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

This guide follows the OxfordAQA International AS and A-level Economics (9640) specification, version 1.2, sections 3.3.2.1 (the law of diminishing returns and returns to scale), 3.3.2.2 (short-run cost curves) and 3.3.2.3 (long-run cost curves). Section 3.3 is the extra International A2 content, assessed in Unit 3. Quantitative skills (section 3.5) can be assessed in any unit, and the specification adds marginal values for A2 work. Every firm, country and figure below is invented for illustration.

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

What you must be able to do

Section	Outcome
3.3.2.1	Distinguish marginal, average and total returns; explain the law of diminishing returns; explain returns to scale; distinguish increasing, constant and decreasing returns to scale; see that both ideas link inputs to output and so shape costs
3.3.2.2	Calculate, draw and interpret marginal, average and total cost; explain the shapes of the curves; explain how factor prices and productivity affect costs and the choice of inputs
3.3.2.3	Explain how short-run and long-run average cost curves relate; explain the L-shaped long-run average cost curve; explain minimum efficient scale and its significance for industry structure and barriers to entry

Returns to a variable factor (3.3.2.1)

The short run is the time during which some input cannot be altered. The long run allows every input to change. In the short run a firm adds a variable input (usually labour) to fixed capital. Three measures describe what happens:

Measure	Meaning	Formula
Total returns (total product, TP)	all output at a given amount of the variable input	read from the data
Average returns (average product, AP)	output per unit of the variable input	TP ÷ units of input
Marginal returns (marginal product, MP)	the addition to output made by employing one more unit of the variable input	change in TP ÷ change in input

The law of diminishing returns says that, with at least one input fixed, adding units of a variable input eventually gives smaller and smaller extra output from each new unit. It describes marginal returns, and it is about the short run only. It does not say total output falls, although it can.

Worked example 1: a herb nursery

A nursery in Country A has one polytunnel (fixed). It adds workers; output is trays a day.

Workers	TP	MP	AP
1	9	9	9.0
2	22	13	11.0
3	36	14	12.0
4	46	10	11.5
5	52	6	10.4
6	55	3	9.2
7	55	0	7.9
8	52	-3	6.5

Working: MP of worker 4 = 46 - 36 = 10; AP at 4 workers = 46 ÷ 4 = 11.5.

• MP rises to worker 3 (tasks are shared and the polytunnel is used better). Diminishing returns start after worker 3: worker 4 adds 10, less than the 14 added by worker 3.
• TP keeps rising until worker 6, is flat at 7 (MP = 0) and falls at 8 (MP = -3): too many people in a fixed space.
• AP rises while MP is above it (workers 1 to 3) and falls once MP is below it. MP cuts AP at AP’s maximum, between 3 and 4 workers.

Returns to scale

Returns to scale concern the long run: all inputs rise in the same proportion. Compare the percentage change in output with the percentage change in inputs.

• Increasing returns: output grows proportionally more than inputs.
• Constant returns: output and inputs rise by the same percentage.
• Decreasing returns: output grows proportionally less than inputs.

Both ideas explain a link between inputs and output, but they differ. Diminishing returns hold one input fixed and change another. Returns to scale change every input together.

Worked example 2: a crate workshop

A workshop in Country B adds “sets” of inputs, each set being one worker and one machine. Each set costs 200 a day, and input prices stay constant.

Sets	Output	Inputs change	Output change	Returns	LRAC
1	50	-	-	-	4.00
2	120	+100%	+140.0%	increasing	3.33
3	210	+50%	+75.0%	increasing	2.86
4	280	+33.3%	+33.3%	constant	2.86
5	350	+25%	+25.0%	constant	2.86
6	390	+20%	+11.4%	decreasing	3.08

Working: from 3 to 4 sets, output rises (280 - 210) ÷ 210 = 33.3%, equal to the input rise (1 ÷ 3). LRAC at 6 sets = 1,200 ÷ 390 = 3.08. With constant input prices, increasing returns mean falling long-run average cost, constant returns mean flat, decreasing returns mean rising.

Short-run cost curves (3.3.2.2)

Fixed costs (FC) do not change with output; variable costs (VC) do. Total cost is TC = FC + VC. Dividing by output Q gives AFC = FC ÷ Q, AVC = VC ÷ Q and ATC = TC ÷ Q (which equals AFC + AVC). Marginal cost is what the next unit adds to TC, found as the change in TC divided by the change in Q.

Worked example 3: from returns to costs

The nursery pays each worker 60 a day (the only variable cost) and fixed costs are 100. Cost per tray follows from the returns table.

Workers	Q (=TP)	VC	TC	AFC	AVC	ATC	MC
1	9	60	160	11.11	6.67	17.78	6.67
2	22	120	220	4.55	5.45	10.00	4.62
3	36	180	280	2.78	5.00	7.78	4.29
4	46	240	340	2.17	5.22	7.39	6.00
5	52	300	400	1.92	5.77	7.69	10.00
6	55	360	460	1.82	6.55	8.36	20.00

Working for 4 workers: ATC = 340 ÷ 46 = 7.39 and AFC + AVC = 2.17 + 5.22 = 7.39. MC of the fourth worker’s 10 trays = 60 ÷ 10 = 6.00. In general MC = wage ÷ MP and AVC = wage ÷ AP.

