Equation of the Budget Line

The budget line is a graphical representation of the budget constraint, which shows the different combinations of two goods that a consumer can afford. The equation of the budget line can be written as:

Budget = (Price of Good X * Quantity of Good X) + (Price of Good Y * Quantity of Good Y)

In this equation, the budget represents the total amount of money available to the consumer, and the prices and quantities of the goods are variables.

Slope of the Budget Line

The slope of the budget line represents the rate at which the consumer can trade one good for another. It is calculated as the ratio of the prices of the two goods.

Slope = Price of Good X / Price of Good Y

The slope of the budget line is negative because as the consumer purchases more of one good, they must give up some of the other good to stay within their budget.

Changes to the Budget Line

Changes in income or prices can cause the budget line to shift or pivot. When income changes, the intercepts of the budget line change, reflecting the new budget constraint. When prices change, the slope of the budget line changes, indicating the new relative prices of the goods.

1. Changes in Income

An increase in income will cause the budget line to shift rightward, as the consumer can now afford more of both goods. A decrease in income will cause the budget line to shift leftward, as the consumer can now afford less of both goods.

2. Changes in Prices

An increase in the price of one good will cause the budget line to pivot inward, as the consumer can now afford less of that good. A decrease in the price of one good will cause the budget line to pivot outward, as the consumer can now afford more of that good.

Sources

• Budget Equation | StudyPug
• 6.1 The Budget Line – Principles of Microeconomics
• How to Calculate the Budget Line

FAQs

What is the budget line?

The budget line is a graphical representation of the budget constraint, showing the various combinations of two goods that a consumer can afford.

What is the equation of the budget line?

The equation of the budget line can be written as:

Budget = (Price of Good X * Quantity of Good X) + (Price of Good Y * Quantity of Good Y)

What does the slope of the budget line represent?

The slope of the budget line represents the rate at which the consumer can trade one good for another. It is calculated as the ratio of the prices of the two goods.

What happens to the budget line when income changes?

When income changes, the intercepts of the budget line change, reflecting the new budget constraint. An increase in income will cause the budget line to shift rightward, while a decrease in income will cause it to shift leftward.

What happens to the budget line when the price of a good changes?

When the price of a good changes, the slope of the budget line changes, indicating the new relative prices of the goods. An increase in the price of one good will cause the budget line to pivot inward, while a decrease in the price of one good will cause it to pivot outward.

What is the relationship between the budget line and consumer choice?

The budget line represents the consumer’s budget constraint, while consumer choice is the selection of a combination of goods that maximizes the consumer’s utility. The optimal choice is the point on the budget line where the consumer’s indifference curve is tangent to the budget line.

How does the budget line change when both income and prices change?

When both income and prices change, the budget line can shift and pivot. The direction and magnitude of the shift and pivot depend on the specific changes in income and prices.

What is the significance of the budget line in economic analysis?

The budget line is a fundamental tool in economic analysis. It is used to study consumer choice, market equilibrium, and the effects of changes in income and prices on consumer behavior.