Cambridge Syllabus Notes

Short‑run and Long‑run Production

These notes cover the material required for Cambridge International AS & A Level Economics (9708) – syllabus requirement 7.5 “Production, costs, revenue & profit (short‑run & long‑run)”. They are organised to match the exact sub‑topics in the syllabus and include the diagrams that candidates must be able to draw.

1. Production in the Short‑run

1.1 The short‑run production function

Definition: The relationship between the quantity of the variable input (usually labour) and the quantity of output produced when at least one factor (normally plant size or capital) is fixed.
Because plant size is fixed, firms cannot change the scale of production instantly; they can only adjust the variable input.
In the syllabus, students must be able to sketch a short‑run production function showing Total Product (TP), Average Product (AP) and Marginal Product (MP) curves and identify the point where MP begins to fall (the onset of diminishing marginal returns).
Brief note on iso‑quant/iso‑cost: In the short‑run the iso‑quant is vertical with respect to the fixed factor, while the iso‑cost line pivates around the fixed‑cost intercept.

1.2 Product concepts and the law of diminishing marginal returns

Total Product (TP): total output produced with a given amount of the variable input.
Average Product (AP): AP = TP ÷ L, where L is the quantity of the variable input.
Marginal Product (MP): MP = ΔTP ÷ ΔL, the extra output from one more unit of the variable input.
Law of Diminishing Marginal Returns: After a certain level of the variable input, MP falls. This creates the characteristic U‑shaped AP and MP curves and underpins the shape of short‑run cost curves.

1.3 Short‑run cost concepts

Cost	Formula	Economic meaning
Fixed Cost (FC)	FC	Cost that does not vary with output (e.g., rent, plant size).
Variable Cost (VC)	VC(Q)	Cost that varies with the level of output (e.g., wages, raw materials).
Total Cost (TC)	TC = FC + VC(Q)	Sum of fixed and variable costs.
Average Variable Cost (AVC)	AVC = VC / Q	Variable cost per unit of output.
Average Total Cost (ATC) (also written AC)	ATC = TC / Q = AFC + AVC	Cost per unit of output including fixed cost.
Marginal Cost (MC)	MC = ΔTC / ΔQ = dTC/dQ	Extra cost of producing one more unit.

The U‑shaped AVC and ATC curves arise because:
- When output is low, each additional unit of labour adds a relatively large amount to TP → MC falls.
- Once MP starts to decline (diminishing returns), each extra unit of labour adds less output → MC rises.
The MC curve cuts both the ATC and AVC curves at their minimum points. This crossing point is the basis of the short‑run profit‑maximising rule.

1.4 Revenue in the short‑run (perfect competition)

Revenue concept	Formula	Interpretation (perfect competition)
Total Revenue (TR)	TR = P × Q	Value of output sold at the market price P.
Average Revenue (AR)	AR = TR / Q = P	Revenue per unit; equals price under perfect competition.
Marginal Revenue (MR)	MR = ΔTR / ΔQ = P	Revenue from selling one more unit; also equals price for a price‑taking firm.

Note: In imperfectly competitive markets MR ≠ P, but the short‑run profit‑maximising condition remains MR = MC.

1.5 Profit, loss, break‑even and the shutdown point

Profit (π): π = TR – TC.
Break‑even (zero‑profit) point: TR = TC ⇔ P = ATC. The firm covers all costs but earns no economic profit.
Shutdown point: The firm stops producing when price falls below the minimum of AVC. Formally, shutdown occurs if P < min AVC. At the shutdown point P = min AVC and the loss equals fixed cost.

1.6 Short‑run decision rule

Step 1 – Find the output where MR = MC (the profit‑maximising or loss‑minimising quantity).
Step 2 – Compare price with the relevant average cost:

If P ≥ ATC → the firm makes a profit (or breaks even).
If min AVC ≤ P < ATC → the firm continues to produce (covers all variable costs) but incurs a loss equal to fixed cost.
If P < min AVC → the firm shuts down in the short‑run.

2. Production in the Long‑run

2.1 Returns to scale (all inputs variable)

When every factor of production can be varied, we examine how output changes when all inputs are increased proportionally.

