Best-known Curves in Arts, Humanities, and Social Sciences

Laffer curve – an inverted-U arch plotting government tax revenue (vertical) against the statutory tax rate (horizontal). Revenue is nil at 0 % and, in theory, again at 100 %, so somewhere in between lies the controversial “T*” that maximises receipts. The sketch still underpins debates about whether rate cuts can ever “pay for themselves.”
Rahn (or Armey) curve – a twin of Laffer but with economic-growth rate on the vertical axis and total public spending as a share of GDP on the horizontal. It likewise humps over, suggesting that beyond a certain size the state stifles growth instead of nurturing it.

Kuznets curve – another inverted U. As per-capita GDP rises, income inequality first widens (industrial take-off) then narrows (mass education, welfare, services). Critics point to countries that never bend down, or bend back up in a “N-shape.”
Environmental Kuznets curve – the same outline for pollution per person instead of inequality. It asks whether getting richer eventually “cleans up” the environment; evidence is mixed and pollutant-specific.
Lorenz curve – start with the 45° equality line, then bow it toward the bottom-right. The deeper the sag, the more unequal the cumulative share of income/wealth. The shaded gap yields the Gini coefficient.
Pareto (80/20) curve – a steep front followed by a long, thin tail when you plot resource share versus population share. It visualises winner-takes-most dynamics from wealth to software bugs.
Calmfors–Driffill curve – an inverted U linking union centralisation and unemployment/inflation outcomes; the worst labour-market performance sits in the middle, not at either extreme of bargaining power.

Phillips curve – a downward swoop between unemployment and inflation (or wage growth). Once a policy work-horse, it flattened or shifted during stagflation and again after 2010, fuelling disputes about expectations and global slack.
Beveridge curve – a bent boomerang: vacancy rate falls as joblessness rises. Outward shifts after a shock signal matching frictions or geographic/skill mismatches.
Okun’s law “curve” – really a straight but important line: every extra percentage point of unemployment roughly subtracts two from GDP growth, reminding forecasters that output gaps have human costs.
Yield curve – the term-structure line that charts interest rates against bond maturities. Its normal upward slope foretells growth; an inversion has preceded most U.S. recessions.
IS-LM curves – two intersecting bends locate macro-equilibrium where real-sector demand (IS) meets money-market supply (LM); policy shifts slide or twist each limb.

J-curve – after a currency devaluation, the trade balance often sinks before it soars, tracing a letter “J.” Contracts are sticky, quantities slow to adjust, so the gain shows up only later.

Diffusion-of-innovation S-curve – cumulative adopters over time crawl, then rocket, then plateau, explaining everything from smartphones to social reforms.
Bass diffusion curve – a mathematically neat S that separates “innovators” (parameter p) from “imitators” (q), letting forecasters time the sales peak.
Gartner hype cycle – a roller-coaster: “technology trigger,” “peak of inflated expectations,” “trough of disillusionment,” “slope of enlightenment,” “plateau of productivity.” It cautions managers that media buzz outruns utility.

Experience (learning-cost) curve – on log–log axes, unit cost slides down by a fixed percentage every time cumulative output doubles; strategists use it to price aggressively and out-scale rivals.
Learning curve (psychological) – performance or time-per-task improves steeply at first, then flattens: “diminishing returns to practice.”
Bathtub curve – in reliability engineering, failure rate over time starts high (infant mortality), runs flat (useful life), then climbs again (wear-out). Maintenance teams plan spares and warranties around it.

Yerkes–Dodson curve – an inverted U between arousal/stress and task performance; both boredom and panic harm results, so designers aim for the “just-right” midpoint.
Ebbinghaus forgetting curve – an exponential plunge of memory retention after learning, then a tail. Spaced-repetition software schedules reviews at the inflection points.

Age–crime curve – arrests or offences spike in late teens, tumble through adulthood, and flatten in old age, appearing robust across eras and cultures.
Demographic-transition curve – tracing birth and death rates through four (sometimes five) stages of development, it produces the famous population “hump” of rapid expansion followed by stabilisation or decline.

Zipf’s law line – plot word frequency against rank on log–log axes and you get an almost perfect straight line with slope ≈ –1: the backbone of search indexing and corpus linguistics.
Heaps’ law curve – vocabulary size grows sub-linearly with corpus length, yielding a concave-upward arc that helps engineers allocate memory for text analytics.
Menzerath–Altmann law – the longer a linguistic unit (word, sentence, phrase), the shorter its average constituents, producing a downward-sloping curve of length versus sub-length.

Freytag’s pyramid – map dramatic tension against story time and you climb to a peak (climax) then descend to resolution, forming a triangle/pyramid still taught in screen-writing handbooks.
Hero’s-journey arc – Joseph Campbell’s circular trek of departure, initiation and return; if unrolled left-to-right the tension line resembles a sine-wave rise, dip and final lift. Modern fiction, film, even advertising borrow it relentlessly.

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