## Defining Short-Run Production Cost

The definition of short-run production cost is the combined fixed and variable costs a company incurs to produce a good or service in the short run. Short-run production experiences fixed production costs because capital is fixed in the short term, such as the size of a warehouse or the pieces of heavy machinery. Fixed costs remain constant regardless of production output. Variable cost changes depending on production output. In the long run, none of the production inputs are fixed, including physical capital.

Do you want to find out why capital is not fixed in the long run? Our explanation Long-run Production Costs will teach you all about it!

**Short-run production costs** are the total of fixed and variable costs incurred by the production of a good or service where factors such as land and heavy machinery cannot change in the short term.

**Fixed production costs** are costs that remain constant regardless of production input or output and cannot change in the short term.

**Variable production costs** are costs that can vary depending on the level of input and output.

And there are still a few more definitions:

The **total cost of production** is the fixed cost plus the variable cost. This is how much it costs a company to operate at a specific quantity of labor and output.

The **marginal cost** is the change in the total cost when producing an additional unit. The marginal cost is important because it will help us identify when we have reached our peak level of output.

**The law of diminishing marginal returns**

The law of diminishing marginal returns states that output increases at a decreasing rate as it approaches the maximum output capacity of the fixed input. As labor increases, the productivity of each additional worker decreases.

Imagine a restaurant. At first, there is just one person working there doing all the tasks like cooking, cleaning, and serving. Then another worker is hired and the first worker can focus on cooking while the second can clean and serve the patrons. The workers are specialized which increases production efficiency allowing them to cook more food and serve more guests. As they hire a third worker, productivity still increases but not as much as after the second worker. Then as more workers get hired, the restaurant gets more and more crowded with cooks, servers, and cleaning staff that they start bumping into each other, there are not enough stoves for the cooks or sinks to clean dishes, and output begins to diminish.

## Short-Run Production Cost Function

Figure 1 below shows the total cost (TC) curve. It is made up of the fixed cost (FC) and the variable cost (VC). Since the total cost is the combination of the variable cost and the fixed cost, the total cost curve runs parallel to the variable cost curve. The fixed cost curve is horizontal because the cost is the same regardless of how much output is produced.

Figure 1. Total cost curve, StudySmarter Originals

In Figure 1, the slope of the total cost curve flattens at first, meaning it increases at a decreasing rate because each additional unit becomes cheaper to produce when the workers can specialize and increase efficiency. Then, the slope begins to increase due to diminishing marginal returns. Of course, the shape of the variable cost curve and the total cost curve can look a little different depending on the situation.

**A refresher: the short-run production function**

The short-run production function will help us calculate the amount of output a company can produce given certain quantities of labor at a fixed level of capital. The short-run production function can be written like this:

$Q=f\left[L,\overline{K}\right]$

Output (Q) is a function of the quantity of labor employed (L) and physical capital (K). Physical capital is fixed in the short run.

As the number of workers increases, so does the quantity of output at a set amount of capital. The marginal product of labor decreases with every additional worker added. This holds true for the law of diminishing marginal returns. The total product (TP) curve is a graphic representation of the production function. It shows how the quantity of the variable input determines the quantity of output at a given quantity of the fixed input.

Figure 2. The total product curve, StudySmarter Originals

In figure 2, the total product curve slopes upward as output increases with each additional unit of labor. However, the curve flattens out as labor increases, indicating that the **additional ****increase **in output is decreasing, which is given by the law of diminishing marginal returns.

## Short-Run Production Cost Curve

To figure out the short-run production cost curve, it is necessary to understand where all the values come from and how they interact.

### Calculating total cost

There are several costs that must be calculated so that we can figure out the per-unit cost of production.

Fixed costs are the costs that remain the same regardless of output. Variable costs change with each unit of output. The total cost (TC) is the combination of fixed cost and variable cost.

$TC=fixed\mathrm{cos}t+variable\mathrm{cos}t$

Next, the marginal cost (MC) is determined when we identify the change in total cost when producing each additional unit. This is the formula for marginal cost:

$MC=\frac{\Delta TC}{\Delta Q}$$MC=\frac{\u2206TC}{\u2206Q}$,

where$\u2206$means "change in", and Q is the quantity of output.

Quantity | Fixed cost | Variable cost | Total cost | Marginal cost |

0 | $10 | $0 | $10 | N/A |

1 | $10 | $25 | $35 | $\frac{\$35-\$10}{1}=\$25$ |

2 | $10 | $36 | $46 | $\frac{\$46-\$35}{2-1}=\$11$ |

3 | $10 | $44 | $54 | $\frac{\$54-\$46}{3-2}=\$8$ |

To learn more about marginal cost, check out our explanation: Marginal Cost

### Calculating average total cost, average variable cost, and average fixed cost

Calculating the average total cost (ATC), the average variable cost (AVC), and the average fixed cost (AFC) is pretty straightforward. We are calculating an average, so we divide the cost by the quantity (Q) to arrive at the per-unit cost.

