MARGINAL COST: FORMULA, CALCULATION AND EXERCISES - DUDAS - 2025

The marginal cost is the change in total cost of production that is caused to producing an additional article. That is, it is the cost resulting from manufacturing one more unit of a product. The purpose of analyzing marginal cost is to determine at what point an organization can achieve economies of scale.

At each level and period of time considered of production, marginal cost includes all costs that vary with the level of production, while other costs that do not vary with production are fixed and therefore have no marginal cost.

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In economic theory, marginal cost becomes an important factor, because a company that is seeking to maximize its profits will manufacture until such time as marginal cost equals marginal revenue.

Typical variable costs included in the calculation are labor and materials. The marginal cost formula can be used in financial models to optimize cash flow generation.

Formulas and function

If the cost function (C) is continuous and differentiable, the marginal cost (CM) is the first derivative of this cost function in relation to the quantity produced (Q):

CM (Q) = dC / dQ = Change in costs / Change in quantity.

Change in costs

At each level of production, production costs can increase or decrease, especially when the need arises to produce more or less volume of production.

If the manufacture of additional units requires the hiring of an extra worker or two and increases the cost of purchasing raw materials, there will be a change in the overall cost of production.

The marginal cost of production includes all costs that vary with the level of production. For example, if a company needs to build a new factory to produce more goods, the cost of building the factory is a marginal cost.

Production costs consist of fixed costs and variable costs. Variable costs refer to the costs required to produce each unit. On the other hand, fixed costs refer to general costs that are distributed among the units produced.

To determine the change in costs, production costs incurred during the first production run are deducted from production costs incurred in the next batch, when production has increased.

Change in quantity

Since it is inevitable that the volume of production will increase or decrease with each level of production, the quantities involved are significant enough to assess the changes made.

An increase or decrease in the volume of goods produced translates into the costs of manufactured goods. Therefore, it is important to know the difference.

To determine changes in quantity, the number of products manufactured in the first production run is deducted from the production volume made in the next production run.

How is marginal cost calculated?

The calculation for marginal cost is used more frequently among manufacturers, as a means of reaching the optimum level of production. Manufacturers examine the cost of adding one more unit to their production schedules.

Calculating marginal cost helps a business determine the point at which increasing the number of items produced will also increase average cost.

When volume increases, marginal cost may also increase if the business needs to add equipment, move to a larger facility, or has difficulty finding a supplier that can provide enough materials.

Calculation

If a company can produce 200 units at a total cost of $ 2,000 and produce 201 costs it $ 2,020, then the average cost per unit will be approx. $ 10 ($ 2,020 / 201 = $ 10.05) and the marginal cost of unit 201 will be $ 20.

Here's the formula for calculating marginal cost: Divide the change in total costs by the change in quantity manufactured. Using the example above, the change in cost is $ 20 ($ 2,020 - 2,000) and the change in quantity is 1 (201-200). 20 divided by 1 equals 20.

When shown on a graph, marginal cost is a curve that tends to follow a U-shape. Costs start out high, until production breaks even when fixed costs are covered.

It stays at that low point for a period, and then it starts to pick up as increased production requires spending money for more employees, equipment, etc.

Understanding the marginal cost of a product helps a company evaluate its profitability and make decisions related to the product, including pricing.

Solved exercises

Example 1

Let's consider a hat maker. Each hat produced requires $ 0.75 worth of plastic and fabric. The hat factory incurs $ 100 in fixed costs per month.

If 50 hats are made per month, then each hat incurs $ 2 ($ 100/50) of fixed costs. In this simple example, the total cost per hat, including plastic and fabric, would be $ 2.75 ($ 2.75 = $ 0.75 + ($ 100/50)).

However, if the production volume is increased and 100 hats are now produced per month, then each hat will incur $ 1 of fixed costs, because the fixed costs are spread over the units produced.

The total cost per hat would then drop to $ 1.75 ($ 1.75 = $ 0.75 + ($ 100/100)). In this situation, the increase in the production volume causes the marginal cost to fall.

Example 2

Manufacturing company X manufactures heating systems. The existing equipment is outdated and does not meet your manufacturing needs, unable to meet the production schedule.

Additional equipment has to be purchased or rented to keep production at the same levels.

Therefore, it is necessary to calculate the marginal cost of the heating systems that will be produced with the new equipment, including the cost of its acquisition.

The graph that represents the marginal cost values ​​indicated in the table is as follows:

It can be seen that the total cost increases as the quantity of the product increases, because greater quantities of the factors of production are required.

Marginal cost decreases to a certain level of production (Quantity = 5). Then it keeps growing along with production.

The marginal cost of producing an additional unit of heating systems at each level of production must take into account a sudden increase in raw materials.

If other suppliers have to be found, the marginal cost may increase due to longer distances and higher raw material prices.

References

1. Will Kenton (2018). Marginal Cost Of Production. Taken from: investopedia.com
2. Wikipedia, the free encyclopedia (2019). Marginal cost. Taken from: en.wikipedia.org.
3. CFI (2019). Marginal Cost Formula. Taken from: corporatefinanceinstitute.com.
4. Shopify (2019). Marginal Cost. Taken from: shopify.com.
5. My Accounting Course (2019). What is a Marginal Cost? Taken from: myaccountingcourse.com.