for example, 20 songs and 4 games.

Unttainable combination is any combination of two products which is impossible to purchase using the given income. All points above the budget line are un-attainable, for example, 30 songs and 6 games.

by Irfanullah Jan, ACCA and last modified on