# Diminishing returns

In economics, diminishing returns is the short form of diminishing marginal returns, the concept that, as more of an input is applied, each additional unit produces less and less additional output. This concept is also known as the law of increasing opportunity cost.

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## A simple example

Suppose that one kilogram (kg) of seed applied to a plot of land produces one metric ton of harvestable crop. You might expect that an additional kg of seed would produce an additional metric ton of output. However, if there are diminishing marginal returns, that additional kg will produce less than one additional metric ton of harvestable crop (on the same land, during the same growing season, and with nothing else but the amount of seeds planted changing). For example, the second kg of seed may only produce a half ton of extra output. And diminishing marginal returns also implies that a third kg of seed will produce an additional crop that is even less than a half ton of additional output. Assume that it is one quarter of a ton.

In economics, the term margin is used to mean difference or extra. (It's on the edge, as with the margin on a piece of paper.) The difference in the investment of seed in these three scenarios is one kg - marginal investment in seed is one kg. And the difference in output, the crops, is one ton for the first kg of seeds, a half ton for the second kg, and one quarter of a ton for the third kg. Thus, the marginal physical product (MPP) of the seed will fall as the total amount of seed planted rises. In this example, the marginal product (or return) equals the extra amount of crop produced divided by the extra amount of seeds planted.

A consequence of diminishing marginal returns is that as total investment increases, the total return on investment as a proportion of the total investment (the average product or return) also decreases. The return from investing the first kg is one ton per kg. The total return when 2 kg of seed are invested is 1.5/2 = 0.75 tons per kg, while the total return when 3 kg are invested is 1.75/3 = 0.58 tons/kg (approximately).

## A law?

The "law" of diminishing marginal returns says that after a possible initial increase in marginal returns, the MPP of an input will fall as the total amount of the input rises (holding all other inputs constant). The "law" is far from universal in its validity, though there are many examples.

For example, most people find that listening to the same piece of music over and over again during a day implies that each additional hearing is less pleasant than the previous one, at least after the initial stage of gaining familiarity with the piece. This is an example of diminishing marginal utility of the piece.

The usual argument in favor of diminishing marginal physical returns is in terms of crowding: if you put too many seeds (or too much fertilizer) in the ground, eventually each additional increment pays off less than previous ones.

### Returns and costs

There is an inverse relationship between returns of inputs and the cost of production. Suppose that a kg of seed costs one Euro (€), and this price doesn't change. There are also other costs, but assume they do not vary with the amount of output. (They are fixed costs.) That means that the first ton of the crop cost one extra € to produce. That is, for the first ton of output, the marginal cost (MC) of the output is 1 €/ton. If there are no other changes, then if the second kg of seeds applied to land produces only 1/2 extra ton of output, the MC equals 1 € per 1/2 ton of output, or 2 € per ton. Similarly, if the third kilo produces 1/4 extra ton, then the MC equals 1 € per 1/4 ton, or 4 € per ton. Thus, diminishing marginal returns imply increasing marginal costs. This also implies rising average costs. In this numerical example, average cost rises from 1 € for 1 ton to 2 € for 1.5 tons to 3 € for 1.75 tons, or from 1 to 1.333 to 1.71 € per ton (approximately).

In this example, the marginal cost equals the extra amount of money spent on seed divided by the extra amount of crop produced, while average cost is the total amount of money spent on seeds divided by the total amount of crop produced. Cost can also be measured in terms of opportunity cost.

## Returns to scale

Note that the marginal returns discussed in this article refer to cases when only one of many inputs is increased, for example the quantity of seed increases, but the amount of land remains constant. If all inputs are increased in proportion, the result is generally constant or increased output - see Economies of scale.

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