Increasing Returns to Scale (IRS): Doubling all inputs more than doubles output. LRAC falls as Q rises.
Constant Returns to Scale (CRS): Doubling all inputs exactly doubles output. LRAC is flat.
Decreasing Returns to Scale (DRS): Doubling all inputs less than doubles output. LRAC rises at high output.

2.2 Long‑run cost curves

Cost	Formula	Interpretation
Long‑run Total Cost (TC_LR)	TC_LR(Q)	Minimum cost of producing Q when all inputs can be varied.
Long‑run Average Cost (LRAC)	LRAC = TC_LR(Q) / Q	Cost per unit when the firm can choose the optimal plant size.
Long‑run Marginal Cost (LRMC)	LRMC = dTC_LR/dQ	Extra cost of one more unit when all inputs are variable.

Envelope relationship: The LRAC curve is the lower envelope of all possible short‑run ATC curves. It touches (is tangent to) the SR‑ATC that corresponds to the plant size the firm would choose at each output level.
The LRAC curve is typically U‑shaped because of IRS at low output, CRS in the middle, and DRS at high output.
Minimum Efficient Scale (MES): The output level at which LRAC is at its lowest. Firms that operate at the MES are said to be at the “efficient scale of production”.
As with the short‑run, LRMC cuts LRAC at its minimum point. This point represents the most cost‑efficient scale.

2.3 Revenue and profit in the long‑run

In a perfectly competitive market the price is still given, so:

AR = MR = P

The long‑run profit‑maximising condition is:

MR = LRMC ⇔ P = LRMC

Because firms can adjust plant size, long‑run equilibrium also requires that price equals the minimum of LRAC:

P = min LRAC

Note for imperfect competition: The condition MR = LRMC still holds, but because MR ≠ P, the long‑run equilibrium price may be above (monopoly) or below (monopolistic competition) LRMC. The syllabus only requires the perfect‑competition case, but the note helps students see the broader application.

If P > min LRAC → firms earn an economic profit; entry is attracted, shifting industry supply rightward and driving price down.
If P < min LRAC → firms incur a loss; exit is induced, shifting supply leftward and pushing price up.
In long‑run competitive equilibrium: P = LRMC = min LRAC and firms earn zero economic profit (normal profit).

2.4 Long‑run decision rule

Choose the plant size that minimises LRAC (the MES).
Produce the output where MR = LRMC = P = min LRAC.
If price is above the MES, expand plant size; if below, contract or exit.

3. Illustrative Example (Short‑run & Long‑run)

3.1 Short‑run data (perfect competition, P = $10)

Fixed Cost (FC) = $100
Variable Cost function: VC(Q) = 2Q + 0.5Q²

Q	VC	TC	TR	Profit (π)	MC	AVC	ATC
8	2·8 + 0.5·8² = 56	100 + 56 = 156	10·8 = 80	‑76	MC = 2 + Q = 10	AVC = 56/8 = 7	ATC = 156/8 = 19.5
10	2·10 + 0.5·10² = 70	100 + 70 = 170	10·10 = 100	‑70	MC = 12	AVC = 7	ATC = 17
12	2·12 + 0.5·12² = 96	100 + 96 = 196	10·12 = 120	‑76	MC = 14	AVC = 8	ATC = 16.3

Analysis

MR = P = $10. The profit‑maximising output is where MR = MC → Q ≈ 8 (MC = 10).
At Q = 8, P > min AVC (= 7), so the firm continues to produce even though it makes a loss.
Because P < ATC, the loss equals fixed cost plus the part of variable cost not covered: π = –$76.
If price fell below the minimum AVC (≈ 7), the firm would shut down.

3.2 Long‑run data (same market, P = $10)

Long‑run total cost function: TC_LR(Q) = 5Q + 0.3Q²

Q	TC_LR	LRAC	LRMC
10	5·10 + 0.3·10² = 80	8.0	LRMC = 5 + 0.6·10 = 11
12	5·12 + 0.3·12² = 96	8.0	LRMC = 5 + 0.6·12 = 12.2
15	5·15 + 0.3·15² = 127.5	8.5	LRMC = 5 + 0.6·15 = 14