# Budget Constraints: Definition & Formula

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• 0:04 Consumer Choices
• 0:34 The Budget Constraint
• 1:40 The Budget Constraint Formula
• 2:39 Final Example
• 3:14 Lesson Summary
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Lesson Transcript
Instructor: James Walsh

M.B.A. Veteran Business and Economics teacher at a number of community colleges and in the for profit sector.

Budget constraints limit consumer choices based on the amount of income they have to spend. In this lesson, you will learn how to determine budget constraints using a formula, as well as how to graph them.

## Consumer Choices

Maria works hard for her money. After she pays the rent and bills, she even has some left over to spend on fun things. There are two things she likes the most: pizza, especially with lots of cheese and veggies, and going to concerts with her friends.

If it were up to Maria, she would eat pizza and go to a concert every night. But she knows if she does that she will run out of money long before payday, and she would get pretty hungry without any pizza! So she has to make a choice between pizza and concerts, and how many of each she will plan to buy.

## The Budget Constraint

Economics can help Maria with this decision. She has what economists call a constraint on her choices, and that is her income. Economists call that a budget constraint, which illustrates the possible combination of two products that don't exceed the budgeted income.

Maria has \$500 left over every month. We can show her possible choices on a graph if we know the prices for pizzas and concerts. Let's say concerts cost \$100 and pizzas cost \$20. The line shows combinations of pizzas and concerts that cost exactly \$500. Her possible choices are known as the budget set, and are shown on the graph appearing here as the area below and to the left of the line:

If Maria spends the whole \$500 on pizza, she will be able to buy 25 of them. That is shown as the horizontal intercept on the graph. Likewise, if she spends it all on concerts, she will go to five. That is the vertical intercept on the graph. Checking the graph, if Maria chooses two concerts and ten pizzas, she will not exceed her budget constraint. But if she chooses four concerts and fifteen pizzas, she will exceed it and be broke.

## The Budget Constraint Formula

We can also define all of the combinations of two things that cost a certain amount with the budget constraint formula:

This is where Y = income, PA = price of item A, and QA= quantity of item A consumed. PB = price of item B, while QB = quantity of item B consumed.

Maria knows that her income to spend is \$500, and what concerts and pizzas cost. When she puts those numbers into the formula, it looks like this:

\$500 = \$100 * QA + \$20 * QB, where QA is the number of concerts and QB is how many pizzas.

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