Talk:Diminishing returns

application of term outside of economics

The law of Diminishing Returns can arguably apply(in both psychosocial and economic senses) to technological progress over time and to increasing social complexity. -Agreed. I have added how it can be explained outside of economic theory. ValTee28 (talk) 04:36, 19 April 2021 (UTC) Zara

Very bad sign: rerouted here from "increasing returns"

I was rerouted here from a page on Economist Brian Arthur. I had been reading about his ideas in a book by Economist Douglass North. I wanted to learn more about increasing returns and its implications. I found quite the opposite. I was back in Econ 101-land. This re-route is a bad sign. If North is a laureate and his ideas, and the ideas of economists who influenced him (which helped him win the prize) are not being represented, then the WikiProject Economics thing is not doing its job, eh? Or is it the job of the project to redirect people away from ideas that clearly show flaws in orthodoxy. If that isn't the purpose, this makes it feel that way. 32TWMV 21:14, 2 March 2023 (UTC) — Preceding unsigned comment added by Samueldee (talk • contribs)

I agree, I was also redirected, and I'd support diminishing returns having it's own page. Or at least a more major section in this article.

098oik (talk) 12:35, 26 July 2023 (UTC)

Likewise! BemusedObserver (talk) 10:32, 27 November 2025 (UTC)

Syntax

This is such a poorly written article. The order of words in just about every sentence is weird and confusing and needs to be completely written. I would do this myself but I don't know what any sentence is trying to say. Nachopath (talk) 10:56, 9 July 2023 (UTC)

Here's an example from the article:

There were some common examples in this concept. For example, social media marketing. When we attempt that using social media marketing will double the profits, however, there could be a chance for great amount of information that published out to public and caused decreasing in profits. In this situation, marketing department should adjust the other variables which were the social media channels they have used, monitoring and analysing.

Nachopath (talk) 11:00, 9 July 2023 (UTC)

I've done my best to re-write it a bit and delete the completely nonsensical stuff. It still needs more work; I think it's mainly the History section that needs attention. I didn't check for factual inaccuracies.

098oik (talk) 12:35, 26 July 2023 (UTC)

This article is excellent, however I'm poorly written. ~2026-38728-73 (talk) 19:04, 1 August 2026 (UTC)

Ceteris paribus is jargon

I won't edit (not my area), but ceteris paribus is a jargon that puts off the non-initiated. As an encyclopedia, Wikipedia should be accessible to the non-specialist educated reader. I suggest the latin expression be changed to "all other things being equal" or the like. Please keep Wikipedia readable; don't let economy get to the unintelligibility of statistics pages... Vmkern (talk) 15:00, 15 January 2024 (UTC)

It should explain what it is. It has been taught to me before. ~2026-38728-73 (talk) 19:24, 1 August 2026 (UTC)

Wrong (non-canonical) definition of diminishing returns

Ultimately diminishing (marginal) returns refers to a concave portion of a production curve. Said another way, it's a situation where the marginal return is decreasing as the input increases. That's the canonical definition, and the one described in the article's opening.

Later in the article, there's a mathematical definition given which is quite different: there diminishing returns is defined as the marginal return being less than 1! The factory floor example (hiring more labour) is also describing this non-canonical and incompatible sense of diminishing returns. BemusedObserver (talk) 10:36, 27 November 2025 (UTC)

