The Law of Diminishing Returns: Definition, Curve, Examples and Where Ad Spend Stops Paying

The law of diminishing returns states that when you keep adding one input, such as labour, fertiliser or ad spend, while the other inputs stay fixed, each extra unit eventually adds less output than the unit before it. Economists also call it the law of diminishing marginal returns, diminishing marginal returns or the law of variable proportions.

In advertising, the fixed factor is the audience a channel can reach in a week, so every channel has a spend level past which the next dollar buys less revenue than the last. This guide works through the economics version, with a worked table, the curve, the three stages and the history, then the advertising half that most economics textbooks stop short of: concave and S-shaped response curves, adstock, marginal ROAS against a break-even line, and how a marketing mix model estimates where each channel stops paying.

What is the law of diminishing returns?

The law of diminishing returns describes the short run, when at least one factor of production cannot change. A farm has a fixed field, a café has one espresso machine, and a marketing team has a fixed audience it can reach this quarter. Adding more of the variable input raises output, but past some point each addition raises it by less.

The law of diminishing returns concerns marginal output, the extra from the last unit, so total output can keep rising after marginal output starts to fall. Returns can also rise before they fall, as when a second cook splits the tasks with the first and adds more than the first did.

Diminishing returns meaning in plain English

More of the same thing helps less and less. The tenth hour of revision adds less to an exam score than the second, because attention is the constraint, and it binds harder the more you add.

The assumptions behind the law

The law of diminishing returns holds under four conditions.

• At least one input is fixed. Without that, you are talking about returns to scale.
• Technology is constant. A better espresso machine shifts the whole curve upward.
• Units of the variable input are interchangeable, so a fall in output comes from the fixed factor and not from a weaker hire.
• The time frame is the short run, when the fixed input cannot be expanded.

Why diminishing returns happen

The mechanism behind the law of diminishing returns is crowding. Each new unit of the variable input gets a smaller share of what cannot grow: machine time, land, counter space, or the people who have not yet seen your advert. The most responsive uses also get taken first, coordination costs rise with headcount, and repetition wears down response.

A worked example: total, marginal and average product

Take a café whose fixed factors are one espresso machine and one counter. The variable input is baristas on shift, and the output is drinks served per hour. The figures are illustrative.

Espresso machines (fixed)	Baristas (variable input)	Total product (drinks/hour)	Marginal product	Average product
1	1	10	10	10.0
1	2	24	14	12.0
1	3	39	15	13.0
1	4	52	13	13.0
1	5	61	9	12.2
1	6	66	5	11.0
1	7	66	0	9.4
1	8	62	-4	7.8

How to read the table

The second and third baristas add more than the first (14 and 15 drinks), because one can pull shots while another takes orders. From the fourth onwards, each hire adds less: 13, then 9, then 5. The seventh adds nothing, and the eighth blocks the counter, so total output falls to 62. Output rises up to the sixth hire even though marginal product has been falling since the fourth.

How to calculate marginal and average product

• Marginal product = change in total product / change in the variable input. From three to four baristas: (52 minus 39) / 1 = 13 drinks.
• Average product = total product / units of the variable input. With five baristas: 61 / 5 = 12.2 drinks each.

The law of diminishing returns curve

Plotting the table gives the law of diminishing returns curve, usually drawn as two panels that share one horizontal axis.

Total product: steep, then flatter, then falling

Total product gets steeper while marginal product rises, flatter as it falls, levels off where it reaches zero, and then turns down. The switch from steeper to flatter is the inflection point, exactly where marginal product peaks.

Marginal product cuts average product at its peak

The bottom panel shows three relationships.

1. Marginal product peaks first, with the third barista, at the inflection point of total product.
2. Marginal product crosses average product at the maximum of average product, with the fourth barista, both at 13. While the last hire beats the average, the average rises; once it falls below, the average falls.
3. Total product peaks where marginal product reaches zero, with the seventh barista.

The three stages of production

Textbooks split the law of diminishing returns curve into three stages, shaded in the figure. In the café, Stage I runs from the first to the fourth barista, Stage II from the fourth to the seventh, and Stage III beyond the seventh.

Stage I: increasing returns

Average product is rising, because each new barista adds more than the current average. The stage ends where marginal product equals average product. Stopping here wastes the fixed factor, since one more hire would raise output per worker.

