Costs
~35 min · WEC13 · 3.3.2
WEC13 · 3.3.2 · 35 min
A firm's curve isn't drawn from convention — it's the mirror image of how productive one more worker is, and you can derive the whole shape from that single fact.
Before you read on
Two or three questions on exactly what this lesson teaches. Being wrong here is fine — it's the fastest way to find out what to pay attention to next.
Every cost curve is built from two pieces
In the short run, at least one factor is fixed — call it capital. Total cost splits cleanly into total fixed cost (TFC, unchanged whatever output is — rent, the machine you already bought) and total variable cost (TVC, which rises with output because it's the cost of the variable factor, usually labour). TC = TFC + TVC. Divide each by output Q and you get the three average measures: AFC = TFC/Q, AVC = TVC/Q, AC = AFC + AVC.
Marginal cost is the cost of one more unit: MC = ΔTC/ΔQ. Because TFC doesn't change with output, ΔTC always equals ΔTVC — marginal cost is driven entirely by the variable factor, which is the fact the whole derivation below rests on.
The law of diminishing returns (spec 3.3.2(2)(b)) says: as you add more of a variable factor to a fixed factor, the marginal product of the variable factor eventually falls. Not immediately — usually marginal product rises for the first few workers (there's enough machinery that an extra pair of hands genuinely helps), then falls once the fixed factor starts becoming the constraint. "Eventually falls" is doing real work in that sentence: the spec doesn't claim marginal product falls from the very first worker, only that it must fall at some point.
This is a short-run law specifically. It describes what happens when ONE factor is fixed and another is added. Diseconomies of scale — long-run average cost rising as output rises — is a completely different mechanism (spec 3.3.2(3)), because in the long run there is no fixed factor at all; every input scales up together. The exam confuses these constantly, in both directions, which is why they get a dedicated trap below.
Mechanism
Why marginal product eventually falls
The fixed factor doesn't expand to meet the extra workers — the same factory floor, the same set of machines, the same amount of physical space now has to be shared by more people. Early on, extra workers let the firm specialise (one person watches the machine, another handles materials, a third does quality control) and output per worker rises. Past some point, though, workers start queuing for the same machine, getting in each other's way, or simply having less capital to work with per person — the fixed factor is now the binding constraint, and each additional worker adds less than the one before. Nothing about the workers changed; what changed is the ratio of variable factor to fixed factor. This is exactly why the law is a short-run law: give the firm time to add more machines and floor space too, and the constraint disappears — which is precisely the move from short-run diminishing returns to long-run economies/diseconomies of scale.
Worked, in full
Deriving MC = wage ÷ marginal product
- 01
Assume labour is the only variable input, paid a constant wage w per worker, and L workers produce Q units. Total variable cost is TVC = wL.
Earns: K — the assumption stated explicitly, not silently baked into the algebra.
- 02
Marginal cost is MC = ΔTC/ΔQ = ΔTVC/ΔQ (fixed cost doesn't change with output, so it drops out of the change). Substituting TVC = wL: MC = w·(ΔL/ΔQ).
Earns: An1 — the substitution shown as a step, not skipped.
- 03
Marginal product of labour is defined as MP_L = ΔQ/ΔL — the extra output from one more worker. ΔL/ΔQ is therefore just 1/MP_L, the reciprocal.
Earns: An2 — recognising the reciprocal relationship rather than treating it as a separate fact to memorise.
- 04
So MC = w/MP_L. Wage is fixed by assumption, so MC and MP_L move in exactly opposite directions: while MP_L rises, MC falls; the instant MP_L starts falling (diminishing returns), MC starts rising; and MC is at its lowest point exactly where MP_L is at its highest — not roughly there, exactly there, because they're mathematical reciprocals of the same underlying quantity.
Earns: Eval — the diagram's shape (falling-then-rising MC) is a direct, forced consequence of this equation, not a separate empirical claim about what cost curves "tend to" look like.
