# Is there any empirical evidence for the so-called “law” of diminishing returns

The "law" of diminishing returns is usually "demonstrated" with made-up examples (programmers working on a software, farmers acquiring land...), but rarely on evidence. Is there any empirical research on actual data to acknowledge and quantify this law?

• I don't think the "law" can be illustrated with acquiring land (unless you keep the labour fixed). Can you be more specific? – Fizz Oct 16 '19 at 3:11
• And generally speaking the "law" is premised on keeping some factor fixed. Are you asking if the premises typically hold? I'm guessing you're not doubting the rather trivial math involved in the proof. – Fizz Oct 16 '19 at 3:18
• "Turgot [11] introduced into economic thought a proposition which has come to be known as the “Law of Diminishing Returns.” [...] Loosely worded, the proposition asserts that as equal quantities of capital and labor are applied successively to a given plot of land, the output resulting from these applications will increase monotonically at first up to a certain point, after which further applications will result in steadily decreasing product increments tending to zero." link.springer.com/chapter/10.1007/978-3-642-80864-7_17 – Fizz Oct 16 '19 at 3:28
• The "law" was apparently initially illustrated with agriculture by many authors, including Turgot. The rationale is: a farmer would first acquire the best (most productive) available plots ; later acquired plots would necessarily have lesser productivity. – Arthur Oct 16 '19 at 22:17
• I am not asking about math derivation, but about real-world, duly-quantified examples. – Arthur Oct 16 '19 at 22:21

The above chart is from Agroecosystems, nitrogen-use efficiency, and nitrogen management by Cassman KG, Dobermann A, Walters DT, and it deals with this sort of question quite extensively for those interested in all the gory details.

• Interesting chart, but wouldn't it be more persuasive (as evidence of diminishing returns in an economic context) if the horizontal axis showed application of N fertiliser (which is clearly an economic input) rather than N accumulation (which sounds more like an effect)? – Adam Bailey Oct 16 '19 at 21:15

There isnt any data because we can demonstrate this fact by the production of anything by holding the number of laborers fixed and increasing the amount of equipment.

Its an logic which holds in reality and thus generates a theory.

You can do it with seeing how many cookies you can bake cookies in an hour with different resources. If its just you, increasing the number of ingredients may increase your yeild or even having another oven may speed up your time. However at some point there will be no gain from getting more ingredients or more equipment- you're simply limited by what you have.

Now what would be interesting is checking if wicksell's law holds (i.e. $$\frac{\partial F^2}{\partial K \partial L} \geq 0$$) however this is also logically sound.

Bottom line we can demonstrate it, but its logically consistent enough for us to take it for granted.

• If "we can demonstrate it" then why do you claim there isn't any data? Either we do not know if it can be demonstrate it, or someone has done so, and there is data. – Giskard Oct 18 '19 at 6:24
• -1 "Bottom line we can demonstrate it, but its logically consistent enough for us to take it for granted." That something is logically consistent does not imply that it occurs in reality, since the assumptions from where you start reasoning do not typically correspond to reality. – user18214 Oct 19 '19 at 11:26
• @Giskard well its trival research. Theres writings in wealth of nations and paul samuelson's Economics. But further than that i dont think its necessary. – EconJohn Oct 20 '19 at 1:33
• @user18214 this is the whole approach of the austrian school and marginalists. – EconJohn Oct 20 '19 at 1:36
• On the word trivial: if something is trivial, then there is no need to show it, because everyone knows it. But in case someone does not know this, the masters can easily give an answer. If getting this empirical data is trivial, then I am afraid I am someone who does not know how. I need your help, please point to such empirical research. – Giskard Oct 20 '19 at 10:23