Stage II: diminishing returns

Average and marginal product both fall, but marginal product is still positive, so total output keeps rising until it peaks where marginal product hits zero. A rational producer operates here: before this stage more input still raises output per worker, and after it the last unit lowers total output.

Stage III: negative returns

Marginal product is negative. In farming this is the fertiliser that burns the crop; in advertising it would be frequency so high that it puts buyers off.

Marginal returns start diminishing after the third barista, one hire before Stage II begins with the fourth.

The point of diminishing returns, and how to find it

The point of diminishing returns, sometimes called the margin of diminishing returns, is the level of input after which each extra unit adds less than the one before. It marks where the law of diminishing returns starts to bite, at the peak of marginal product and the inflection point of total product.

Finding it in a table

Calculate marginal product for every step and find the largest value. The point of diminishing returns comes straight after it. In the café, marginal product peaks at 15 with the third barista, so diminishing returns set in with the fourth.

Finding it on a curve

With a smooth production function, it is where the second derivative of output with respect to the input equals zero, which is also where the total product curve is steepest.

The point of diminishing returns is not the optimal point

The law of diminishing returns tells you the next unit is worth less than the last. Whether to buy it depends on price and cost.

Keep adding the input while the value of its marginal product exceeds its cost. Suppose, for illustration, that each drink earns the café $4 after ingredients and a barista costs $25 an hour. The fifth barista adds 9 drinks, worth $36, so that hire pays. The sixth adds 5 drinks, worth $20, so it does not. The café should staff five baristas, two past the point of diminishing returns. Ad spend follows the same rule, with marginal ROAS in place of marginal product.

Diminishing marginal returns vs diminishing marginal utility vs returns to scale

Three ideas get confused because they share vocabulary. OpenStax's Principles of Economics defines the first two separately: the law of diminishing returns concerns adding resources to production, while diminishing marginal utility concerns consumption, where each additional unit tends to satisfy less than earlier ones. Decreasing returns to scale, the third idea, means a proportional increase in all inputs produces a less than proportional increase in output.

Concept	What changes	Time frame	Example
Diminishing returns	One input rises, the others stay fixed	Short run	A sixth barista at one machine adds 5 drinks an hour
Diminishing marginal utility	The quantity you consume rises	Any period	A third coffee pleases you less than the first
Decreasing returns to scale	All inputs rise in the same proportion	Long run	Doubling cafés, staff and machines less than doubles output

Why the law applies only in the short run

The law of diminishing returns needs a fixed factor, and the short run is the period in which at least one factor is fixed. In the long run the café can buy a second machine, which resets the curve.

What is the opposite of diminishing returns?

In the short run, the opposite is increasing marginal returns, the Stage I region. In the long run, it is increasing returns to scale, where doubling every input more than doubles output. That usually comes from specialisation and from equipment that only pays at scale. Network effects, where a marketplace grows more useful as users join, are a related idea on the demand side.

History of the law of diminishing returns

Turgot gave the first recorded statement in 1767, and four British economists reached it independently in 1815.

Turgot and the spring, 1767

The French economist Anne Robert Jacques Turgot (1727 to 1781) set out the law in his 1767 observations on a memoir by Saint-Péravy: "The earth's fertility resembles a spring that is being pressed downwards by the addition of successive weights." In his analogy the first small weights leave no visible result, the spring then gives way, and after that each added weight moves it less. That is increasing returns followed by diminishing returns, the same order as Stage I and Stage II in the café chart.

1815: West, Malthus, Ricardo and Torrens

The law of diminishing returns entered British political economy in 1815, during the debate over the Corn Laws. Edward West's Essay set out diminishing returns to land cultivation and the theory of differential rent that year, independently of but at the same time as Thomas Malthus, David Ricardo and Robert Torrens.

Ricardo and successive doses of capital

Ricardo used the law to explain rent. In his 1817 Principles of Political Economy and Taxation, successive portions of capital on the same land yield 100, 90, 80 and 70, and the rent of 60 is the sum of each earlier portion's surplus over the last. McGraw-Hill's economics text calls this the intensive margin of cultivation, and notes that without diminishing returns you could grow the world's food supply in a flower pot. Francis Edgeworth (1845 to 1926) later became the first to separate average product from marginal product explicitly, the distinction the café chart depends on.

The law of diminishing returns in everyday life

It shows up wherever one thing is fixed and you keep adding another.

