Cost Structure
Understanding your cost structure is a fundamental step in business decision-making. It helps guide efforts to minimize costs, set appropriate prices, recognize economies of scale, and make informed decisions about whether to continue operations. It also plays a key role in understanding the supply curve. Generally, there are two types of costs: Fixed Costs and Variable Costs.
Fixed Costs
Fixed costs are expenses that do not change with the level of output. They must be paid regardless of how much you produce and typically remain constant in the short term. Examples include rent and utilities.
Note: Fixed costs can become variable in the long run. For instance, your rent may increase or decrease after the contract period ends, making it variable over time.
Variable Costs
Variable costs are expenses that scale directly with the amount of output produced. As production increases, these costs rise; as production decreases, they fall. Variable costs are flexible and are closely tied to the level of activity. Examples include raw materials, labor, shipping, etc.
Cost Functions: Notation
To better understand the cost structure, let’s first define some key cost notations. (Curious about the function? Check the link at the bottom of this post.)
- Variable Cost: \(VC(Q)\)
- Fixed Cost: \(FC\)
- Total Cost: \(TC(Q) = VC(Q) + FC\)
The notation \(VC(Q)\) indicates that variable cost is a function of output quantity \(Q\), meaning it changes depending on how much is produced.
Similarly, \(TC(Q)\) means that total cost varies depending on \(Q\). Why? Look at the right side of the formula: while \(FC\) is fixed (it has no parentheses like \((Q)\), indicating it’s a constant), \(VC(Q)\) changes depending on the quantity \(Q\).
Example
Let’s work through an example to better understand and build on these concepts.
Variable cost \(VC\) increases as \(Q\) increases because producing more output usually requires more electricity, labor, materials, etc. So, we define:
\(VC(Q) = 0.7Q^2 + 10Q\)
And fixed cost \(FC\) is constant regardless of output quantity \(Q\), let:
\(FC = 1000\)
Then, the total cost function becomes:
$$TC(Q) = VC(Q) + FC$$
$$=0.7Q^2 + 10Q + 1000$$
If we calculate FC, VC, and TC for different values of Q and display them in a table, it would look like this. (Note: The far-left column simply represents the row number, and <num> stands for numeric values.)
| Q | FC | VC(Q) | TC(Q) |
|---|---|---|---|
| 1 | 1000 | 10.7 | 1010.7 |
| 2 | 1000 | 22.8 | 1022.8 |
| 3 | 1000 | 36.3 | 1036.3 |
| … | … | … | … |
| 148 | 1000 | 16812.8 | 17812.8 |
| 149 | 1000 | 17030.7 | 18030.7 |
| 150 | 1000 | 17250.0 | 18250.0 |
Economies of Scale
Today, we explored fixed and variable costs, and how they respond to changes in the quantity of output. In our next post, we’ll dive into the concept of economies of scale—what it is, and why it occurs—building on our understanding of fixed and variable costs.