The Law of Diminishing Marginal Returns

Beside the conclusion that "supply = demand", the law of diminishing marginal returns (or the law of diminishing marginal product) is probably the most frequently cited concept from microeconomics. Suppose we keep everything constant, except for one single input factor, for instance L. If we increase the number of hours worked, we will probably produce more. The law of diminishing marginal returns states that the increase will eventually become smaller and smaller when the number of hours worked is large enough. To use an example: Suppose you start a firm that produces photocopies. You buy a powerful copying machine and you are the only worker. Say that you work one hour per day. You probably will not be able to make many copies during that time. The machine needs fifteen minutes to warm up, you need to prepare things, etc. If you increase the number of hours worked by one hour, you will probably make more copies during the second hour than during the first. Consequently, the marginal product is higher during the second hour than during the first, and over that interval, we therefore have increasing marginal product.
However, if you continue to increase the number of hours, you will eventually not produce many more copies per additional hour. You will become too tired to work. The same thing will happen if you hire other people to work for you:eventually, additional hours or additional workers produce very little additional output. If you, for instance, hire several people, the space will become crowded and the workers will become less efficient. This “law” is based on experience and speculation, but is not considered particularly controversial. We will use it when we construct the product curve.

The Product Curve in the Short Run

If we keep the amount of capital constant, the quantity produced is a just function of the number of hours worked, L. In Figure 7.1, we see a typical product curve with associated average and marginal product curves.
The product curve has a few typical features: In the beginning, when the number of hours worked is low, production increases slowly, and later it becomes steeper and steeper. Eventually it reaches a maximum and thereafter it decreases. After we have drawn the product curve, we want to construct the curves for the average and marginal product of labor. (The corresponding values for capital are not as interesting, since capital is a fixed cost in the short run.) To do that, we first observe that there is a simple method to find the value of the average product.

Production in the Long Run

In the long run, both labor and capital are variable inputs. That means that the quantity produced is a function of both L and K, where either of them can be changed, i.e. q = f( L,K). It is usually the case that, the same quantity can be produced with different combination of labor and capital. Workers can, at least to some extent, be substituted for machines, and vice versa. This idea can be illustrated in a graph that is very similar to the indifference curves in consumer theory ). An isoquant ("iso" = similar/same; "quant" = quantity) is a curve that shows different combinations of L and K that produce the same quantity of the single good (still assuming that the production is efficient). They are usually drawn in a way that is similar to indifference curves. Since we have diminishing marginal returns, they must slope less and less steep to the right. In Figure 7.2, you can see an example. Start by looking at point A. With that combination of labor and capital (L1,K1) a maximum of q = 10 units of the good can be produced. The same quantity could also have been produced with the combination (L2,K2), point B. If one wants to increase the production to 23 units, one can choose, for instance, point C, where both the amount of capital and of labor has been increased. Consequently, one can move from A to C only in the long run. In the short run, K is fixed. If one wants to increase production, one therefore has to choose the same K. If one wants to produce 23 units in the short run (assuming we start at point A), one has to choose the combination (L4,K1), point D, and if one wants to produce 41 units, one has to choose the combination (L5,K1), point E.

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