• Exam revision (fixed: attention span). The sixth hour in one sitting adds far less than the first.
• Cooks in a small kitchen (fixed: stoves). The fourth cook mostly waits for a burner.
• Fertiliser on one field (fixed: land). Past a point, extra fertiliser damages the crop.
• Agents on a help desk (fixed: the specialists they escalate to). Queue times fall quickly with the first hires, then barely move.
• Discount depth in a promotion (fixed: the shoppers who would ever buy). Each extra point of discount tends to win fewer new buyers.
• Ad frequency to one audience (fixed: the audience). Early exposures inform, later ones mostly repeat, and very high frequency can irritate.

Is the law of diminishing returns universal? It holds wherever a genuinely fixed factor exists and the variable input keeps rising. It says nothing about the long run, when the fixed factor can grow, and returns can rise before they fall (Stage I).

The law of diminishing returns in advertising: the response curve

An advertising response curve plots incremental revenue against spend in one channel, and its shape follows from the law of diminishing returns. The audience a channel can reach in a week is the fixed factor. The first dollars reach the most responsive people; later dollars buy repeat frequency or less likely buyers.

Why ad spend saturates

A Google paper on Bayesian media mix modeling states it directly: "Advertising usually has lag effects and diminishing returns, which are hard to capture using linear regression" (Jin, Wang, Sun, Chan and Koehler, Google, 2017). A straight-line model ignores the law of diminishing returns by assuming the millionth dollar works as hard as the first.

What the evidence says about advertising response

A meta-analysis of 872 short-term brand advertising elasticities from 57 studies published between 1960 and 2008 found an average elasticity of 0.12, well below the earlier meta-analytic mean of 0.22, with only 53% of the estimates significantly greater than zero.

An elasticity of 0.12 means a 1% increase in advertising goes with roughly a 0.12% increase in sales. If it held constant, simple arithmetic (our calculation, not the study's) implies that doubling spend lifts sales by about 8.7%, because 2 raised to the power 0.12 is 1.087, and that ten times the spend lifts sales by about 32%.

Concave or S-shaped: saturation curves and the Hill function

Google's Meridian and Meta's Robyn both write the law of diminishing returns down as a Hill function, which has its origins in pharmacology (Hill, 1910) as an empirical receptor model. In words, the response equals the media input raised to the power S, divided by the sum of that input raised to the power S and K raised to the power S.

• K is the half-saturation point, the media level at which the channel delivers half of its maximum effect. Meridian calls it ec. In Jin et al. the curve is applied after adstock and plotted against scaled media spend, so K has to be converted back to dollars before it is compared with a weekly budget.
• S is the slope. Jin et al. show that a slope above 1 is convex close to zero and produces an S shape, while a slope below 1 is more concave close to zero and flattens faster.

Google's Meridian documentation draws the line in the same place: a slope at or below 1 is concave, and a slope above 1 is S-shaped, convex at low spend and concave at high spend. For the Hill function itself, the turn falls somewhat below the half-saturation point, at about 0.58 K for a slope of 2. Meridian's default prior assumes the concave shape, because S-shaped curves can cause problems for budget optimisation and can lead to convergence issues.

The half-saturation point

At K the channel delivers half of its ceiling, and at twice K on a concave curve with a slope of 1 it delivers two thirds. A channel whose adstocked media level sits well beyond its estimated K is a saturation candidate before anyone checks its marginal ROAS.

When an S-curve is real, and when it is an artefact

An S-curve implies a threshold below which spend is too thin to register, as with a television burst too small to build reach. Flexible curvature can also fit a convex start to noise in a short history, and an optimiser then sees a false reward for jumping past the threshold. Treat an estimated S-curve as a hypothesis to test with an experiment before it moves budget.

Do not trust the curve beyond the spend you have tested

A response curve is estimated from the spend levels a channel actually ran at. If a channel has never spent more than $80k a week, everything above $80k is extrapolation with no data behind it. Scale in steps and re-estimate, or test the higher level directly.

Adstock: the carryover effect that is not diminishing returns

Adstock is a separate effect from the law of diminishing returns, although both are transforms applied to media inside a marketing mix model. Adstock spreads spend over time and is linear in spend; saturation is the non-linear part.

• Adstock models when an advert works. An advert seen this week can still drive sales in later weeks, so the model spreads each week's spend forward at a decay rate. The decay chart in our complete guide to marketing mix modeling shows the shape.
• Saturation models how much each extra dollar in a period can buy.

