# Relationship between production and costs

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

• describe the relationship between production and costs

What determines the shape of the marginal cost curve? In order to answer this question, we need to go back to the law of diminishing returns, which states that as more of a variable input is used, while all the other inputs are fixed (remain the same), each additional unit of the variable input will eventually produce less and less additional output. In economics, we say that the marginal product (MP) of the variable input will decline.

In our example of Best Barber, the variable input is the number of barbers and the output is the quantity of haircuts. The marginal product is the contribution each additional haircutter adds to total haircuts.

Total product and marginal product of barbers

 Quantity of labour Q Quantity of haircuts TP Marginal product MP 0 0 --- 1 16 16 2 40 24 3 60 20 4 72 12 5 80 8 6 84 4

As the number of barbers increases from zero to one in the table, output increases from zero to 16 for a marginal gain of 16; as the number rises from one to two barbers, output increases from 16 to 40, a marginal gain of 24. From that point onwards, however, the marginal gain in output diminishes as each additional barber is added. For example, as the number of barbers rises from two to three, the marginal output gain is only 20; and as the number rises from three to four, the marginal gain is only 12.

To understand the reason behind this pattern, consider that a one-man barbershop is an extremely busy operation. The single barber needs to do everything: greet clients entering the shop, answer the phone, cut hair, sweep up and operate the cash register. A second barber reduces the level of disruption from jumping back and forth between these tasks, and allows a greater division of labour and specialisation. The result can be greater increasing marginal returns. However, as other barbers are added, the advantage of each additional barber is less, since the specialisation of labour can only go so far. The addition of a sixth, seventh or eighth barber simply to greet people at the door will have less impact than the second barber did. This is the pattern of diminishing marginal returns. At some point, you may even see negative returns as the additional barbers begin bumping elbows and getting in each other’s way. In this case, the addition of still more barbers would actually cause output to decrease.

How does this then influence marginal cost?

In our example. we assumed that a barber is paid R160 per day, which is the variable cost. Every time a barber is added, the variable cost increases by R160.

If the first barber is added, the marginal product of this barber is 16 haircuts. The marginal cost is the

$$\text{change in total cost} \over \text{change in haircuts}$$

and since change in haircuts is equal to the marginal product, it can be written as

$$\text{change in total cost} \over \text{marginal product}$$

Therefore, the marginal cost for the first barber is

$$\text{ } = {\text{R160} \over \text{16}}$$

$$\text{ } = {\text{R10}}$$

• What is the marginal cost for the second barber?
• What is the marginal cost for the third barber?

For the second barber it is 160 ÷ 24 = R6,67 and for third barber R160 ÷ 20 = R8,00.

In the following table the marginal cost is added.

Marginal product and marginal cost for Best Barber

 Quantity of labour Quantity of haircuts Marginal product (MP) Total cost (TC) (rand) Marginal cost (MC) (rand) 0 0 --- 320 --- 1 16 16 480 10,00 2 40 24 640 6,67 3 60 20 800 8,00 4 72 12 960 13,33 5 80 8 1 120 20,00 6 84 4 1 280 40,00

Look closely at the data for the marginal product and marginal cost.

### What happens to marginal cost if marginal product increases from 16 to 24?

Think again. It decreases. As the marginal product increases from 16 to 24, the marginal cost decreases from R10 to R6,67.

Correct. It decreases. As the marginal product increases from 16 to 24, the marginal cost decreases from R10 to R6,67.

Think again. It decreases. As the marginal product increases from 16 to 24, the marginal cost decreases from R10 to R6,67.

### What happens to marginal cost if marginal product decreases from 20 to 12?

Correct. It increases. As the marginal product decreases from 20 to 12, the marginal cost increases from R8,00 to R13,33.

Think again. It increases. As the marginal product decreases from 20 to 12, the marginal cost increases from R8,00 to R13,33.

Think again. It increases. As the marginal product decreases from 20 to 12, the marginal cost increases from R8,00 to R13,33.

What we can conclude from this is as marginal product increases, marginal cost decreases, and as marginal product decreases, marginal cost rises. The law of diminishing returns is therefore the reason why marginal cost rises.

Graphically, this can be depicted as follows:

The declining part of the marginal product curve indicates the law of diminishing returns, while the rising part of the marginal cost curve indicates the impact of the law of diminishing returns on marginal cost. The diagram shows the marginal product of barbers (labour). At first, by adding a barber, the marginal product rises, but then starts to fall and the law of diminishing returns sets in. The diagram indicates the marginal cost curve for haircuts, and it is the inverse of the marginal product curve. As the marginal product rises, the marginal cost declines, and as the marginal product falls, the marginal cost increases.

#### Activity

Do the following activity to see if you understand the relationship between production and costs:

### Complete the following paragraphs by selecting the correct options:

The following two diagrams represent the marginal product and the marginal cost for Blaker Maker: Variable input labour Marginal product (MP) 0 --- 1 500 2 1000 3 1500 4 1000 5 500 6 250 7 0 Quantity of ornaments Q Marginal cost MC (rand) 0 --- 1 000 30 2 000 20 3 000 15 4 000 20 5 000 25 6 000 40 7 000 60

1. By adding the first three workers, the marginal product (increases; declines). After adding the fourth, fifth, sixth and seventh workers, marginal product (increases; decreases). The law of diminishing returns is represented by the (rising; falling) part of the marginal product curve.

2. The marginal cost (falls; rises) for the first 3 000 units. After increasing production from 4 000 to 7 000, the marginal cost (falls; rises).

3. As marginal product rises, marginal cost (rises; falls), and as marginal product decreases, marginal cost (rises; falls).

1. By adding the first three workers, the marginal product increases. After adding the fourth, fifth, sixth and seventh worker, marginal product decreases. The law of diminishing returns is represented by the falling part of the marginal product curve.   2. The marginal cost falls for the first 3 000 units. After increasing production from 4 000 to 7 000, the marginal cost rises.  3. As marginal product rises, marginal cost falls, and as marginal product decreases, marginal cost rises.