# Marginal cost

After you have worked through this section of the learning unit, you should be able to:

• describe marginal cost
• calculate marginal cost

Marginal cost is the additional cost of producing one more unit of output. It is therefore not the cost per unit of all units being produced, but only the next one.

If data on total cost is available in increments of one unit of output, it is easy to calculate it, as the following activity demonstrates.

### The following data is provided:

The total cost to produce three units = R100.
The total cost to produce four units = R110.
The total cost to produce five units = R122.

• Calculate the marginal cost of producing the fourth unit.
• Calculate the marginal cost of producing the fifth unit.

The marginal cost of producing the fourth unit = the total cost of producing four units – the total cost to produce three units = R110 – R100 = R10. The marginal cost of producing the fifth unit = the total cost of producing five units – the total cost to produce four units = R122 – R120 = R12.

Let's take an example where we have production data for intervals of more than one unit change, as in the case of Best Barber.

At an output level of 72 haircuts, the total cost is R960.

At an output level of 80 haircuts, the total cost is R1 120.

In this case, the marginal cost is calculated by taking the change in total cost and dividing it by the change in total product.

$$\text{Marginal cost} = {\text{change in TC } \over \text{change in TP}}$$

The change in total cost (TC):

$$\text{} = {\text{the total cost of 80 haircuts - the total cost of 72 haircuts}}$$

$$\text{} = {\text{R1120 - R960}}$$

$$\text{} = {\text{R160}}$$

The change in quantity (TP):

$$\text{} = {\text{80 haircuts - 72 haircuts}}$$

$$\text{} = {\text{8 haircuts}}$$

The marginal cost is therefore:

$$\text{} = {\text{ R160} \over \text{ 8}}$$

$$\text{} = {\text{ R20}}$$

### Use the following data to calculate the marginal cost:

At an output level of 40, the total cost is R640.

At an output level of 60, the total cost is R800.

The marginal cost is therefore R _______.

The change in total cost is R800 – R640 = R160.

The change in haircuts = 60 – 40 = 20.

The marginal cost = R160 ÷ 20 = R8.

In the following table, the marginal cost of haircuts for Best Barber is added to the cost data:

The marginal cost of haircuts for Best Barber

 Quantity of labour Quantity of haircuts Total fixed costs (TFC) (rand) Total variable costs (TVC) (rand) Total cost (TC) (rand) Marginal cost (MC) (rand) 0 0 320 0 320 --- 1 16 320 160 480 10,00 2 40 320 320 640 6,67 3 60 320 480 800 8,00 4 72 320 640 960 13,33 5 80 320 800 1 120 20,00 6 84 320 960 1 280 40,00 7 82 320 1 120 1 440 80,00

The data used to calculate marginal cost is highlighted, and the formula that is used is

$$\text{MC} = {\text{∆ TC} \over \text{∆ Q}}$$

The important thing to notice about marginal cost is that it first decreases, reaches a minimum and then increases. It is the increasing part of marginal cost that we are mainly interested in.

#### Activity

Do the following activity to see if you understand marginal cost:

### Complete the following table for the marginal cost for Blaker Maker, a firm that manufactures garden ornaments by filling in the correct amounts:

 Quantity of ornaments TP Total fixed cost TFC (rand) Total variable cost TVC (rand) Total cost TC (rand) Marginal cost MC (rand) 0 20 000 0 20 000 --- 1 000 20 000 30 000 50 000 30 2 000 20 000 50 000 70 000 20 3 000 20 000 65 000 85 000 4 000 20 000 85 000 105 000 20 5 000 20 000 110 00 130 000 6 000 20 000 150 00 170 000 40 7 000 20 000 210 00 230 000

Marginal cost is calculated by taking the change in total cost and dividing it by the change in total product.

$$\text{MC} = {\text{∆ TC} \over \text{∆ TP}}$$

For the 3000th unit, it is

$$\text{MC} = {\text{R85 000 - R70 000} \over \text{R3 000 - R2 000}}$$

$$\text{} = {\text{R15}}$$

For the 5000th unit, it is

$$\text{MC} = {\text{R130 000 - R105 000} \over \text{R5 000 - R4 000}}$$

$$\text{} = {\text{R25}}$$

For the 7000th unit, it is

$$\text{MC} = {\text{R230 000 - R170 000} \over \text{R7 000 - R6 000}}$$

$$\text{} = {\text{R60}}$$

 Quantity of ornaments TP Total fixed cost TFC (rand) Total variable cost TVC (rand) Total cost TC (rand) Marginal cost MC (rand) 0 20 000 0 20 000 --- 1 000 20 000 30 000 50 000 30 2 000 20 000 50 000 70 000 20 3 000 20 000 65 000 85 000 15 4 000 20 000 85 000 105 000 20 5 000 20 000 110 00 130 000 25 6 000 20 000 150 00 170 000 40 7 000 20 000 210 00 230 000 60