# What Is a Budget Constraint and How Do You Use the Equation?

Updated September 30, 2022

For businesses and individuals alike, there is usually a finite supply of funds that they can spend on goods or services. This means that within their budgets, a spending strategy can help to calculate the limit, which is the constraints of their budget. Understanding what these constraints are and knowing some helpful calculations to determine how much to spend and on what is vital for those who keep to particular budgets. In this article, we define what a budget constraint is, explain how they work, describe opportunity costs and sunken costs, and offer helpful examples.

## What is a budget constraint?

A budget constraint is a term of economics, which refers to the combined amount of items you can afford within the limitations of your funds. For instance, if you're a marketing executive with a \$2,000 budget for advertizing materials, this figure establishes the top limit of the amount of materials you can afford. Here, the cost of each item and the minimum quantity you require determines how many you can purchase within the constraints of your budget.

Time can also relate to this principle. For managers with staff who have a finite amount of hours in their workday, it's helpful to work out how much time they may spend on each task they set out to accomplish. In this example, the calculation may vary across work weeks as business priorities shift and employee availability changes. Regardless, calculating the constraints on your budget can be helpful for reassessing productivity for the week to come.

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## How do budget constraints work?

It's common for there to be many considerations when calculating what you can do within the limitations of your budget. Conducting a constraint calculation can help to determine the proportion of each expenditure you can afford. If you're a department manager, for instance, working out the constraints to your budget can be helpful in finding if the budget you have is sufficient for your required spending. Knowing how much you can spend on expenditures like supplies, training materials, and salaries, and how much of each you can afford, is key to determining if you require additional funding.

It may be beneficial when using a constraint equation to consider just two sets of items at a time. This can make it easier to determine the limitations of particular costs. Considering only a few expenses at a time simplifies the equation and allows you to compare how important each is in relation to the other. If you know you require a minimum supply of one resource, you can factor that into your budget. Then, you calculate how much of a secondary resource you can afford. This reduces the complexity of the calculation and makes it faster to complete.

## Budget constraint equation

The following equation can help you to calculate the constraints of your budget:

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

In the above equation, P1 is the cost of the first item, and P2 is the cost of the second item. M represents the amount of money available in the budget. Q1 and Q2 represent the quantity of each item for which you're calculating the purchase costs. Expressing this calculation verbally, you might say that the cost of the total number of the first set of items added to the cost of the total number of the second set of items equals the funds you have available to spend.

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## What is opportunity cost?

Opportunity cost is the amount of funds you've allocated to a single item preferentially over others. For instance, if you spend \$100 on dinner in a restaurant, that amount of money represents the opportunity cost. In this instance, the opportunity cost is the money you didn't allocate to buying groceries or clothing. In the context of businesses, opportunity cost may be the money you spend on rewarding employees with gift cards at the end of the year, rather than simply spending the money on paying them to work.

When determining the constraints of your budget, calculating your opportunity cost can influence your financial decisions. Imagine that a department spends \$300 month on a coffee machine for its employees, whereas supplying instant coffee costs about \$50 a month. Here, the opportunity cost is the difference between these two values, representing the expense of the potential opportunity, which is \$250 a month. After a year, this means a \$3,000 opportunity cost. When assessing the constraints of your budget, you may decide that this is a worthwhile cost, or reassign that spending to more deserving expenses.

## What is sunk cost?

Sunk costs are the expenses you've paid, which you can't recover. These costs can include labour, or relate to other financial expenses such as consumables like office supplies. In a personal context, you may purchase a two-hour theatre ticket, but walk out after 15 minutes because you weren't enjoying the production. Here, what you spent on the show is a sunk cost, which you aren't likely to get back.

The same applies to a company when they abandon investments, such as recalling faulty products they've manufactured. They may write off the money and time spent on materials, labour, and planning as sunk costs. With constraints to budgets, since these decisions only consider your current financial situation, any past sunk costs don't factor into constraint equations.

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## Examples of budget constraints

Reviewing hypothetical examples of calculations for budget constraints can be helpful in understanding how they work in a real life context. Regardless of whether you use this equation to establish the limitations to your personal or professional budgets, breaking them down can be insightful. Below are a few helpful examples of situations where you might use constraint equations:

### Example of constraint calculations for personal budgets

Martin has a weekly budget of \$15 a week to buy rice and cans of tuna. At Martin's local grocery store, a bag of rice costs \$5 and the cans of tuna cost \$1 each. If Martin spent the whole \$15 amount on just rice, he can afford three bags. Martin can express this option using the following equation:

(rice x 3) + (tuna x 0) = \$15

If Martin spends the full \$15 on only cans of tuna, he can afford 15 cans. Applying the equation, that calculates as:

(rice x 0) + (tuna x 15) = \$15

Martin needs both rice and tuna, meaning he requires his equation to factor in both items to figure out how much of each he can afford when he purchases them together from the same budget. To do this, he can rework his equation until the sum of the values before the equals sign matches that after it, or the M value representing his budget. For example, if he knows he needs at least two bags of rice, he can then balance the equation to include a complimentary value for his other item, the tuna. The equation may look like this:

(rice x 2) + (tuna x 5) = \$15

Resolving this equation, it becomes:

(\$5 x 2) + (\$1 x 5) = \$15

\$10 + \$5 = \$15

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### Example of constraint calculations for a business

SoulBoi Shoes is a trendy footwear brand which resonates with its consumers through advertizing. It has a monthly budget of \$6,000 to spend on television and social media ads. The television slot costs them \$300 per occasion, while their social media ads cost \$200 a post. If the brand purchases only television slots, they can afford 20 screenings a month, meaning their equation is:

(television x 20) + (social media x 0) = \$6,000

If Soulboi Shoes purchase only social media posts, they can afford 30 posts, and their equation is:

(television x 0) + (social media x 30) = \$6,000

To maximize their marketing channels, Soulboi knows they benefit from purchasing both television and social media costs. Because of this, they factor both types into their constraint calculation to determine how many occasions on each channel they can afford within their \$6000 budget. They also know that the minimum number of social media posts to provide a significant return on investment is 15 per month, so this is an opportunity cost. From this, they work out that they can afford 15 social media posts, and use the remaining budget to pay for television slots. Their equation, in this case, is:

(television x 10) + (social media x 15) = \$6,000

If they resolve this equation, it becomes:

(\$300 x 10) + (\$200 x 15) = \$6,000

\$3000 + \$3000 = \$6,000

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