In any manufacturing industry, when production quantity changes, the total cost of production also changes. This change in total cost is called marginal cost. If you want to know how to calculate marginal cost, then read through this article.
In finance & economics, the change in total cost which arises when quantity produced is changed by 1 unit is called marginal cost. The term marginal cost implies that the cost per unit depends upon the total number of units produced. Mathematically, marginal cost (MC) is stated as 1st derivative of the total cost (TC) with respect to quantity (Q). It is to be noted that the marginal cost changes with the change in volume. At each level of production, the marginal cost is the cost of the production of next unit referring to the basic volume.
MC = dTC / dQ
Generally, marginal cost at each level of production includes additional costs which are required to produce the next unit. For example, if you are building a new factory, the marginal cost includes the cost of extra vehicles used.
In relation to fixed cost and variable cost,
MC = dTC / dQ = d (FC + VC) / dQ = dVC / dQ
Here,
MC is marginal cost
TC is total cost
Q is quantity
FC is fixed cost
VC is variable cost &
d is the change in production unit.
As fixed cost does not change with production quantity, it is taken out of the equation when it is differentiated. It means that the marginal cost does not depend upon fixed costs. However, it can be related to average cost.
As, AC = FC + VC / Q
So, MC = AC + (δAC / δq) q
Steps for calculation
- Deduct the first production level from the second production level to get the production change.
- Deduct the cost for the first production level from the cost at second production level to get the cost change.
- Now divide the cost change by the production change. The final result which you will get after dividing will be the marginal cost between two production levels.
For example, let us assume a company which spends $ 1,000 to produce 100 units and $ 1,700 to produce 150 units.
Now,
Production change = 150 units – 100 units = 50 units
Cost change = $ 1,7000 – $ 1,000 = $ 700
Therefore, Marginal cost = $ 700 / 50 units = $ 14
Here marginal cost of the company for production level one to production level two is Rs 14.
Ex 2. Let us assume this data
| Cakes (Q) | Fixed cost (FC) | Variable cost (VC) | Total cost (TC = FC + VC) | Average total cost (ATC = TC/Q) |
| 19.53 | $ 200 | $ 50 | $ 250 | $ 12.80 |
| 38.16 | $ 200 | $ 100 | $ 300 | $ 7.86 |
| 55.90 | $ 200 | $ 150 | $ 350 | $ 6.26 |
| 72.80 | $z 200 | $ 200 | $ 400 | $ 5.49 |
| 104.17 | $ 200 | $ 300 | $ 500 | $ 4.80 |
| 132.50 | $ 200 | $ 400 | $ 600 | $ 4.53 |
| 157.99 | $ 200 | $ 500 | $ 700 | $ 4.43 |
| 191.36 | $ 200 | $ 650 | $ 850 | $ 4.44 |
Now, as MC = δ TC /Δq
So,
| Cakes (Q) | Fixed cost (FC) | Variable cost (VC) | Total cost (TC = FC + VC) | Average total cost (ATC = TC/Q) | Marginal cost (MC = δTC / δQ) |
| 19.53 | $ 200 | $ 50 | $ 250 | $ 12.80 | $ 2.56 |
| 38.16 | $ 200 | $ 100 | $ 300 | $ 7.86 | $ 2.68 |
| 55.90 | $ 200 | $ 150 | $ 350 | $ 6.26 | $ 2.82 |
| 72.80 | $ 200 | $ 200 | $ 400 | $ 5.49 | $ 2.96 |
| 104.17 | $ 200 | $ 300 | $ 500 | $ 4.80 | $ 3.19 |
| 132.50 | $ 200 | $ 400 | $ 600 | $ 4.53 | $ 3.53 |
| 157.99 | $ 200 | $ 500 | $ 700 | $ 4.43 | $ 3.92 |
| 191.36 | $ 200 | $ 650 | $ 850 | $ 4.44 | $ 4.49 |
In simpler words, we can say that marginal cost is the additional cost required to produce an extra unit of a product.
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