Diminishing returns

In economics, diminishing returns are the decrease in marginal (incremental) output of a production process as the amount of a single factor of production is incrementally increased, holding all other factors of production equal (ceteris paribus).^[1] The law of diminishing returns (also known as the law of diminishing marginal productivity) states that in productive processes, increasing a factor of production by one unit, while holding all other production factors constant, will at some point return a lower unit of output per incremental unit of input.^[2]^[3] The law of diminishing returns does not cause a decrease in overall production capabilities, rather it defines a point on a production curve whereby producing an additional unit of output will result in a loss and is known as negative returns. Under diminishing returns, output remains positive, but productivity and efficiency decrease.

The modern understanding of the law adds the dimension of holding other outputs equal, since a given process is understood to be able to produce co-products.^[4] An example would be a factory increasing its saleable product, but also increasing its CO₂ production, for the same input increase.^[2] The law of diminishing returns is a fundamental principle of both micro and macro economics and it plays a central role in production theory.^[5]

The concept of diminishing returns can be explained by considering other theories such as the concept of exponential growth.^[6] It is commonly understood that growth will not continue to rise exponentially, rather it is subject to different forms of constraints such as limited availability of resources and capitalisation which can cause economic stagnation.^[7] This example of production holds true to this common understanding as production is subject to the four factors of production which are land, labour, capital and enterprise.^[8] These factors have the ability to influence economic growth and can eventually limit or inhibit continuous exponential growth.^[9] Therefore, as a result of these constraints the production process will eventually reach a point of maximum yield on the production curve and this is where marginal output will stagnate and move towards zero.^[10] Innovation in the form of technological advances or managerial progress can minimise or eliminate diminishing returns to restore productivity and efficiency and to generate profit.^[11]

This idea can be understood outside of economics theory, for example, population. The population size on Earth is growing rapidly, but this will not continue forever (exponentially). Constraints such as resources will see the population growth stagnate at some point and begin to decline.^[6] Similarly, it will begin to decline towards zero but not actually become a negative value, the same idea as in the diminishing rate of return inevitable to the production process.

The point of diminishing returns can be realised, by use of the second derivative in the above production function.

Which can be simplified to: Q= f(L,K).

This signifies that output (Q) is dependent on a function of all variable (L) and fixed (K) inputs in the production process. This is the basis to understand. What is important to understand after this is the math behind Marginal Product. MP= ΔTP/ ΔL.

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This formula is important to relate back to diminishing rates of return. It finds the change in total product divided by change in labour.

The Marginal Product formula suggests that MP should increase in the short run with increased labour. In the long run, this increase in workers will either have no effect or a negative effect on the output. This is due to the effect of fixed costs as a function of output, in the long run.

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Returns and costs[edit]

There is an inverse relationship between returns of inputs and the cost of production,^[24] although other features such as input market conditions can also affect production costs. Suppose that a kilogram of seed costs one dollar, and this price does not change. Assume for simplicity that there are no fixed costs. One kilogram of seeds yields one ton of crop, so the first ton of the crop costs one dollar to produce. That is, for the first ton of output, the marginal cost as well as the average cost of the output is per ton. If there are no other changes, then if the second kilogram of seeds applied to land produces only half the output of the first (showing diminishing returns), the marginal cost would equal per half ton of output, or per ton, and the average cost is per 3/2 tons of output, or /3 per ton of output. Similarly, if the third kilogram of seeds yields only a quarter ton, then the marginal cost equals per quarter ton or per ton, and the average cost is per 7/4 tons, or /7 per ton of output. Thus, diminishing marginal returns imply increasing marginal costs and increasing average costs.

Cost is measured in terms of opportunity cost. In this case the law also applies to societies – the opportunity cost of producing a single unit of a good generally increases as a society attempts to produce more of that good. This explains the bowed-out shape of the production possibilities frontier.

Justification[edit]

Ceteris paribus[edit]

Part of the reason one input is altered ceteris paribus, is the idea of disposability of inputs.^[25] With this assumption, essentially that some inputs are above the efficient level. Meaning, they can decrease without perceivable impact on output, after the manner of excessive fertiliser on a field.

If input disposability is assumed, then increasing the principal input, while decreasing those excess inputs, could result in the same "diminished return", as if the principal input was changed certeris paribus. While considered "hard" inputs, like labour and assets, diminishing returns would hold true. In the modern accounting era where inputs can be traced back to movements of financial capital, the same case may reflect constant, or increasing returns.

It is necessary to be clear of the "fine structure"^[4] of the inputs before proceeding. In this, ceteris paribus is disambiguating.