Marginal cost is used by entities to understand what level of output is required to maintain profit. Generally, the increasing output will increase the cost. This can reduce profit if there can’t be an increase in selling price. What is a marginal cost?

**Definition of Marginal Cost**

1. Marginal cost is the increase in total cost as a result of an increase in the units produced.

2. It is defined as the increment in total cost when output increases.

**Key Explanations**

Marginal cost is an incremental cost. And it is measured based on an increase in total cost and output. However, the total cost is made up of fixed costs and variable costs. You should know that fixed costs will not increase even when there is an increase in production output. In other words, fixed cost is a constant element of the total cost. Examples are the depreciation of plants and machinery, the salary of a supervisor, and so on.

Variable cost element of total cost increases as output increases. An example is the wages of labor and raw materials that enter the production process. To increase output, more raw materials will be required as well as more workers. This will lead to an increase in total cost.

Total cost may increase at a decreasing rate if the entity can utilize the economics of large-scale production. Producing in large quantities results in buying more raw materials at lower prices. As well as, using a few more laborers to do more tasks. This will lead to an increase in total cost but at a decreasing rate. The result will be more profit for the entity at the same selling price.

Knowing the marginal cost will help a business understand the level of cost that will break even. That is the output at which the cost equals revenue. Therefore, the entity’s management will know the level of output that will earn profit for the firm.

**The formula for Marginal Cost (MC)**

The formula for MC: **change in cost ÷ change in output**

A differentiation formula can be used if the equation of cost function is known. Therefore MC is **DTC ÷ dQ**

Where DTC is the derivative of total cost and dQ is the derivative for the Quantity or output.

**Examples of Marginal Cost**

The table below shows what happens to total cost when an entity increases output daily for five days. The marginal cost is also calculated in the third column.

MC = change in total cost ÷ change in output.

The MC is calculated from day 2. Why? On day 1 there was in change or increase in output. The first marginal cost is calculated by subtracting day 1 total cost from day 2 and dividing it by the difference of day 1 and day 2 output. That is (72000 – 50000) ÷ (64 – 50). This gives 22000 ÷ 14. And the answer is 1571.4 Naira.

The second marginal coat follows the same pattern. This time, day 2 total cost is subtracted from day 3 TC. Also is the output. That is, (84000 – 72000) ÷ (69 – 64). This gives 14000 ÷ 5. And the final answer is 2400 Naira. You can go on to calculate day 4 and day 5 marginal cost.

Another example is the case of a total cost function. In this case, the DTC ÷ dQ formula will be used. A cost function is given below:

**TC = 100 + 5Q**

The cost function reveals the two elements of the total cost. Fixed cost and variable cost. 100 is the fixed cost. That means it won’t change regardless of the Quantity. While 5Q is the variable cost. This means it will change as output changes. If the output is 3 units, the variable cost will be 5 × 3. That’s 15 Naira.

From the above function, the Marginal cost is calculated using the differentiation formula. MC = DTC ÷ dQ

Therefore, MC is 5 Naira. But how?

MC = dTC/dQ (100) + dTC/dQ (5Q)

The derivative of a constant (that is, 100) is zero. And the derivative of a linear function 5Q (that is, the power is 1 or 5Q¹) is the number beside the letter.

So, MC = 0 + 5

Therefore, MC = 5

**Importance of Marginal Cost**

If all things are equal, marginal cost can be used to determine when to increase production output. It tells the number of outputs that will make total cost = total revenue. From here, the entrepreneur will know at what number of output it requires to make a profit. However, this is only possible when marginal cost is applied in an aspect of cost accounting known as marginal costing.

**Conclusion**

Marginal cost is an incremental cost. It is the cost that results from an increase in total cost to an increase in output. When applied, an entrepreneur can know it’s the break-even point and the number of output to produce that will lead to profit.

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