Short Run Production Cost

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.

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.

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.

$TC=fixed\cos t+variable\cos t$

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{∆TC}{∆Q}$,

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

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:

Table 2. Different types of costs, StudySmarter

Short-Run Production Cost Graph

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

Figure 3. Short run production cost curve, StudySmarter Originals

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.

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.

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.

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.