You might be wrong. One of them might be referring to the integral and the other the derivative. It is quite possible that the integral accumulation properties change when the proportionality goes below 1. The quotient rule in the form I would use, is that the derivative of the 'area' (y'x-xy') per the denominator squared is proportional to the derivative of the proportion of the two. Another way is through partial derivatives and calculating two ways at once, partial derivatives mentally and total derivative on paper. This fixes the ordering issue in calculations. Besides that say one has a situation where y'/x'<1. That could mean that if the slope is constant than y>x. At certain points where the concavity changes the slope is locally constant there. If the description of the number of workers depends on the original number of workers, then one has W=y'/y data. Thus one gets (W-x'/x)*(y/x). Assuming x'=1 we get (W-1/x)*(y/x). But more importantly if one assumes x'=0, then we get Wy/x. Now for this to be able to decrease after increasing, it is evident that W<1, so the top of the curve gets 'squeezed', to be smaller than the average proportion y/x. Thus the curve is squeezing at the top because it is less than average. That is a necessary condition for y'/x' to be less than y/x. Thus the curve is flying past and below y=ax, the proportionality. Thus it is likely that the two definitions are actually compatible. I would actually have to do a bigger check to see if I'm right, but it is not a guarantee that these definitions are incompatible due to some calculus and the type of wording of the problem. The wording of a problem drastically affects the calculus of the problem and most people who speak English better than Math treat these things as the same when they are quite different because that is the ignored reality we live in. ~2026-38728-73 (talk) 19:42, 1 August 2026 (UTC)

Running the calculations again, I see that if x'=1 (via dy/dx rules) a more accurate answer gives (y'/y-1/x)*(y/x). Now if y'<1, ( the 'proportion proportion' is defined by (y'/y-1/x), defining the top-graph squeezing). Now y'/y must be less than 1/x, for the squeezing to begin. Now suppose we use the 2nd derivative. That would mean y should vanish. Thus y' is "locally" (neighborhood, really) constant (a minimum). Now that means y'/y=W. Thus we see (y'/y)'=-y'/y^2. Thus the condition implies: dA+A/y=0, for this to work. Since y' is at a minimum, we see -y'/y^2 is the derivative of y'/y at that location. Thus it is locally is described by (-y'/y^2*(x-x_0)+(y'/y)). Now we plug that in: ((-y'/y^2*(x-x_0)+(y'/y))-1/x)*(y/x). Now if the curve was always accelerating upward (the whole time) (and also increasing and greater than zero) then y'/x'>y/x, since the future slope is greater than the average slope. The moment this changes, the curve is deaccelerating. Thus one must find where y'=y/x. That then shows us that x=y/y' is the location of interest, correct? Thus xy'-y=0 gives us that location. If that equation is true, we can understand the neighborhood around it. Thus locally we have: y'=y/x, giving the local solution ln(y)=ln(x)+c, that is a line, as noted. That would mean that y/x does NOT change near here, indeed since y=0. Now y'/y=G(t), thus: (y/x)/y=A. Thus A=1/x is also a location of interest. Thus we have Ax=1 as a location of interest. Thus x=1/A is of interest. We then use ln(y'/x')-ln(y/x) to describe more (the squeeze type 2). We get (y'/y-x'/x)-(ln(y)-ln(x)). This must equal zero. We know that (y'/y-x'/x)*(y/x) should equal zero. Thus: ln(y)-ln(x) should equal zero at the location of interest. Thus the location of interest also requires y=x. Given that Ax=1, Ay=1, thus y'=1 is the location of interest. Thus the definitions are compatible under certain smoothness conditions and some inequalities (non-negativity of 1st and 0th derivative). I will correct this if anything stupid pops up. ~2026-38728-73 (talk) 20:23, 1 August 2026 (UTC)

Made a mistake. (y'/y)'=-(y')^2/y^2. However it still matches the overall condition. I'm tired and forgot to eat again. I am a rigid thinker at times. I focused on the (many other and 'unnecessary' but world protective) tasks at hand. ~2026-38728-73 (talk) 20:31, 1 August 2026 (UTC)

Another possible stupid mistake. I likely meant y'/y=1 and Ay'/y=1. And another big one it should be: (ln(y')-ln(x'))-(ln(y)-ln(x)). I'm dumb. Thus yx'-y'x=0. Thus I might be wrong here. I'm likely wrong. A possible counterxample is arctan(x)-0.001x. My bad?! But what about the growth condition? We get (1/(x^2+1)-0.001)/(arctan(x)-0.001x). If y'/y>1 then we have minimum growth y(0)*e^x, right? The slope is y(0)*e^x. Thus provided x>0, we see y(0)>=1 for this to work. So I might be correct. I'd rather display my train of thought than give a good clean answer. Life is not clean nor happy. I shouldn't expect either. I'd tell it like it is. ~2026-38728-73 (talk) 20:42, 1 August 2026 (UTC)