Why marginal cost always crosses average cost exactly at its lowest point
In plain terms
Forget firms for a second and think about your test average. Say you've sat four tests and you're averaging 80%. You sit a fifth. Score 85% on it — above your current average — and that new score pulls your average UP, to a bit over 80%. Score 75% instead — below your current average — and it drags your average DOWN. Now here's the part that matters: your average only stays exactly still if your newest score exactly equals it. So your average keeps falling for as long as each new test comes in under it, keeps rising for as long as each new test comes in over it, and it can only be sitting at its lowest possible value at the one moment your newest score flips from being below the average to being above it. There's no test result that could produce the lowest average anywhere else — one test earlier, it was still being dragged down; one test later, it's already being pulled up.
Your "newest test score" is the marginal quantity — the cost of the extra unit, MC. Your "running average" is the average quantity — AC, or AVC if you only average the variable part. When MC sits below AC, the next unit is cheaper than what's already being averaged in, so it pulls AC down, same as an 75% pulling down an 80% average. When MC sits above AC, the next unit costs more than the average, so it pulls AC up, same as an 85%. AC keeps falling exactly as long as MC < AC and starts rising the moment MC > AC — so the one output level where AC stops falling and starts rising has to be the exact output where MC = AC. Nowhere else works.
Formally
MC intersects AC — and, by the identical logic, AVC — exactly at each curve's minimum because of a property forced on any marginal quantity relative to its own average, not a drawing convention. Whenever MC < AC, adding that unit necessarily pulls AC down (AC is falling); whenever MC > AC, adding that unit necessarily pulls AC up (AC is rising). AC can therefore be stationary — neither rising nor falling — only at the output where MC = AC. Because AC is falling at every output below that point and rising at every output above it, that stationary point cannot be anything but a minimum. This is exactly what the diagram's common-error note above means by "provable from the definition of a marginal quantity relative to an average": the same reciprocal relationship that gives MC and AVC their shape (MC = wage ÷ MP_L, AVC = wage ÷ AP_L) is what forces them to cross at the average's lowest point, not a separate fact to memorise alongside it.
x-axis: Output, Q · y-axis: Cost, £
- AFC
- Falls continuously, approaching but never reaching zero — a fixed amount spread over ever more units.
- AVC
- U-shaped, falling then rising.
- AC
- U-shaped, above AVC by a shrinking gap (the gap is AFC, which keeps falling).
- MC
- U-shaped, falls then rises more steeply than AVC or AC.
- MC crosses AVC at AVC's minimum
- Forced by the same logic as MC crossing AC — see the self-explain prompt.
- MC crosses AC at AC's minimum
- When MC < AC, the next unit pulls the average down; when MC > AC, the next unit pulls it up. AC can only be at its own minimum at the exact point where MC neither pulls it up nor down — i.e. where MC = AC.
Common error: Drawing MC crossing AC anywhere except exactly at AC's minimum point.
Correct: Both crossing points (MC/AVC and MC/AC) land precisely at the respective curve's minimum — not approximately, and this is provable from the definition of a marginal quantity relative to an average, not just a drawing convention to memorise.
In your own words
In one sentence: why must MC cross AC exactly at AC's minimum, rather than slightly before or after it?
Complete it yourself
Complete the chain — deriving AVC = wage ÷ average product
- 01
Average product of labour is defined as AP_L = Q/L — total output divided by the number of workers.
- 02
Average variable cost is AVC = TVC/Q. Substituting TVC = wL: AVC = wL/Q.
Named traps
- diminishing-returns-vs-diseconomies-of-scale
- Confirmed directly in an examiner report checked this session: "Diminishing returns is a short-run phenomenon, diseconomies of scale is where LRAC is rising and a rise in output is unlikely to result in a fall in total costs." The exam tests both directions of this confusion — don't reach for "diminishing returns" on a long-run/LRAC question, and don't reach for "diseconomies of scale" on a short-run/fixed-factor question. If the question mentions a fixed factor at all, it's short-run; if every factor is variable, it's long-run.