Carryover vs saturation

A channel with a long memory, such as brand television, pays back over many weeks. Fit it with too short a decay and the model can understate the channel's return, because much of its effect lands outside the window, and part of that shortfall can show up as saturation the channel does not have. Estimate adstock and saturation together, per channel, over enough history for the tail to show.

Typical decay rates by channel

Meta's Robyn documentation gives rule-of-thumb geometric decay rates from weekly models: TV between 0.3 and 0.8, out of home, print and radio between 0.1 and 0.4, and digital between 0.0 and 0.3. A decay rate (theta) of 0.75 means 75% of one period's advertising carries over into the next. Robyn's team calls these figures anecdotal, so treat them as starting points for priors.

Marginal ROAS and the break-even line

Marginal ROAS is the law of diminishing returns measured in dollars.

• Average ROAS is the revenue a channel drove divided by its total spend, including the cheap early dollars.
• Marginal ROAS (mROAS) is the extra revenue from the next dollar. Meridian's glossary defines marginal ROI as the derivative of the response curve, approximately the return on the next dollar beyond current spend, and treats a channel as saturated once marginal ROI becomes small, noting that "saturation is a general term, and no specific threshold is defined."

Our guide to ROAS covers platform, incremental and marginal ROAS in more depth.

Average ROAS vs marginal ROAS

Take an illustrative channel whose weekly incremental revenue follows a concave curve: revenue = $500k x spend / (spend + $100k). The numbers are hypothetical.

Weekly spend	Incremental revenue	Average ROAS	Marginal ROAS
$50k	$166.7k	3.33	2.22
$100k	$250.0k	2.50	1.25
$150k	$300.0k	2.00	0.80
$200k	$333.3k	1.67	0.56

At $150k a week the channel reports an average ROAS of 2.00 while the last dollar returns 80 cents. On a concave curve, average ROAS always sits above marginal ROAS, because it still carries the early dollars.

Revenue break-even vs profit break-even

• Revenue break-even is a marginal ROAS of 1.0, where the next dollar of media returns a dollar of revenue. On this curve that happens at about $124k a week.
• Profit break-even is a marginal ROAS of 1 divided by gross margin. At a 40% gross margin, each extra media dollar needs $2.50 of revenue, so break-even marginal ROAS is 2.5, reached at about $41k a week.

A team working to revenue break-even would triple spend from $41k to $124k a week, and every dollar in that range loses money once cost of goods is counted. Agree which line applies with finance before anyone opens the optimiser.

How marketing mix modeling finds where each channel stops paying

A marketing mix model turns the law of diminishing returns into a number per channel, in six steps.

1. Assemble weekly spend per channel, the outcome, and controls such as price, promotions and seasonality, over enough history that each channel has run at a range of spend levels.
2. Apply adstock, so each channel's effect decays over later weeks at its own rate.
3. Apply saturation through a Hill or similar curve, so the model learns each channel's half-saturation point and slope. On a concave curve (Hill slope at or below 1), returns diminish from the first dollar, so the point of diminishing returns is at zero spend and the number that matters is where marginal ROAS crosses break-even. On an S-shaped curve (slope above 1), the point of diminishing returns is the inflection point. It sits below K, at K multiplied by ((S minus 1) divided by (S plus 1)) raised to the power 1/S.
4. Estimate response curves with uncertainty, so every point on each curve carries a credible interval.
5. Read marginal ROAS at current spend. A channel that is past its point of diminishing returns, with its whole interval below break-even, is overfunded.
6. Reallocate from low to high marginal ROAS until marginal returns are roughly equal and above break-even, within contracts, minimum spends and channel capacity.

Equalise marginal returns, then check the break-even

Step six contains two tests. On concave curves, equal marginal returns maximise revenue for a fixed budget: if one channel's last dollar returns 0.80 and another's returns 1.35, moving a dollar between them gains 55 cents. The break-even check asks whether the budget should be that large at all, and in TV at least, many advertisers fail it. A study of TV advertising across 288 brands (Shapiro, Hitsch and Tuchman, Econometrica, 2021) found negative ROI at the margin for more than 80% of them, implying over-investment by most firms, and an overall ROI on the observed advertising schedule that was positive for only one third.