I'm stupid. It should have the minimum solution y(0)*e^x, with slope y(0)*e^x, thus y>=y(0) is the condition. That would mean that y' can be anything?? But y' would always be increasing? But if it goes from 1 to less than 1 that is no longer true. The possible violation of the minimum solution occurs when y'<1. But does it occur at greater numbers? It can really be any decrease in y', rather than a decrease past 1, right? So could it deaccelerate at 2? We see y'/y=n-x. The solution is: k*e^((n-x)^2/2). k can be anything, so the post is correct? I'd rather just prove it. But the deacceleration 'curvature' is given by p^2+p_q. Thus for that one needs p_q=p^2 at the critical location. We see k is annihlated by the growth condition? Thus we get: k*(n-x)*e^(-(n-x)^2/2) as the velocity. Yep the original post is correct. However caution must be used when dealing with y'/y and y'. They are different. The acceleration is (k*(n-x)^2-k)*e^(-(n-x)^2/2), which only the sign matters, and k is unrestricted. So I was wrong but wanted to make sure and prove it for unusual wordings that may be ignored. I should likely look up the definitions in more detail just to be sure. ~2026-38728-73 (talk) 20:57, 1 August 2026 (UTC)

I think I found why it is stated like this. It might be that it is a global condition rather than a local condition. If f(2x)/2<f(x), then would it have to diminish at ANY point in the curve? A cool example is via ((2x^2-1)X(x/2))^(inf)*(1-x^2/2). What does that produce? The answer might be the cosine function and is a way of integrating it into hardware. So these dilational superfunctions must be studied in detail for non-point-wise mathematical language. This is far from resolved. It might be completely fine at a global level, just locally it doesn't tell you where the boundary is. I will take some time to study this while studying hardware acceleration tonight because the formulas here are very important for economics and computers. I'd rather learn as much as I can and really make sure it is 100% false before saying it is poorly written. Most of this is not economics at all, it is infinite recursion of operators, that is well above an economist's understanding so this must be verified from another perspective because studying economics in a normal way of thinking won't fix this at all. These are problems that require far more training to interpret correctly. Proving/disproving them would be a good idea. I wonder what they are actually saying. I won't assume any single interpretation, because that is not fair and far too easy. ~2026-38728-73 (talk) 21:08, 1 August 2026 (UTC)

It seems by intuition that these are global statements. They refer to everywhere on the curve and most of these statements are mathematically equivalant (the doubling relations). I'd have to check what is supposed to be said. It seems like the inequalities are another way of expressing the concavity. It seems by reading it that it is a illustration of a particular motion of the curve for people to understand without calculus. It is a small test that omits the larger conditions. However it makes sense if the number 2 or doubling was just an example. It describes what must happen in a 'pseudo-discrete' system. One can define that in a footnote (a lot of math)? Suppose it is a constraint that has some unknown expansion algorithm that would make the statement accurate. It describes how one would approach the situation. It is mainly for a visual introduction, rather than a mathematical one so it is inaccurate but quite helpful. It helps a lot. If one rigorously treated it, 2 is a placeholder for any number. If one looks at the data for doubling only and considered the rest of the data as irrelevant then this might be correct under certain interpolations. Data storage for the curve must be accounted for to perform calculus in the real world. If one redefines calculus under that basis and had closure of operations in that basis then it would work like a charm. It would consider non-power-or-two multiplication as an illegal operation that is not stored in the data structure. Thus removing and interpolating with all operations would redefine calculus to support such an example as actually truthful in that data type. One might view this as a kind of projection. Thus it means that any values that are not used simply don't exist at all in the first place and never existed matching human intuition. ~2026-38728-73 (talk) 21:34, 1 August 2026 (UTC)