- shift-both-curves-or-shift-neither
- Confirmed in an examiner report, and now pinned to its exact location (Jan 2020, Q7c — Tesla, the level-exemplar's own style-anchor below — the Section B overview paragraph specifically, not the later per-question recap which restates the same finding in different words): on a question about a fall in variable costs, "only a small percentage of candidates correctly shifted both AC and MC curves downwards" — most shifted only one. Any change to variable cost affects both AVC (and therefore AC) and MC simultaneously, because both are built from the same TVC. Shifting one without the other is the single most commonly missed diagram move on this topic — and, per the real mark scheme itself, costs a Knowledge mark as well as an Analysis mark on this exact question type (see the warn-flag before the level-exemplar below).
- cheaper-inputs-can-mean-lower-quality
- Confirmed directly in the real Jan 2020 mark scheme for the Tesla question this lesson's level-exemplar is modelled on, in its evaluation cluster: "Using cheaper car parts may result in a fall in consumer demand... as consumers switch to better quality cars sold by competitors." A fall in the price of an input isn't automatically a free win for the firm — if the lower price reflects lower quality rather than a genuine market saving, the finished product can become less attractive, and the resulting fall in demand can offset some or all of the AC/MC cost advantage. This is a distinct evaluative angle from the magnitude/share-of-total-variable-cost condition used in the level-exemplar's L4 answer below — a real Level-4 evaluation only needs one well-developed condition, but knowing more than one exists means you're not stuck if the scenario in front of you doesn't suit the magnitude angle.
- afc-is-not-ac
- Confirmed in an examiner report on a question asking candidates to calculate average FIXED cost from a table: "many were not able to identify the calculation of fixed costs from the information; instead, they opted for average costs as their answer." AFC = TFC/Q only — leaving out variable costs is the entire point of the calculation, not an error to correct toward AC.
- state-the-units
- Confirmed in an examiner report: a candidate lost a mark on an otherwise-correct total cost calculation "because they omitted 'billions'" from the answer. A numerically correct answer without the stated unit from the data (millions, billions, per unit, per year) is marked as incomplete, not merely untidy.
- shift-both-only-when-the-stimulus-says-variable
- The "shift both curves" rule above applies to a VARIABLE cost change specifically — that one has no exceptions, because AVC and MC are both built from TVC. A cost the stimulus explicitly calls FIXED behaves differently: confirmed in an examiner report on a question about a rise in fixed compliance costs, "many did not pick up that fixed costs rising would only shift the average costs and not the marginal costs. Many mistakenly shifted both and then could not access the two analysis marks." — the mark scheme there explicitly blocked the analysis marks for a candidate who shifted MC as well. So: cost stated as variable → shift AC and MC both, always. Cost stated as fixed → shift AC only, MC untouched. When a stimulus doesn't commit to either category, examiners have marked it more loosely — a real mark scheme on a cost-fall-from-relocation question accepted "a downward shift in AC" alone OR "a downward shift in both AC and MC" as equally correct. Read which category the stimulus actually names before choosing which curves to move.
Beyond the spec
The spec asks you to derive cost curves from diminishing marginal productivity but doesn't ask why productivity often rises before it falls. Knowing why closes the one gap in the mechanism above — without it, "marginal product eventually falls" sounds like an assumption rather than something with its own cause.
Adam Smith's account of the division of labour (An Inquiry into the Nature and Causes of the Wealth of Nations, 1776) is the classic explanation for why marginal product rises before it falls: his famous pin-factory example describes output per worker rising sharply once a single worker's job is split into specialised tasks — drawing the wire, straightening it, cutting it, sharpening the point — each done by a different person who gets faster through repetition. That's the mechanism behind the RISING portion of marginal product with the first few workers added to a fixed factor. The falling portion — the part the spec actually names diminishing returns — sets in once there are more workers than there are useful specialised tasks to split between them, and the fixed factor (the number of workstations, machines, or physical space) becomes the binding constraint instead. The same firm, the same production process, two different mechanisms, one after the other.
