The Law of Diminishing Marginal Returns

The Law of Diminishing Marginal Returns

Although this topic is called 'Costs and revenues', it is important that we look at the law of diminishing marginal returns first because it is from this law that the cost curves are derived. To start with, we need to define a few terms.

Before commencing the bulk of the topic, it is important to make a few assumptions. The following analysis applies to the short run only. The short run is defined as the period of time where at least one factor of production is fixed. Only in the long run can we assume that the amount of capital (e.g. machines) can vary.

For simplicity, we will only be dealing with capital and labour, and ignoring the other two factors of production; land and the entrepreneur. So, in the short run, we will assume that capital is fixed, but the firm can vary the amount of labour used.

Now we need to define the terms that we will be using.

  • Total product This is the quantity of output produced by a given number of workers over a given period of time. Remember the amount of capital (or machines) is fixed.
  • Average productThis is the quantity of output per unit of input. In this model, the input is labour. In other words, we are dealing with the output per worker, on average.
  • Marginal productThe addition to total output produced by one extra unit of input (again, labour). It is the extra output produced at the margin (i.e. by adding a marginal unit of labour).

At this point it is worth looking at the relationship between the total, average and the marginal in more detail. It will come up again when we look at costs and then revenues, so it is important that you understand it fully.

Look at the table below. Let us assume that the firm in question is making computer laser printers and they have four machines in the factory (capital = 4).

Capital Labour (L) Marginal product (MP) Total product (TP) Average product (AP)
4 0 - 0 -
4 1 5 5 5.0
4 2 8 13 6.5
4 3 10 23 7.7
4 4 11 34 8.5
4 5 10 44 8.8
4 6 7 51 8.5
4 7 4 55 7.9
4 8 1 56 7.0
4 9 -2 54 6.0

Remember that capital is fixed in the short run. I have assumed that capital is fixed at 4 units (or machines, in this case).

The second column shows the progressive addition of units of labour.

The third column shows marginal product (MP). Each figure represents the output produced as a result of adding an extra worker. So, for instance, the addition of the seventh worker results in an increase in output of 4 units. Once the fourth worker is added, another 11 units are produced, etc. Notice that marginal product rises quite quickly, peaks at 11, and then begins to fall, reaching a negative figure for the ninth worker. Diminishing Marginal Returns (DMR) set in after the fourth worker. Go to the last section in this Learn It for the full explanation of DMR.

The fourth column gives total product (TP). This is calculated quite easily by adding, cumulatively, the marginal products. The first worker makes 5 units, so the total is 5. The second worker adds a further 8 units, so the total is now 13 (5 + 8), and so on. In fact, you can work out the marginals from the totals. Take the sixth worker, for example. His marginal product is 7. This can be calculated by taking the TP from six workers and subtracting the TP from five workers (51 - 44). Algebraically:

MP6 = TP6 − TP5. (i.e. 7 = 51 − 44).

The fifth column gives average product (AP). The figures in this column represent output (or product) per worker. The average product once the eighth worker has been added is 7. This was calculated by taking the TP with eight workers and dividing by the number of workers (also eight). Algebraically:

Average product

Now try and work out the table below to see if you understand what is going on. Click the relevant area in the table to display the answer.

The Law of Diminishing Marginal Returns

Here are the relevant curves. They have been plotted using the figures from the first table; not the one you have just filled in.

Plots

Notice that the point at which diminishing marginal returns sets in is to the left of the point where diminishing average returns begins. Also, the total product keeps rising even though the marginal, and the average, product is falling. This is not hard to understand. Just because the marginal product is falling, it is still positive. Hence, these extra workers may well be adding less than previous workers, but they are still contributing to the grand total. Total product keeps rising, albeit at a diminishing rate. It is only when the marginal product is negative, with the addition of the ninth worker that total product starts to fall.

Finally, notice that the marginal product curve cuts the average product curve at its highest point, where it is momentarily flat. It is important that you understand why this happens because this concept is applied to the cost and revenue curves. I think it deserves its own little section:

Imagine you are with a group of friends, waiting at the bus stop in anticipation of a great Friday night out. You all decide to check that you have enough money for the frivolities that lie ahead.

There are nine of you and, coincidentally, you all have exactly £20 each. This means that the average amount of money that each of you holds is also £20.

Your tenth friend is late, but finally arrives. He only has £10 on him. This means that between you the total amount of money is £190, and the new average is £190 divided by 10, which is £19. The arrival of your tenth friend has reduced the average because the amount he added to the total, the marginal, was less than the prevailing average.

If your tenth friend had had £30 on him, the new total would have been £210, and the new average would have been £210 divided by 10, which is £21. The arrival of your tenth friend would have increased the average because the amount he added to the total, the marginal, was more than the prevailing average.

If your tenth friend had also exactly £20 on him, then the average would have remained unchanged; £200 divided by 10 is still £20.

This is exactly what is going on with the average and marginal product curves. When the marginal curve is above the average curve, then the average is rising. When the marginal curve is below the average curve, then the average is falling. When the marginal is the same as the average (which is where they cross) then the average remains the same.

The issue is not whether the marginal is rising or falling, but whether it is above or below the average curve. In the diagram, you can see that the marginal product curve rises to start with and then begins to fall, but the average product curve only starts to fall when the marginal product curve drops below the average product curve.

Note: the textbook definition: If a firm increases output by adding variable labour to fixed capital then eventually diminishing marginal returns (physical product of labour) will set in. In other words, at some point an extra worker will add less output to the grand total than the previous worker.

In our initial example, the factory has four machines. As the first, second, third and fourth workers are added; they each have at least one machine each to work on. In fact the marginal product continually increases because each worker can do a different job and so get the products finished quicker.

But when you add the fifth, sixth, seventh, etc. workers, somebody will be standing around doing nothing and adding little to total output. The marginal product is still positive, perhaps they can take over when one of the initial workers gets tired, but the total product rises at a slower rate. The ninth worker has a negative marginal product. His addition has resulted in a fall in total output. We have now reached the point where 'too many cooks spoil the broth', as the saying goes.

It is for these reasons that the marginal product curve looks as it does (rises, peaks and then falls). Also, the shape of the average product curve is directly dependent on the marginal product curve for the reasons explained in the section called 'Why the marginal curve cuts the average curve where it is momentarily flat'. So we have explained where these product curves come from. At the end of the next Learn-It (called 'Costs and their curves') you will see that the cost curves are derived from these product curves. In other words, the cost curves are derived from the law of diminishing marginal returns.

The title of this Learn-It is 'the law of diminishing marginal returns'. Why is it a law? It is something that is accepted by just about all economists as being true in all situations, just like nearly everybody accepts the laws of the land.

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