# What Is a Budget Constraint? (With Example)

Updated March 10, 2023

Most businesses have limited funds to spend on goods and services. They must, therefore, be selective about how much they spend on each item within their budget constraints. To stay within that budget, they need to determine how much to spend on various items and related costs. In this article, we discuss what budget constraints are, explain how they work and explore opportunity costs and sunk costs.

Related: How To Create a Flexible Budget (With Example)

Key takeaways

• Budget constraint is the total amount of items you can afford within a current budget.

• Budget constraint illustrates the range of choices available within that budget.

• Opportunity cost is the amount or item you give up in exchange for something else.

• Sunk cost is the amount spent in the past and cannot be recovered.

## What is a budget constraint?

A budget constraint is an economic term referring to the combined amount of items you can afford within the amount of income available to you. For example, if you are a sales professional with a \$1,000 budget for promotional items, this sets the upper limit on items you can purchase. The cost of each item and the minimum quantity you need would determine how many you can buy within your budget.

The same principle of budget constraint can also be applied to time. If you are a manager, your employees only have a certain number of hours in a workday, which means you need to determine how much of their time they should spend on the various things they need to accomplish. The calculation may vary from week to week as your business priorities change and your employees' available time adjusts since some weeks include holidays or employees might take time off.

Related: What Is a Budget?

## How do budget constraints work?

When calculating budget constraints, you normally have a number of things under consideration for which you are trying to budget. However, it's easier to understand how budget constraints work if you just consider two sets of items. You could spend your entire budget on item one, or you could spend it all on item two. Alternatively, you could buy a combination of some of item one and some of item two. The proportions of each item you purchase would be constrained by your budget.

If you are managing a department, calculating your budget constraint can help you determine whether the amount budgeted to you is adequate for your needs. Knowing how many things such as salaries, supplies and training materials you can afford within your budget constraint can help you determine if you need to request additional funding from your senior management.

## Budget constraint equation

You can use the following equation to help calculate budget constraint:

(P1 x Q1) + (P2 x Q2) = m

In this equation, P1 is the cost of the first item, P2 is the cost of the second item and m is the amount of money available. Q1 and Q2 represent the quantity of each item you are purchasing. You could express this equation verbally by saying that the cost of the total number of X items added to the cost of the total number of Y items must equal the amount of money or income you have available.

If you draw this equation on a graph where the x-axis represents quantities of one item and the y-axis represents quantities of the other, it should plot a straight diagonal line sloping down from the left side to the right side. This line is called the budget line. Any point along the budget line indicates the quantities of each item you could purchase within your budget. If the price of one or both items changes, you would need to adjust this line accordingly.

## What is opportunity cost?

Opportunity cost is the term economists give to the amount of money you've allocated to one item in preference to other items. For example, if you spend \$50 on a gift for a friend, that \$50 represents the opportunity cost. In other words, it's the money you didn't spend on eating at an expensive restaurant, concert tickets or for some other purpose.

For a business, opportunity cost could be the time and money spent on a team-building weekend for your employees, as opposed to having the employees work and spending the same amount of money elsewhere.

Identifying the opportunity cost can influence the financial decisions you make when determining your budget constraint. If your business spends \$10,000 per month on a catering service to provide lunch for employees, whereas installing vending machines would cost \$2,000 per month, the opportunity cost of using a caterer is \$8,000. Over a year, that would be \$96,000 of your total operating costs. If you're looking to increase spending on other items, you might consider the vending machine option.

Related: How To Calculate Opportunity Cost: Steps and Examples

## What is sunk cost?

Sunk costs refer to costs that you incurred in the past that you can't recover. These costs may be financial or in terms of time or labor. For example, if you buy a ticket to see a two-hour movie and walk out after 10 minutes because you don't like the movie, the money you spent on the movie ticket would be a sunk cost. Similarly, if a company abandons a new product that doesn't sell or live up to expectations, the time and money spent developing it would be written off as a sunk cost.

Since budget constraint decisions take into account your current financial situation, any past losses or sunk costs should not factor into your budget planning.

Read more: Four Examples of Sunk Cost

## Example 1

Jo has a budget of \$20 per week with which to buy bread and orange juice. At Jo's local grocery store, a loaf of bread costs \$2 and a bottle of orange juice costs \$4. If Jo spent \$20 only on bread, she could buy 10 loaves. You can express this using the budget constraint equation:

(P1 x Q1) + (P2 x Q2) = m

(Bread x 10) + (juice x 0) = \$20

If Jo spent \$20 only on orange juice, she could buy five bottles. Using the above equation, this would be:

(Bread x 0) + (juice x 5) = \$20

Jo wants to buy both bread and orange juice. This means she needs to calculate how much of each she can buy within her budget. If she plots a budget line on a graph showing quantities of bread on the x-axis and orange juice on the y-axis, she could use that to see how much bread she could buy, depending on how much juice she purchases.

For example, if she buys three bottles of orange juice, she could purchase four loaves of bread.

Using the equation, this would be:

(Bread x 4) + (juice x 3) = \$20

If you resolve this equation, it becomes:

(\$2 x 4) + (\$4 x 3) = 20

\$8 + \$12 = \$20

### Example 2

The Bread Co. has \$1,000 a month to spend on radio and social media advertising. The radio spots cost \$200 each and the social media ads are \$100 each. If the company buys only radio spots, the equation would be:

(P1 x Q1) + (P2 x Q2) = m

(Radio x 5) + (social media x 0) = \$1,000

If the Bread Co. bought only social media spots, the equation would be:

(Radio x 0) + (social media x 10) = \$1,000

The company wants to buy both, so it uses the budget constraint calculation to see how much of each can be bought within the current \$1,000 budget. The graph plot line would show many radio spots could be purchased depending on the number of social media ads bought.

Using the equation, this would be:

(Radio x 4) + (social media x 2) = \$1,000

If you resolve this equation, it becomes:

(\$200 x 4) + (\$100 x 2) = 1,000

\$800 + \$200 = \$1,000