This exact question type — an 8-mark Section-B "examine the impact on profit" sub-question, like the Tesla one above — is NOT marked with L1-L4 level descriptors the way a 20-mark Section C essay is. The real Jan 2020 mark scheme for it is flat: Knowledge 2 / Application 2 / Analysis 2 / Evaluate 2, every mark tied to one specific named bullet (e.g. "Increase in profit maximising output from 0Q1 to 0Q2 (1)"), capped per quadrant regardless of how well-argued the surrounding prose is. Confirmed by contrast on the same paper: question 7(e), a genuine 20-mark essay, is explicitly instructed "Answers must be credited by using the level descriptors" — 7(c) carries no such instruction. This has a concrete consequence worth knowing before you revise this question type: the real Knowledge marks require the diagram to show BOTH "original supernormal profit/loss area" AND "new supernormal profit/loss area after MC and AC shift down" — so an AC-only diagram (the single-curve error named in the trap-taxonomy above) doesn't just cost the Analysis mark the trap already warns about, it costs a Knowledge mark too, roughly halving the achievable total before Application or Evaluation are even considered. The L1-L4 progression below still shows what separates a stronger answer from a weaker one, but revise THIS question type by drilling the specific creditable bullets in each of the four 2-mark quadrants, not by aiming for a holistic "Level 4" quality the way you would for a 20-mark essay.
Same question, every level
Discuss the likely impact of a fall in the price of raw materials on a firm's short-run average and marginal cost curves. (VERIDIAN-original question, written in the style confirmed across multiple WEC13 series — Tesla, Uniqlo, India, Bangladesh — where this exact fall-in-variable-costs pattern recurs as an 8-mark Knowledge/Analysis/Application/Evaluation item; not a reproduction of any single past-paper question.)
8 marks available
Raw materials are a cost to the firm, so if they get cheaper the firm's average cost curve shifts down.
States that AC falls without saying why — no reference to TVC or AVC — and never mentions MC at all. This is the single-curve error the examiner report singles out directly: "only a small percentage of candidates correctly shifted both AC and MC curves downwards." No diagram.
Costs content — a named company or industry whose costs rise or fall, traced through to AC, MC, and profit — is one of the most consistently-tested sub-topics on the whole paper, appearing in at least 8 of the 15 series reviewed for this course, as an MCQ, a Section-B calculation, or a Section-B diagram question. Before reading the pattern below, look at what these eight real series actually asked for and see if you can name the two-step skill that never actually changes.
- Jan 2020Tesla — examine the effect of a FALL in variable costs on profit; the examiner report's own headline finding was that only a small percentage of candidates shifted both AC and MC down together.
- Jan 2021Tata Steel — a total-cost calculation from revenue and profit data, where a mark was lost purely for omitting the stated unit (billions).
- Oct 2021A sports-footwear firm in the USA — a total-cost-by-output table, asking exactly which interval diminishing returns start to set in.
- Oct 2022Samsung/Foxconn's factory in India — the effect on profit of relocating production to cut costs; the one series where the mark scheme accepted shifting AC alone OR AC-and-MC together, because the stimulus never committed the cost change to fixed or variable.
- Jan 2023A textile manufacturer in Botswana — an average-variable-cost calculation from TR, TC and TFC.
- Oct 2023An unnamed shirt manufacturer — an average-FIXED-cost calculation from a total-cost table, the exact AFC-vs-AC confusion this lesson's own trap-taxonomy names.
- Jan 2024A garment manufacturer in Bangladesh — the effect of a 50% RISE in energy costs on profit, with energy stated explicitly as a variable cost, so both AC and MC had to shift up together.
- Jun 2024Uniqlo — a total-cost calculation and the effect of a cost reduction on profit, in the same series as a separate marginal-cost-from-a-table question on a small hairdressing business.
Retrieval — with feedback on every choice
A firm's total cost of producing 0 to 6 units is: 0 units £20, 1 unit £26, 2 units £31, 3 units £35, 4 units £41, 5 units £49, 6 units £59.
