The sum of the total fixed and variable costs for any given level of production

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Say you're approached with a business offer from a savvy individual. They explain that they need 100 million dollars in overhead costs, but "it's not that big of a deal," they say. "How is 100 million dollars overhead not a big deal?" you exclaim. The individual says, "don't worry that 100 million dollars seem like a lot now, but when we are producing 1 billion products worldwide, it's really only 10 cents per unit sold".

Is this person crazy? Is he thinking that we can make up 100 million dollars with only 10 cents per sale going towards it? Well, the first thing we recommend is you walk away from that conman who wants your money, but secondly, he's surprisingly not wrong. Fixed costs and variable costs operate differently in a business's production, and we'll explain why the offer isn't so bad in this explanation.

Fixed Cost vs. Variable Cost Definition

Understanding different types of costs are essential for businesses to develop a strategy of providing quality products and making a profit. The two kinds of business costs are fixed costs and variable costs.Fixed costs are expenditures that occur regardless of output level. Rent, advertising, and administrative costs belong to the fixed cost category. These costs do not change whether the business produces one or a thousand units.

Fixed costs are business costs that occur regardless of output level.

See the list below of examples of various kinds of fixed costs.

Rent, lease, salaries, utilities, bills, insurance, loan repayment, depreciation, property taxes, legal expenses, advertising, production machinery, and more, depending on the type of business, are all fixed costs.

The other business cost is variable costs. Variable costs are associated with the production or rendering of a service. This means that variable costs will change whether a business produces one or one thousand units of output.

Variable Costs are business costs that fluctuate as output changes.

See the list below of examples of a few of the many kinds of variable costs.

Raw materials, hourly laborers, production supplies, sales commission, shipping, packaging, energy to production machinery, and other industry-specific production costs are all variable costs.

A business that understands how each cost changes and interacts with its production can more effectively minimize costs to improve its business.

Fixed vs. Variable Cost Pricing Model

Total cost tends to decrease at first and then increase later because of how fixed and variable costs react differently to changes in output.

Fixed costs are the elements of production that don't change with output; hence the name "fixed". Because of this, fixed costs are very high at low production levels. This is deceptive, though, as when output increases, the fixed costs become spread across a more extensive range of production. While this doesn't make fixed costs lower, it lowers the cost per unit for fixed costs.

A business with an overhead of 100 million may seem like a steep fixed cost. However, all expenses are paid for from the profit of selling output. So if the business sold 1 unit of production, it would need to cost 100 million. This contrasts sharply with changes in production. If output increases to 1 billion, the price per unit is only 10 cents.

In theory, fixed costs aren't affected by changes in output; however, the fixed production elements have a soft cap on how much output can be handled. Imagine a giant factory that's 5km in area. This factory can easily produce 1 unit or 1,000 units. Despite the building being a fixed cost, there is still a limit to how much production it can hold. Even with a large factory, supporting 100 billion production units would be challenging.

Variable costs can be difficult to understand as they change twice during production. Initially, variable costs start relatively high. This is because producing low quantities doesn't provide efficiency benefits. That changes when output increases enough that variable costs trend downward. Initially, variable costs decreased due to economies of scale.

One element of economies of scale is specialization, also known as the experience curve. This occurs as workers become familiar with and knowledgeable about the production process and become better while providing insights to improve production structure.

Despite economies of scale occurring as output increases, eventually, the opposite will happen. Past a point, diseconomies of scale begin to increase production costs. When production grows too large, it can lead to a loss of efficiency because it becomes hard to manage everything.

Fixed Cost vs. Variable cost: Cost-Based Pricing

Fixed and variable costs help businesses determine cost-based pricing, as the cost of producing a good is the summation of both. Cost-based pricing is the practice of sellers asking for a price that is derived from the cost of producing the item. This is common in competitive markets where sellers seek the lowest price to beat their rivals.

Knowing the nuances of fixed costs can give producers the option to increase their output quantities to offset significant overhead expenses. Additionally, understanding the U-shaped variable cost will allow businesses to produce at quantities that are the most cost-efficient. By finding the balance between minimizing fixed and variable costs, firms can charge the lowest price possible, beating out the competition.

Fixed and Variable Cost Formula

Businesses can use fixed and variable costs to calculate the various concepts to help them maximize their outcomes. Using these formulas can allow companies to determine how changes to their output level can reduce average fixed costs or find the optimal level of variable cost.

A firm's total cost is the sum of its production and non-production costs. Total costs are calculated by summating fixed costs like rent and salaries to variable costs like raw materials and hourly laborers.

Variable costs can be listed as average variable cost per unit or total variable cost.

