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S5 Economics paper 4: error drills on cost and scale
S5 Economics paper 4: error drills on cost and scale
Ten items target the four commonest slips: treating a dollar amount as a percentage, confusing average with marginal cost, expecting a lump-sum tax to move marginal cost, and swapping output growth with input growth. Each item is recomputed.
Direct answers Items 01 to 03 recompute average cost and the size of a cost fall, 04 to 06 handle a split long-run average cost, minimum efficient scale and returns to scale, 07 to 09 use a cubic cost function for the minimum, a higher output and a lump-sum tax, and 10 corrects a percentage slip.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 25 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S5 Economics Long-run Cost and Economies of Scale |
| Level | S5 |
02 Questions (10 items)
- FoundationA firm’s total cost is $6,000 at an output of 200 units. Find the average cost.
- FoundationA firm has fixed cost $900 and variable cost $15 per unit at an output of 40 units. Find total cost, average cost and average fixed cost.
- FoundationLong-run average cost is $80 at 200 units and $64 at 400 units. Find the percentage fall and name the scale effect.
- IntermediateLong-run average cost is 3,200 / Q + 18 + 0.02Q. Find average cost at Q = 400 and Q = 200, and the percentage by which 200 units is higher.
- IntermediateMinimum long-run average cost occurs at 250 units and market demand is 1,750 units. How many firms can reach that cost?
- IntermediateIf all inputs double and output rises from 200 to 340 units, what returns to scale is shown and what is the output increase?
- ChallengeLong-run total cost is Q cubed minus 24Q squared plus 300Q. Find the average cost function, the output at minimum average cost and that average cost.
- ChallengeUsing the same cost function, find average cost at Q = 18 and the percentage above the minimum, then marginal cost at Q = 20.
- ChallengeWith the same cost function the government charges a lump-sum tax of $600 per period. Find average cost at Q = 12 and state how marginal cost changes.
- Error redoA student sees long-run average cost fall from $38 to $34 and says cost dropped $4, that is 4%. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | $30 per unit (6,000 / 200). | Average cost is total cost divided by output. |
| 2 | Total cost $1,500 (900 + 15 x 40), average cost $37.50 (1,500 / 40), average fixed cost $22.50 (900 / 40). | Compute total cost first, then divide; average fixed cost spreads only the fixed part. |
| 3 | A fall of 20% (16 / 80), which is economies of scale. | Long-run average cost falling with scale means economies of scale. |
| 4 | Q = 400 gives $34 (8 + 18 + 8); Q = 200 gives $38 (16 + 18 + 4), which is $4 or 11.76% higher. | Substitute each term at the same output before comparing. |
| 5 | Seven firms (1,750 / 250). | A smaller minimum efficient scale lets the market support more efficient firms. |
| 6 | Decreasing returns to scale; output rises only 70% (140 / 200). | Output rising by less than inputs pushes long-run average cost up. |
| 7 | Average cost is Q squared minus 24Q plus 300; the minimum is at Q = 12 with average cost $156. | At the average cost minimum, marginal cost equals average cost. |
| 8 | At Q = 18 average cost is $192, 23.1% above $156; marginal cost at Q = 20 is $540. | Average and marginal cost are different curves and cannot be swapped. |
| 9 | Average cost rises from $156 to $206 (156 + 50); marginal cost is unchanged. | A lump-sum tax lifts average cost only and leaves the cost of one more unit alone. |
| 10 | The fall must be divided by the original value: $4 / $38 is 10.5%, not 4%. | Percentage change uses the original value as the base; a dollar amount is not a percentage point. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
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