Reasons for the shapes

1. MC falls while MP rises (workers 1 to 3: MC 6.67, 4.62, 4.29), then rises once diminishing returns set in, because each extra worker costs the same but adds less. MC is therefore the mirror image of MP, which is why it is U-shaped (or “tick”-shaped).
2. AVC is the mirror image of AP. It falls to 5.00 at worker 3, where AP is highest, then rises.
3. AFC always falls as output rises: a fixed sum is spread over more units.
4. ATC is AFC + AVC. It falls at first (both parts fall), then rises when rising AVC outweighs falling AFC. Its minimum is further right than AVC’s minimum (worker 4, not worker 3).
5. MC cuts AVC and ATC at their minimum points. When MC is below the average, it pulls the average down; when above, it pulls it up. In the table MC (6.00) is below ATC (7.39) at 4 workers, and above (10.00 against 7.69) at 5, so the curves cross between those outputs.

cost
 |  MC           /
 |   \        ATC/
 |    \  _.-'''-/_   AVC
 |     \/  _.-'/
 |     /\.-'  /       MC cuts AVC and ATC at their lowest points
 +---------------------- output

Fixed cost adds to TC and ATC, not to MC or AVC. If fixed costs rose from 100 to 160, ATC at 4 workers would be 400 ÷ 46 = 8.70 (up from 7.39), while MC and AVC would be unchanged.

Factor prices, productivity and the choice of inputs

A rise in a variable input’s price shifts MC, AVC and ATC up. A rise in productivity (higher AP and MP) shifts them down. If training lifted output by 25% at every level of labour, 4 workers would make 57.5 trays, AVC would be 240 ÷ 57.5 = 4.17 rather than 5.22 (down 20.0%), and ATC would be 340 ÷ 57.5 = 5.91.

Worked example 4: choosing between methods

A firm can make 100 units by method L (8 workers, 2 machines) or method K (3 workers, 6 machines). A machine costs 40 a day.

• Wage 50: L = 8(50) + 2(40) = 480; K = 3(50) + 6(40) = 390. K is cheaper.
• Wage 30: L = 320; K = 330. L is cheaper.
• The methods cost the same when 8w + 80 = 3w + 240, so w = 32.

A firm tends to use more of the input that has become relatively cheaper, but machinery is hard to change quickly, so the response is larger in the long run.

Long-run cost curves (3.3.2.3)

In the long run the firm chooses the plant size with the lowest average cost for each output. Each plant has its own short-run average cost curve (SRAC).

Worked example 5: three plant sizes

SRAC (cost per unit, invented) for small, medium and large plants at six outputs:

Output	Small	Medium	Large	Lowest (LRAC)
200	6.00	9.30	21.20	6.00 (small)
400	7.00	6.15	11.40	6.15 (medium)
800	10.50	5.47	6.80	5.47 (medium)
1,000	12.40	5.70	6.00	5.70 (medium)
1,500	17.27	6.70	5.17	5.17 (large)
2,000	22.20	7.95	5.00	5.00 (large)

The long-run average cost (LRAC) curve is the lower edge of all the SRAC curves, which touches each SRAC at one output. With many possible plant sizes it is a smooth curve. At low output the firm uses a small plant, because its low fixed cost beats the spreading of a big plant’s fixed cost.

The L-shaped LRAC. With a large plant at output 3,000, SRAC is 5.33, above its 5.00 at 2,000. But a firm can build a second large plant: two plants each making 1,500 give 5.17. So LRAC stays almost flat at large outputs, and the curve can be L-shaped (falling, then flat) rather than U-shaped.

Minimum efficient scale and market structure

Minimum efficient scale (MES) is the smallest output that achieves the lowest possible LRAC. Take a stylised L-shaped LRAC in units of thousands:

Output	50	100	200	300	400	500	800
LRAC	9.0	6.0	4.5	3.8	3.5	3.4	3.4

MES is 500. Significance:

• Industry structure. If total market demand is 1,500, three firms could each produce at MES (1,500 ÷ 500). If demand is 600, only one firm can reach MES with room to spare (600 ÷ 500 = 1.2), so the market tends towards monopoly. A high MES relative to demand means few firms.
• Barriers to entry. A new firm entering at output 100 has LRAC of 6.0, which is (6.0 - 3.4) ÷ 3.4 = 76.5% above an established firm at MES. At output 200 the gap is 32.4%. Entrants must start large, with heavy borrowing and risk, or accept a cost disadvantage.
• Limits. If MES is small relative to the market, many firms survive and the barrier is weak.

Evaluating: does a rise in output always raise cost per unit?

Chain: more output needs more variable input; with fixed capital MP eventually falls; so MC rises; so ATC rises once MC exceeds it. Then qualify: the rise may start late if MP rises first; it eases in the long run when capital can change; training or technology can raise MP.

Common errors

• Writing that diminishing returns means total output falls. It means marginal output falls; TP can still rise.
• Using “diminishing returns” for the long run, or “decreasing returns to scale” for the short run.
• Drawing MC so that it misses the lowest points of AVC and ATC.
• Calling MES the output where profit is greatest. It is where LRAC is first lowest.

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.