$ATC=\frac{TC}{Q}AVC=\frac{VC}{Q}AFC=\frac{FC}{Q}$

Now, let us take a look at table 3 where we combine all the calculations we just learned. Here, we will use a fictional data set for Company C, where we are also including units of labor to see the changes in output for each additional unit of labor. We are assuming here that labor is the only variable input of production for Company C:

Labor | Quantity | Fixed cost | Variable cost | Total cost | Marginal cost | Average total cost (ATC) | Average variable cost (AVC) | Average fixed cost (AFC) |

0 | 0 | $75 | $0 | $75 | N/A | N/A | N/A | N/A |

1 | 15 | $75 | $60 | $135 | $4 | $9 | $4 | $5 |

2 | 36 | $75 | $120 | $195 | $1.67 | $5.42 | $3.33 | $2.08 |

3 | 52 | $75 | $180 | $255 | $3.75 | $4.9 | $3.46 | $1.44 |

4 | 62 | $75 | $240 | $315 | $6 | $5.08 | $3.87 | $1.21 |

5 | 69 | $75 | $300 | $375 | $8.57 | $5.43 | $4.35 | $1.09 |

6 | 74 | $75 | $360 | $435 | $12 | $5.88 | $4.86 | $1.01 |

Table 2. Different types of costs, StudySmarter

There is so much more to learn about average costs! Take a look at our explanation: Average Cost

## Short-Run Production Cost Graph

The short-run production cost graph shows the interaction between the different cost curves.

Take a look at figure 3 above. The average fixed cost (AFC) curve drops sharply with the initial increase in the quantity produced, but the decrease slows down as the quantity becomes larger because the fixed cost does not change and is continuously divided by a larger and larger quantity.

The marginal cost (MC) curve decreases initially because the marginal cost of each additional unit of labor decreases as workers specialize. Then, as the law of diminishing returns sets in, the marginal cost begins to increase again as the benefits from workers specializing are exhausted and the benefit of each additional unit of labor shrinks.

Point A is where MC and AVC intersect at the minimum average variable cost. Point B is where MC and ATC intersect at the minimum average total cost.

The minimum costs are important. Read our explanation on Cost Minimization to find out why!

If we want to calculate the cost of production at a specific output level, Q, we multiply the quantity and the corresponding cost on the ATC curve at that quantity.

$Totalproduction\mathrm{cos}t=Q\times ATC$## Short-Run Production Cost Examples

Some short-run production cost examples are fixed costs and variable costs.

An example of a fixed short-run production cost is capital. Capital is usually something that is not easily purchased or replaced -- think about warehouse space, heavy machinery, an oven in a pizza parlor, new trucks and boats for shipping business, or larger office space to hold more employees. It is only fixed in the short run because, in the long run, a firm can choose to invest in expanding their capital if they deem it profitable.

Blue Firm produces 12 gadgets at $30 per unit. Their average fixed costs amount to $10. What is the total production cost? How much of it is fixed cost and how much of it is variable cost?

Total production cost:

$12\times \$30=\$360$The fixed cost is:

$12\times \$10=\$120$

The total variable cost is:

$\$360-\$120=\$240$

Wages for administrative workers can be considered a fixed cost, if we assume that the number of administrative people at the firm stays the same regardless of how much the firm produces. But production workers are a variable cost because the firm can decide to hire more or fewer workers depending on how many goods they are producing.

Other examples of variable short-run production costs are the costs of inputs and labor. Examples of inputs are the metal used to produce car bodies, the flour used in pizza crust, the polyester and cotton used in clothing, agave used to produce tequila, or the clay sourced to make porcelain. These are all input products or ingredients that are required in the production of a good. The more final goods that the firm produces, the more inputs it will require.

Red Firm produces 225 widgets at $16 per unit. Their average fixed cost is $4. What is their total variable cost?

First, we need to calculate the total production cost and the total fixed cost.

Total production cost:

$225\times \$16=\$3,600$Total fixed cost:

$225\times \$4=\$900$

This means that the total variable cost is:

$\$3,600-\$900=\$2,700$

## Short Run Production Cost - Key takeaways

- Short-run production costs are the total of fixed and variable costs incurred by the production of a good or service where factors such as land and heavy machinery cannot change in the short term.
- Fixed costs remain constant regardless of production output. Variable costs can change depending on production output. In the long run, none of the variables are fixed, including physical capital.
- The marginal cost is the change in the total cost with each additional unit of output.
- Fixed costs are the costs that remain the same regardless of output. Variable costs change with each unit of output. The total cost is the sum of fixed cost and variable cost.

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##### Frequently Asked Questions about Short Run Production Cost

What is short run production cost?

Short run production cost is the total of fixed and variable costs incurred by the production of a good or service where factors such as land and heavy machinery cannot change in the short term.

How to derive short-run production cost.

To derive the short-run production cost we combine a firm's fixed costs and its variable costs to determine its total cost of production.

How to graph a short-run production cost.

The short-run production cost graph includes several components: the marginal cost, the average total cost, the average variable cost, and the average fixed cost.

What is the formula for calculating a short-run production cost?

The formula for calculating the short-run production cost is the quantity of output multiplied by the average total cost at the given quantity.

What are examples of short-run costs?

Some short-run production cost examples are fixed costs like capital and variable costs like the cost of inputs used in producing other products.

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