OxfordAQA International AS and A-level Economics: Returns, scale and cost curves (9640) – Revision Notes

These notes condense sections 3.3.2.1 to 3.3.2.3 of the OxfordAQA International AS and A-level Economics (9640) specification, version 1.2: diminishing returns and returns to scale, short-run cost curves and long-run cost curves. Section 3.3 is the extra International A2 content (Unit 3). For full explanations and longer worked examples, use the study guide. All firms and figures here are invented.

Also useful: the practice questions, the AS costs revision notes, the course hub, the printable checklist and the free 10-minute diagnostics.

Key terms

Term	Meaning
Short run	Time during which some input cannot be altered
Long run	Time long enough for every input to change
Total returns	Total output (TP) from a given amount of the variable input
Average returns	Output per unit of the variable input: TP ÷ input
Marginal returns	What one more unit of the variable input adds to output
Law of diminishing returns	With one input fixed, extra units of a variable input eventually add less and less to output
Returns to scale	How output responds when every input is scaled by the same factor
Marginal cost	Extra total cost of one more unit of output
Minimum efficient scale (MES)	Lowest output at which long-run average cost reaches its minimum

Returns: the two ideas side by side

	Diminishing returns	Returns to scale
Period	Short run	Long run
Inputs	Some held fixed, one varied	Every input scaled together
Asks	What does one extra worker add?	What happens to output if everything doubles?
Result	Marginal product eventually falls	Output rises by more than, the same as, or less than inputs
Link to cost	Shapes MC, AVC and ATC	Shapes LRAC

Returns to scale test. Compare percentage changes. Output up more than inputs: increasing. Equal: constant. Less: decreasing.

Relationships between product curves.

• While MP is higher than AP, AP climbs; once MP is lower, AP drops. MP crosses AP at AP’s peak.
• TP rises while MP is positive, peaks when MP = 0, and falls when MP is negative.
• Diminishing returns begin where MP reaches its peak, not where TP peaks.

Worked reminder 1: marginal and average returns

A button workshop adds workers to a fixed set of machines.

Workers	1	2	3	4	5
TP	6	16	27	33	36
MP	6	10	11	6	3
AP	6.0	8.0	9.0	8.25	7.2

MP of worker 4 = 33 - 27 = 6. Diminishing returns begin after worker 3 (MP peaks at 11). AP is highest at 3 workers (9.0) and falls at 4 because the new worker’s MP (6) is below the average.

Short-run cost formulae

Measure	Formula
TC	FC + VC
AFC	FC ÷ Q
AVC	VC ÷ Q
ATC	AFC + AVC, or TC ÷ Q
MC	extra TC ÷ extra Q
MC and AVC from returns	MC = input price ÷ MP; AVC = input price ÷ AP (one variable input)

Worked reminder 2: a cost table

Fixed cost is 150. Output in units, costs in currency units (invented).

Q	10	20	30	40
TC	230	290	380	520
VC	80	140	230	370
AVC	8.00	7.00	7.67	9.25
ATC	23.00	14.50	12.67	13.00
MC (per unit over the previous 10)	8	6	9	14

MC from 20 to 30 = (380 - 290) ÷ 10 = 9. ATC is lowest at 30 (12.67): MC of 9 is below ATC, so ATC falls; MC of 14 is above ATC at 40 (13.00), so ATC rises. The crossing lies between 30 and 40.

Why the short-run curves have their shapes

• MC: falls while MP rises, then rises when diminishing returns set in (same wage, less extra output).
• AFC: always falls with output (fixed cost shared out) and gets close to the horizontal axis.
• AVC: falls while AP rises, then rises. Minimum where AP is highest.
• ATC: the vertical sum of AFC and AVC. Its minimum comes at a higher output than AVC’s, since AFC keeps dropping for a while after AVC turns up.
• Marginal-average rule: MC cuts AVC and ATC at their lowest points. A marginal value below an average pulls it down; above it pulls it up.
• Fixed cost: a rise lifts TC by the amount of the rise and ATC by that amount divided by output; it leaves MC and AVC alone.

cost
 |\                 MC
 | \               /
 |  \     ATC     /
 |   \__.-''''-._/ 
 |      \_AVC_./     MC crosses AVC and ATC at their minima
 +-------------------- output

Factor prices, productivity and the choice of inputs

• A rise in the price of a variable input shifts MC, AVC and ATC up; a fall shifts them down.
• Higher productivity (higher MP and AP) lowers MC and AVC. If output per worker rises 25% with the wage unchanged, AVC falls by 20% (1 ÷ 1.25 = 0.8).
• Firms switch towards the input that is relatively cheaper, if the technology allows. With a wage of 40 and a machine at 40 a day, a method using 5 workers and 2 machines costs 280; a method using 2 workers and 5 machines costs 280 as well, so at a wage of 50 the costs are 330 and 300 and the machine-heavy method wins. Switching is easier in the long run.

