Costs of Production: Short Run and Long Run

The costs a firm faces determine its supply decisions, its profitability, and ultimately whether it survives. Cost curves are the supply-side half of every market-structure diagram in this course: paired with the revenue curves from the previous lesson, they pin down the profit-maximising output, the level of profit, and the firm's efficiency. Economists distinguish carefully between short-run and long-run costs because cost behaviour depends fundamentally on whether all factors of production can be varied or only some. This lesson builds the cost toolkit from the ground up — total, average and marginal cost; the law of diminishing marginal returns that gives short-run curves their shape; and the way each cost curve relates to the others — so that every later diagram can be read with confidence.

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Spec Mapping

AQA A-Level Economics (7136) — this lesson is core 4.1.4 Production, costs and revenue: short-run and long-run production, the law of diminishing returns, and the relationship between the cost curves. It supplies the cost framework for 4.1.5 Market structure (every firm-level diagram) and underpins the supply curve used across 4.1.2 Price determination.

• Paper 1: multiple choice on cost definitions/calculations + essay material on efficiency and the firm's supply decision.
• Paper 3: data-response requiring cost calculations (MC, AVC, ATC) and a chain linking diminishing returns to rising costs and supply.

Assessment Objectives developed here:

AO	Skill	In this lesson
AO1	Knowledge	Define TFC/TVC/TC, AFC/AVC/ATC/MC; state the law of diminishing marginal returns
AO2	Application	Compute cost schedules; apply the shutdown rule to a named loss-making firm
AO3	Analysis	Chain diminishing returns → rising MC → upward-sloping supply; explain MC cutting AC at its minimum
AO4	Evaluation	Assess the realism of smooth U-shaped curves and the limits of static cost theory

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The Short Run and the Long Run

In economics, the distinction between the short run and the long run is not based on calendar time but on the flexibility of factors of production. The short run is any period over which at least one factor is fixed; the long run is the period over which the firm can vary all its factors and so change its entire scale of operation.

Time Period	Definition	Example
Short run	At least one factor of production is fixed (typically capital — factories, machinery, land)	A bakery cannot build a new oven overnight
Long run	All factors of production are variable — the firm can change the scale of its entire operation	The bakery can relocate to larger premises, buy more ovens, hire more staff
Very long run	The state of technology itself changes	New baking technology transforms what is possible

This matters because the two periods are governed by different economic laws. The short run is dominated by the law of diminishing marginal returns — a consequence of adding a variable factor to a fixed one. The long run is dominated by economies and diseconomies of scale (the subject of the next lesson) — a consequence of changing the scale of all factors at once. Keeping the two apart is one of the most important disciplines in this part of the course.

graph LR
  A["How many factors are fixed?"] --> B["At least one fixed = SHORT RUN"]
  A --> C["None fixed, all variable = LONG RUN"]
  B --> D["Governed by diminishing marginal returns"]
  C --> E["Governed by economies/diseconomies of scale"]

Exam Tip: Students commonly define the short run as "a short period of time" — this loses marks. The short run is defined by the existence of a fixed factor, not by a length of time. For a nuclear power station the short run might be a decade (the time to plan and build a new plant); for a market stall, a few hours. The economic question is always "can the firm change its capital?", not "how long is it?".

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Short-Run Costs

Fixed and Variable Costs

The first division is between costs that do, and do not, vary with output.

Cost Type	Definition	Examples	Behaviour
Total Fixed Cost (TFC)	Costs that do not vary with output in the short run	Rent, insurance, salaries of permanent staff, loan repayments	Constant — a horizontal line
Total Variable Cost (TVC)	Costs that vary directly with output	Raw materials, energy, wages of temporary staff, packaging	Rises as output rises
Total Cost (TC)	The sum of the two	$TC = TFC + TVC$TC=TFC+TVC	Rises with output; the vertical gap between TC and TVC always equals TFC

Because fixed costs must be paid whether the firm produces one unit or a million, they are sunk in the short run in the sense that producing more does not increase them. This single fact drives much of what follows — most importantly the shutdown decision, where fixed costs are ignored entirely because they cannot be avoided by halting production.

Average and Marginal Costs

From the totals we derive the per-unit concepts that populate the standard cost diagram.

Concept	Formula	Interpretation
Average Fixed Cost (AFC)	$AFC = TFC \div Q$AFC=TFC÷Q	Falls continuously as output rises — TFC spread over more units ("spreading the overheads")
Average Variable Cost (AVC)	$AVC = TVC \div Q$AVC=TVC÷Q	U-shaped — falls then rises as diminishing returns set in
Average Total Cost (ATC or AC)	$ATC = TC \div Q = AFC + AVC$ATC=TC÷Q=AFC+AVC	U-shaped — the vertical gap above AVC equals AFC and narrows as output rises
Marginal Cost (MC)	$MC = \dfrac{\Delta TC}{\Delta Q}$MC=ΔQΔTC​	The cost of one more unit — the single most important cost concept for decision-making

Two relationships are worth committing to memory. First, because $ATC = AFC + AVC$ATC=AFC+AVC, the vertical distance between the ATC and AVC curves at any output equals AFC — and since AFC falls continuously, the two curves converge as output rises but never meet. Second, MC reflects only the change in variable cost (fixed cost does not change with output), so MC is unaffected by fixed costs — a point that trips up many candidates in calculation questions.