Between which output levels do diminishing returns start to set in? (VERIDIAN-original — written in the same style as a confirmed real past-paper question type, not a reproduction of it.)
A firm producing 10,000 units has total costs of £18,000, of which £5,000 is total fixed cost.
What is its average variable cost? (VERIDIAN-original, same calculation type as a confirmed real past-paper question.)
Assume, as in the chain-drill above, that labour is the only variable input, paid a constant wage. A firm's average variable cost is currently falling as output rises. Which one of the following must also be true?
A firm's supplier raises the price it charges per unit of raw material. Which one of the following correctly describes the effect on the firm's short-run AC and MC curves? (VERIDIAN-original — targets the trap named above: an examiner report found only a small percentage of candidates correctly shifted both curves.)
A firm producing 4,000 units has total costs of £12,000, of which £8,000 is total fixed cost.
What is its average fixed cost? (VERIDIAN-original — targets the trap named above: an examiner report found many candidates asked for average fixed cost instead calculated average cost.)
- TC = TFC + TVC. AFC = TFC/Q, AVC = TVC/Q, AC = AFC + AVC. MC = ΔTC/ΔQ = ΔTVC/ΔQ.
- MC = wage ÷ MP_L. AVC = wage ÷ AP_L. Both fall while product rises, rise once it falls.
- MC crosses AVC and AC exactly at each curve's minimum — provable, not a drawing convention.
- Diminishing returns = short run, one factor fixed. Diseconomies of scale = long run, nothing fixed. Different mechanisms.
- A cost the stimulus calls variable shifts AC and MC together; a cost it calls fixed shifts AC only, not MC.
- Always state the unit from the data (millions / billions / per unit) in a calculation answer.
Not affiliated with or endorsed by Pearson Edexcel. Every quotation and figure attributed to a mark scheme or examiner report in this lesson was independently verified against the primary Pearson document, not carried over from prior course material.
A firm's total cost of producing 0 to 6 units is: 0 units £20, 1 unit £26, 2 units £31, 3 units £35, 4 units £41, 5 units £49, 6 units £59.
Between which output levels do diminishing returns start to set in? (VERIDIAN-original — written in the same style as a confirmed real past-paper question type, not a reproduction of it.)
- A1–2 units
Marginal costs by unit are: 1st £6, 2nd £5, 3rd £4, 4th £6, 5th £8, 6th £10. From the 1st to the 2nd unit, MC falls (£6→£5) — returns are still increasing here, not diminishing.
- B2–3 units
MC keeps falling through this interval too (£5→£4, the lowest point in the whole sequence) — still increasing returns, one step before the turning point.
- 3–4 units
Correct. MC falls to its minimum producing the 3rd unit (£4), then rises producing the 4th (£6) — the first increase in the sequence. That's the exact interval where diminishing returns set in: work out every marginal cost first, then find where the sequence turns from falling to rising, rather than guessing from the shape of the totals.
- D4–5 units
MC has already risen once by this point (£4→£6) and rises again here (£6→£8) — diminishing returns are already well established, not just beginning.
Traps tested: Misreads falling mc as rising · Off by one interval · Identifies established not onset
A firm producing 10,000 units has total costs of £18,000, of which £5,000 is total fixed cost.
What is its average variable cost? (VERIDIAN-original, same calculation type as a confirmed real past-paper question.)
- A£1.80
This is total cost divided by output (AC = £18,000/10,000) — it hasn't removed the fixed-cost component at all, so it's average cost, not average VARIABLE cost specifically.
- £1.30
Correct. TVC = TC − TFC = £18,000 − £5,000 = £13,000. AVC = TVC/Q = £13,000/10,000 = £1.30. Check it yourself: AFC + AVC should equal AC (£0.50 + £1.30 = £1.80 ✓).
- C£0.50
This is total fixed cost divided by output (AFC = £5,000/10,000) — the average FIXED cost, using the wrong half of total cost entirely.
