© Chris Rodda 2011 (free for teachers to reproduce) 1

THE LAW OF DIMINISHING MARGINAL RETURNS

When one of the factors of production is held fixed in supply, successive additions of the other factors will lead to an increase in returns up to a point, but beyond this point returns will diminish. This famous law was first written about by a Frenchman, Anne Robert Jacques Turgot and then alluded to by Thomas Malthus in his Essay on the Principle of Population (1798). The law was discussed in England during debates on free trade and the Corn Laws. Sometimes textbooks call it the law of decreasing (marginal) returns or the law of variable proportions. First we assume that there is a fixed amount of land, for example 100 acres. There is also fixed amount of capital; a combine harvester, tractor and a barn. The amount of entrepreneurship available is the same too. The variable factor in this model is labour and we also assume that each person is homogenous; that is each unit of labour has identical abilities and physical characteristics to start with. Remember that the definition of the short run in economics is, when at least one factor of production is fixed in supply, so this is a short-run model that we are building. Imagine the farm grows wheat. There are a number of jobs that need doing at harvest time and these must be done quickly before weather ruins the crop. First the wheat must be cut and gathered, the wheat and chaff must then be separated. The wheat has then to be carted to the barn, weighed, dried out in some instances, and then stored. All the farm machinery needs maintained, the paperwork completed and last but not least breakfast, lunch and dinner prepared. One man working alone will have difficulty doing all these tasks. With each person specializing there will be gains in productivity as we saw when we looked at the division of labour earlier in the course. When a second worker is employed the tasks are shared. They each become more skilled in the tasks that they specialize in and save time previously wasted by switching between tasks. However both have to stop when a piece of machinery breaks down or one of them stops for lunch. Employing yet another person may once again improve their productivity. The harvest may continue as workers take their lunch in rotation for example. But employing a fourth worker might mean productivity begins to fall (diminish). The gains made by employing the fourth are not as great as employing the third worker. Eventually adding more employees might even lead to an overall decrease in production as they become bored with nothing to do and begin to interfere with production. The table below shows what happens as each extra worker is employed. We are mainly interested in the increase in output gained from each additional unit of labour, or the marginal physical product. Marginal means the next unit, so the marginal physical product (MPP) is the amount by which production rises when one extra worker is employed. MPP is calculated by measuring the change in total physical production per worker. The average physical product (APP) is simply the total physical product (TPP) divided by the number of workers N.B. The Greek letter delta (Δ) is used to mean ‘change’.

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Table.

Number of

workers n

Total Physical Product

(TPP) tonnes of wheat

Marginal Physical

Product (MPP)

€

ΔTPPΔn

Average Physical

Product (APP)

€

TPPn

0

0

0

1

100

€

100 − 01

= 100

100

2

300

€

300 −1001

= 200

150

3

900

€

900 − 3001

= 600

300

4

1200

€

1200 − 9001

= 300

300

5

1300

€

1300 −12001

= 100

260

6

1200

€

1200 −13001

= −100

200

Note that when we graph APP and MPP that MPP cuts the APP curve at APP’s highest point and when the third worker is employed. This is the point at which DIMINISHING MARGINAL returns sets in. On the TPP curve, diminishing marginal returns occurs at the point of inflection, where TPP stops accelerating. NOTE: The marginal physical product curve is plotted at the mid points. That is MPP = 100 is plotted against 0.5 units of labour, MPP is 200 when units of labour is 1.5.

© Chris Rodda 2011 (free for teachers to reproduce) 3

70 1 2 3 4 5 6

1400

0

200

400

600

800

1000

1200

number of workers

tonnes o

f w

heat

TPP

diminishing MARGINAL returns

70 1 2 3 4 5 6

700

-200

-100

0

100

200

300

400

500

600

number of workers

Physic

al product

MPP

APP

4

Why does MPP cut the APP curve at the highest point of APP?

It is important to remember why MPP cuts APP at APP’s highest point and that when you sketch these curves you show this accurately. Many students find this hard to understand but it is really just a simple mathematical point. Economics teachers are fond of using cricket scores to help explain this. Suppose a batsman comes to the wicket and scores 10 runs. The marginal score (how many runs are added to the total is 10 and the average score is 10 (10 divided by 1)

Batsman Score (marginal) Total score Average Score 1 10 10 10

If a second batsman scores 30 runs, the marginal is 30 (how many runs he adds) but the average is now 40 divided by 2 which equals 20. Notice the average score went up. This is because the marginal score is greater than the previous average. 30 is greater than 10, so the average went up.

Batsman Score (marginal) Total score Average Score 1 10 10 10 2 30 40 20

If a third batsman scores 20 runs, the total goes up to 60. But 20 is equal to the previous average so the average will stay the same.

Batsman Score (marginal) Total score Average Score 1 10 10 10 2 30 40 20 3 20 60 20

If a fourth batsman scores only 10 runs then the total rises to 70 but the average must now fall.

Batsman Score (marginal) Total score Average Score 1 10 10 10 2 30 40 20 3 20 60 20 4 10 70 17.5

So if the marginal score is greater than the previous average then the new average will increase. If the marginal score is lower than the previous average the average will fall.

Uses of the law of diminishing marginal returns The law of diminishing marginal returns explains why the shape of cost curves are U shaped in the short run. This is explained in the next section. The law also helps us to understand that rising populations can often result in less income per capita unless there is also an increase in the quantities or quality of capital too.