Calibrate the curve with an experiment

Curves estimated from observational data can be wrong in ways fit statistics will not reveal. A lift experiment gives the model an independent point on the curve, and our guide to incrementality testing explains how those results enter the model as priors or constraints. Once the curves are calibrated, what-if analysis tests budget scenarios against them before any money moves.

A reallocation example: why the best average ROAS is often the most saturated

Take two channels, an illustrative $200k weekly budget and hypothetical response curves.

• Paid social: incremental revenue = $500k x spend / (spend + $100k). At $150k a week it returns $300k, an average ROAS of 2.00 and a marginal ROAS of 0.80.
• Connected TV (CTV): incremental revenue = $360k x spend / (spend + $150k). At $50k a week it returns $90k, an average ROAS of 1.80 and a marginal ROAS of 1.35.

Paid social leads on average ROAS, but CTV leads on marginal ROAS.

Move $30k a week from social to CTV. Social at $120k returns $272.7k (average ROAS 2.27, marginal ROAS 1.03). CTV at $80k returns $125.2k (average ROAS 1.57, marginal ROAS 1.02). Combined incremental revenue rises from $390.0k to $397.9k a week, about 2% more, or roughly $413k a year on an unchanged budget. The two marginal returns are now almost equal, so this split is close to the best one available on these curves.

Social's average rose as its budget fell, because the dollars removed were its least productive. CTV's average fell as its budget rose, while the business made more money. The channel with the best average ROAS is often the one funded hardest, because it looked best, and each round of funding pushed it further along its curve.

The break-even check still applies. Both channels now return about $1.02 on the marginal dollar, which clears revenue break-even but falls well short of the 2.5 a business with a 40% gross margin needs. For that business, the next conversation is the size of the budget as well as its split. Our guide to media planning covers how an allocation like this becomes a flighted plan.

Frequently asked questions

What is the law of diminishing returns in simple terms?

The law of diminishing returns says that if you keep adding more of one input while everything else stays fixed, each extra unit eventually adds less than the one before. It is also called the law of diminishing marginal returns or the law of variable proportions. Total output can keep rising for a while; the extra output from each additional unit shrinks.

Who came up with the law of diminishing returns?

The first recorded statement came from the French economist Turgot in 1767, who compared soil fertility to a spring pressed down by successive weights. In 1815, Edward West, Thomas Malthus, David Ricardo and Robert Torrens each set out diminishing returns to land independently. Ricardo used it to explain rent through successive doses of capital on the same land, now taught as the intensive margin of cultivation.

What are the three stages of the law of diminishing returns?

In Stage I (increasing returns), average product rises, and the stage ends where marginal product equals average product. In Stage II (diminishing returns), marginal and average product both fall but total output still rises, until marginal product reaches zero. In Stage III (negative returns), each extra unit lowers total output. Rational producers operate in Stage II.

Is the law of diminishing returns short run or long run?

It is a short-run law. It requires at least one fixed input, such as land, machinery or the audience a channel can reach this quarter. When all inputs can change together, economists talk about returns to scale instead. Decreasing returns to scale is a separate, long-run concept.

How do you calculate the point of diminishing returns?

Work out marginal product for each extra unit of input by dividing the change in total output by the change in input. The point of diminishing returns comes straight after marginal product peaks. On a smooth curve it is the inflection point, where the second derivative of output equals zero. Whether to stop there depends on price and cost.

How does the law of diminishing returns apply to advertising?

Each channel can only reach so many responsive people in a period, so extra spend buys repeat frequency and less likely buyers. That gives every channel a response curve with diminishing marginal returns. Marketing mix models estimate those curves, separate them from adstock carryover, and read marginal ROAS at current spend, so budget can move from saturated channels to channels with headroom.

How we approach it at Aryma

Applying the law of diminishing returns to a media budget is a modelling problem followed by an allocation problem. Our Peripheral Agentic MMM post argues that the statistical core of a model, such as adstock specification and saturation curves, should stay human-built, with AI agents working around it.

Aryma Nebula, our agentic spend optimiser, turns MMM outputs into weekly and monthly budget allocation decisions. In Aryma Dimension, eMMMy joins the call and draws saturation curves from your own model mid-conversation. Inside ArymaEdge, eMMMy interprets saturation curves and answers the headroom question, such as how far Meta Video can scale before returns start to fall.

If your response curves need building first, see our custom solutions. For help finding where your own channels stop paying, get in touch with us.