- D£2.30
This comes from adding fixed cost to total cost instead of subtracting it (£18,000+£5,000=£23,000, ÷10,000) — a sign error. Average variable cost removes fixed cost from the total; it doesn't add it back in.
Traps tested: Computed ac not avc · Afc is not avc · Sign error added not subtracted
Assume, as in the chain-drill above, that labour is the only variable input, paid a constant wage. A firm's average variable cost is currently falling as output rises. Which one of the following must also be true?
- Average product of labour is rising
Correct. AVC = wage ÷ average product, so AVC can only fall while average product rises — they're reciprocals of the same relationship, derived in the chain-drill above.
- BMarginal cost is above average variable cost
The opposite is required — MC must be BELOW AVC to pull it down. If MC exceeded AVC, AVC would be rising, not falling.
- CThe firm is experiencing diseconomies of scale
Diseconomies of scale is a long-run, LRAC concept — AVC is a short-run curve. A falling short-run AVC says nothing about the firm's long-run cost structure.
- DTotal fixed cost is falling
TFC doesn't change with output by definition (that's what makes it fixed) — it has no bearing on whether AVC specifically is rising or falling.
Traps tested: Direction reversed · Diminishing returns vs diseconomies · Conflates fixed and variable
A firm's supplier raises the price it charges per unit of raw material. Which one of the following correctly describes the effect on the firm's short-run AC and MC curves? (VERIDIAN-original — targets the trap named above: an examiner report found only a small percentage of candidates correctly shifted both curves.)
- Both AC and MC shift upwards
Correct. A pricier raw material raises total variable cost at every output level, so it raises average variable cost (and therefore AC) AND raises marginal cost, since the extra material needed for one more unit now costs more too — both curves are built from the same TVC, so a variable-cost change always moves both together.
- BOnly AC shifts upwards; MC is unaffected
This is the single-curve error the examiner report describes directly — MC is also built from TVC (MC = ΔTVC/ΔQ), so a rise in the per-unit cost of a variable input raises the cost of producing one more unit too, not just the average.
- COnly MC shifts upwards; AC is unaffected
The reverse error — AC is built from AVC, which is also driven by TVC, so it shifts too. Both curves respond to the same variable-cost change; neither is immune.
- DNeither curve shifts; only AFC is affected
Raw materials are a variable cost, not a fixed one — AFC (built from TFC) is completely untouched by a change in the price of an input that varies with output. This mixes up which cost category the change belongs to.
Traps tested: Shifts only average not marginal · Shifts only marginal not average · Conflates fixed and variable
A firm producing 4,000 units has total costs of £12,000, of which £8,000 is total fixed cost.
What is its average fixed cost? (VERIDIAN-original — targets the trap named above: an examiner report found many candidates asked for average fixed cost instead calculated average cost.)
- A£1.00
This is total VARIABLE cost divided by output — AVC = (£12,000 − £8,000)/4,000 = £1.00. The question asked for average FIXED cost, which doesn't touch the variable component at all.
- £2.00
Correct. AFC = TFC/Q = £8,000/4,000 = £2.00. Total cost isn't needed for this calculation at all — that's the whole point of isolating the fixed component.
- C£3.00
This is total cost divided by output (AC = £12,000/4,000) — exactly the trap named above: leaving the variable-cost component IN is what makes this average cost, not average fixed cost.
- D£0.50
This inverts the ratio (Q/TFC = 4,000/8,000) rather than dividing fixed cost by output. AFC is always cost over quantity, not quantity over cost.
Traps tested: Computed avc not afc · Afc is not ac · Inverted ratio
Practice this for real
This site teaches the mechanism; the exam is sat on Pearson's own real questions. Go find and attempt these yourself — nothing here substitutes for actually sitting a timed paper.
Pearson's official past-papers portalSelect International Advanced Level → Economics → any series, then look for WEC13.
Up next
Economies and Diseconomies of Scale
Economies of scale and diminishing returns look like the same story told twice — they aren't. One is about a fixed factor being shared by more workers this month; the other is about what happens when there is no fixed factor left to share.
35 min