Worked example: a short-run cost schedule

Take a hypothetical firm with fixed cost of £100 (per period). Variable cost rises with output as shown. All figures are illustrative.

Q	TFC (£)	TVC (£)	TC (£)	AFC (£)	AVC (£)	ATC (£)	MC (£)
0	100	0	100	—	—	—	—
1	100	60	160	100.0	60.0	160.0	60
2	100	100	200	50.0	50.0	100.0	40
3	100	132	232	33.3	44.0	77.3	32
4	100	180	280	25.0	45.0	70.0	48
5	100	250	350	20.0	50.0	70.0	70
6	100	348	448	16.7	58.0	74.7	98

Notice how MC reaches its minimum (£32 at Q = 3) before AVC bottoms out (£44 at Q = 3) and well before ATC bottoms out (£70 around Q = 4–5). This ordering is no accident — it follows directly from the marginal–average relationship developed below, and it is exactly what the cost diagram must show.

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The Law of Diminishing Marginal Returns

The law of diminishing marginal returns (the law of variable proportions) is the engine that shapes short-run cost curves. It states:

As successive units of a variable factor (e.g. labour) are added to a fixed factor (e.g. capital), there comes a point beyond which the marginal product of the variable factor begins to fall.

Numerical example: a small farm

Workers (L)	Total Product (TP)	Marginal Product (MP)	Average Product (AP)	Stage
0	0	—	—	—
1	10	10	10.0	Increasing returns
2	25	15	12.5	Increasing returns
3	45	20	15.0	Increasing returns
4	60	15	15.0	Diminishing returns begin
5	70	10	14.0	Diminishing returns
6	75	5	12.5	Diminishing returns
7	75	0	10.7	Zero marginal returns
8	70	−5	8.75	Negative returns

Marginal product peaks at the third worker (MP = 20) and then declines. The link to costs is direct and inverse: when the marginal product of labour is rising, each extra unit of output requires less additional labour, so marginal cost is falling; once marginal product begins to fall, each extra unit of output requires more labour, so marginal cost rises. The MC curve is, in effect, the marginal-product curve turned upside down (given a fixed wage). This is why MC is U-shaped — and why the law of diminishing returns is the cause, not merely a correlate, of rising costs.

Why diminishing returns occur

When a fixed factor (say, a factory floor of given size) is combined with ever more units of a variable factor (workers), each additional worker has progressively less capital to work with — fewer machines, less bench space, more queueing for shared equipment. Coordination becomes harder and congestion sets in. The result is that each extra worker adds less to output than the one before. Crucially, this is not about workers being less able — they are assumed identical — but about the worsening ratio of variable to fixed factors. That is why the law is also called the law of variable proportions.

The three product curves and how they fit together

It pays to be precise about the relationship between total, marginal and average product, because the cost curves are derived directly from them. Total product (TP) is total output for a given amount of the variable factor; marginal product (MP) is the addition to total product from one more unit of the variable factor; average product (AP) is total product per unit of the variable factor. Three facts follow and are regularly examined. First, while MP is positive TP is rising; when MP is zero TP is at its maximum; when MP is negative TP is falling. Second, the same marginal–average rule that governs costs governs products in reverse: MP cuts AP at the maximum of AP (when the marginal worker is more productive than the average, the average rises, and vice versa). Third — and this is the connection to costs — because the wage per worker is constant, marginal cost moves inversely to marginal product, and average variable cost moves inversely to average product. So the inverted-U of MP becomes the U of MC, and the inverted-U of AP becomes the U of AVC. Understanding this derivation, rather than memorising the curve shapes, is what separates a mechanical answer from an analytical one.

The early stage of increasing marginal returns — visible as the rising portion of MP — arises because the first few workers allow gains from specialisation and the division of labour: with too few workers each must perform many tasks and the fixed capital sits idle, whereas adding workers lets each specialise and lets the capital be used intensively. Only once the fixed factor starts to become the binding constraint does the law of diminishing marginal returns take over. The short-run cost curves are therefore the story of two opposing forces — specialisation gains early, factor-ratio losses later — resolved into the familiar U-shapes.

Exam Tip: Diminishing returns is a short-run concept requiring at least one fixed factor. Do not confuse it with diseconomies of scale, a long-run concept about what happens when all factors are increased together. Examiners penalise this confusion heavily. A reliable tell: if the firm is adding workers to a fixed plant, it is diminishing returns; if it is building a bigger plant entirely, it is (dis)economies of scale.

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The Relationship Between Marginal and Average Costs

The relationship between any marginal and its average is a mathematical necessity, not an economic assumption:

• When MC < AC, the average is being pulled down (the new unit costs less than the running average);
• When MC > AC, the average is being pushed up;
• Therefore MC cuts AC at AC's minimum point — the only place where the average is momentarily neither rising nor falling.

The classic analogy is a batsman's cricket average: a new innings below the average drags it down, a new innings above it lifts it up, and the average stops falling exactly when the latest score equals it. The same logic applies to MC and AVC: marginal cost passes through the minimum of AVC too. Because AFC is always falling, the minimum of ATC lies to the right of the minimum of AVC — the still-falling AFC keeps ATC declining for a while even after AVC has turned up. This explains the ordering observed in the worked schedule, and it is the single most-tested feature of the cost diagram.