Short-run costs and the law of diminishing returns

Short run and long run

• Short run: at least one factor (usually capital: factory, machines) is fixed.
• Long run: all factors can be varied; the firm can change its scale.

Diminishing marginal productivity

• Total product (TP): total output.
• Marginal product (MP) = ΔTP / ΔL, the extra output from one more worker.
• Average product (AP) = TP / L.

Law of diminishing returns: as more of a variable factor is added to a fixed factor, the marginal product of the variable factor will eventually fall. At first MP may rise (specialisation), but workers end up sharing the same machines and space.

MP rises to 14, then diminishing returns set in from the 3rd worker.

Cost formulae

• TC = TFC + TVC
• Fixed costs do not change with output (rent, interest); variable costs do (raw materials, hourly wages).
• AFC = TFC / Q (always falling); AVC = TVC / Q; ATC (AC) = TC / Q = AFC + AVC
• Marginal cost MC = ΔTC / ΔQ (equal to ΔTVC / ΔQ, since fixed cost does not change).

Shapes, described in words

Draw cost on the vertical axis and output on the horizontal. MC is a 'tick' shape: it falls while MP rises, then rises once diminishing returns set in. AVC and ATC are U-shaped. MC cuts AVC and then ATC at their minimum points: when the marginal is below the average it pulls the average down; when above, it pulls it up. The gap between ATC and AVC is AFC, which narrows as output rises.

Worked example

Fixed cost is $100 and each worker costs $40. Using the table, find ATC with 4 workers and MC per unit for the 4th worker.

1. Output with 4 workers = 44.
2. TC = 100 + 4 x 40 = $260.
3. ATC = 260 / 44 = $5.91.
4. The 4th worker adds 8 units for $40, so MC = 40 / 8 = $5 per unit.

Answer: ATC = $5.91; MC = $5.

Check yourself

1. Using the table (TP: 10, 24, 36, 44, 48, 50 for 1 to 6 workers), find the marginal product of the 5th worker.
   Show answer

   4 units. MP = 48 - 44 = 4 units.

2. Using the same table, find the average product with 3 workers.
   Show answer

   12 units. AP = 36 / 3 = 12 units per worker.

3. A firm has fixed costs of $5,000 and variable costs of $7,000 when it produces 400 units. Find average total cost.
   Show answer

   $30. ATC = (5,000 + 7,000) / 400 = $30.

4. For the same firm (fixed costs $5,000, output 400), find average fixed cost.
   Show answer

   $12.50. AFC = 5,000 / 400 = $12.50.

5. Total cost rises from $2,400 to $2,520 when output rises from 100 to 110 units. Find marginal cost per unit.
   Show answer

   $12. MC = ΔTC / ΔQ = 120 / 10 = $12.

6. The law of diminishing returns applies
   • in the short run, when at least one factor is fixed
   • only in the long run
   • only to firms in perfect competition
   • only when wages rise
   Show answer

   in the short run, when at least one factor is fixed. It describes adding a variable factor to a fixed factor.

7. The marginal cost curve cuts the average total cost curve
   • at the maximum point of ATC
   • where ATC equals AFC
   • at the minimum point of ATC
   • where output is zero
   Show answer

   at the minimum point of ATC. While MC < ATC, ATC falls; once MC > ATC, ATC rises; so they meet at the minimum.

8. Which is most likely to be a fixed cost for a factory in the short run?
   • Raw materials
   • Electricity used by machines
   • Packaging
   • Rent on the building
   Show answer

   Rent on the building. Rent does not change with output.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Economics specification (XEC11/YEC11), Unit 3 Business behaviour and Appendices 6 and 7

Last updated 8 November 2026. Spotted a mistake? Tell us.