\(\hbox{Total Cost}=\hbox{Fixed Costs}+\hbox{(Variable Costs}\times\hbox{Output)}\)

Average total cost is a basic formula for firms looking to maximize profit, as they can produce where the average total cost is the lowest. Or determine if selling at a higher quantity with lower profit margins will yield greater returns.

\(\hbox{Average Total Cost}=\frac{\hbox{Total Costs}}{\hbox{Output}}\)

\(\hbox{Average Total Cost}=\frac{\hbox{Fixed Costs}+\hbox{(Variable Costs}\times\hbox{Output)} }{\hbox{Output}}\)

Average variable costs can be helpful to determine how much the production of 1 unit costs. This can be important in determining the price and value of the product.

\(\hbox{Average Total Cost}=\frac{\hbox{Total Costs}-\hbox{Fixed Costs} }{\hbox{Output}}\)

Average fixed will trend downwards as fixed costs are constant, so as output increases, average fixed costs will decrease dramatically.

\(\hbox{Average Fixed Cost}=\frac{\hbox{Fixed Costs} }{\hbox{Output}}\)

Fixed Cost vs. Variable Cost Graph

Graphing the different costs can provide insight into how each one plays a role in production. The shape and structure of total, variable, and fixed costs will differ based on industry environments. The graph below demonstrates linear variable costs, which is not always the case.

The graphs shown in this section are samples; each business will have different variables and parameters that change the steepness and shape of the graph.

Fig. 1. Total Costs, Variable Costs, and Fixed Costs, StudySmarter Originals

Figure 1 above shows that fixed cost is a horizontal line, meaning the price is the same at all quantity levels. Variable cost, in this case, increases at a fixed rate, meaning that, to produce a higher quantity, the cost per unit will increase. The total cost line is the summation of fixed and variable costs. Because of this, it starts at the fixed cost price and then rises at the same slope as variable costs.

Another way of analyzing production costs is by tracking the rise and fall of average costs. Average total costs (purple curve) are essential as companies looking to minimize costs want to produce at the lowest point of the average total cost curve. This graph also provides insight into fixed costs (teal curve) and how they interact as the output increases. Fixed costs start very high at low output quantities but quickly dilute and spread out.

Fig. 2. Average Total, Variable and Fixed Costs, StudySmarter Originals

The average variable cost (dark blue curve) is in a U shape because of economies of scale factors at the mid-level output. However, these effects diminish at higher output levels, as diseconomies of scale raise the cost dramatically at high output levels.

Fixed vs. Variable Costs Examples

The best way to understand fixed and variable costs is to view an example, so see the example below of a business's production costs.

Bert is looking to open a business that sells dog toothbrushes, "That's toothbrushes for dogs!" exclaims Bert with a grin. Bert hires a marketing and business expert to create a business plan with financial estimates. The business expert reports his findings below for Bert's potential production options.

Table 1. Fixed and Variable Costs Example

Table 1 above lists the cost breakdown across five different production quantities.As is consistent with the definition of fixed costs, they remain constant at all production levels. It costs Bert $2,000 annually for rent and utilities to make the toothbrushes in his shed.

When Bert makes only a few toothbrushes, he is slow and makes mistakes. However, if he produces a large quantity, he will get into a good rhythm and work more efficiently; this is reflected in decreasing variable costs. If Bert were to try to push himself to produce 5,000 toothbrushes, he would get tired and make a few mistakes. This is reflected in the increasing variable cost at high levels of production.

Fig. 3. Another Satisfied Customer

Bert is thrilled about the business forecast the expert provided him. He also discovers that consumer doggy dental business competitors sell their toothbrushes at $8. Bert will also sell his product at the market price of $8; with that, Bert tries to decide what quantity to produce.

Table 2. Total Costs and Revenue Example

Bert now has to decide whether he wants to maximize profit or maximize time efficiency. This is because he earns more profit per unit, producing 1,000 units than 5,000 units. However, they make a higher overall profit producing at 5,000 units. Either option he can choose provides different benefits.

Fixed cost vs. Variable cost - Key takeaways

• Fixed costs are constant production expenses that occur regardless of changes in output. Fixed costs become more diluted as output increases.
• Variable costs are production expenses that change with the level of output. These costs generally decrease at first, then increase later on.
• Economies of scale occur due to efficiencies from producing at higher quantities. These can be experience curves or more efficient production practices.
• A business's total cost will always increase as output increases. However, the rate at which it increases can change. The average total curve demonstrates how costs increase slower at mid-level outputs.

References

1. Figure 3: https://commons.wikimedia.org/wiki/File:BeagleToothbrush2.jpg

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