Long-run cost curves

• Each plant size has an SRAC curve. The LRAC curve shows the lowest average cost for each output when all inputs can change: it is the lower edge of the SRAC curves.
• Increasing returns to scale (with constant input prices) give falling LRAC; constant returns give flat LRAC; decreasing returns give rising LRAC.
• L-shaped LRAC: it falls steeply at first and then flattens. A firm can often copy a plant it already runs well, so average cost need not rise at large outputs. The specification names this shape explicitly; a U-shape is the alternative if diseconomies of scale appear.
• MES: the output where LRAC first reaches its minimum.

Significance of MES

MES compared with market size	Likely industry structure	Barrier to entry
Small	Many firms	Low
Moderate (market holds a few MES-sized firms)	Few firms	Medium to high
Large (about the size of the market)	One firm, or very few	High

Worked reminder 3: if MES is 250 units and the market takes 1,000 units, the market can hold 1,000 ÷ 250 = 4 firms producing at MES. A new entrant making 50 units would have LRAC well above those firms, which deters entry unless it can start larger.

Evaluation prompts

• Do diminishing returns always raise unit costs? Costs per unit rise only when MC is above the average; early output can have rising MP.
• Is the long run a fixed time? No: it depends on the industry (a shop lease versus a power station).
• Does a high MES prove monopoly? Not necessarily: it matters relative to demand, and potential rivals matter.
• Do lower costs reach consumers? Only if competition or regulation passes savings on.

Quick self-test

1. Define marginal product.
2. Five workers make 40 units and six make 46. Find the marginal product of the sixth worker and the average product at six workers.
3. Four workers make 32 units; a fifth takes the total to 37. What is the average product at five workers, and what has happened to it?
4. Fixed cost is 500, variable cost per unit is 6 and output is 250. Find ATC.
5. A worker is paid 40 a day and the marginal product is 8 units a day. Find marginal cost.
6. All inputs rise 20% and output rises 30%. What type of returns, and what happens to LRAC if input prices are constant?
7. All inputs double and output goes from 100 to 180. What type of returns?
8. Explain why diminishing returns and decreasing returns to scale are different.
9. State why MC cuts ATC at the minimum of ATC.
10. Name the effect on a market of MES being 80% of market demand.

Answers

1. The extra output from one more unit of a variable input, other inputs fixed.
2. MP = 46 - 40 = 6; AP = 46 ÷ 6 = 7.67.
3. AP = 37 ÷ 5 = 7.4, down from 8.0, because the fifth worker’s MP (5) is below the average.
4. AFC = 500 ÷ 250 = 2; ATC = 2 + 6 = 8.
5. MC = 40 ÷ 8 = 5.
6. Increasing returns (30% > 20%); LRAC falls.
7. Output rises 80% while inputs rise 100%: decreasing returns to scale.
8. Diminishing returns: one input fixed, short run, falling marginal output. Decreasing returns to scale: all inputs rise together, long run, output rises proportionally less.
9. When MC is below ATC each extra unit costs less than the average, pulling ATC down; when above, it pulls ATC up; so they meet at the minimum.
10. Only one firm can reach MES, so the market tends towards monopoly and entry is hard.

Where marks are usually lost

• Describing diminishing returns as falling total output; it is falling marginal output.
• Mixing up the short run and the long run, for example using returns to scale for a fixed factory.
• Saying MC meets ATC “at the minimum of MC”.
• Forgetting that fixed cost does not change MC or AVC.
• Quoting a cost figure without the working, or the wrong denominator (dividing by workers instead of output).
• Stating that MES is the output of maximum profit.
• Drawing an LRAC that lies above part of an SRAC curve; it touches each SRAC at one point and never rises above it.
• Describing a diagram without naming axes and curves.

Official syllabus

OxfordAQA International AS and A-level Economics (9640) specification, version 1.2, sections 3.3.2.1, 3.3.2.2 and 3.3.2.3 and section 3.5. First teaching September 2020, first AS exams May/June 2021, first A-level exams May/June 2022. Published by OxfordAQA.