The table below gives the following costs of a firm:
| Output (units) | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| TVC (Rs) | 24 | 29 | 33 | 39 | 47 |
| TC (Rs) | 44 | 49 | 53 | 59 | 67 |
Given below are two statements:
Assertion (A): The SMC of the 7th unit (Rs 8) is greater than the AVC at 6 units, so AVC rises from 6 to 7 units.
Reason (R): Among these levels of output, SMC is the lowest at 6 units of output.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) is true but (R) is false.
Work out AVC and SMC from the table.
\( \displaystyle \text{AVC at 6} = \frac{39}{6} = 6.5, \quad \text{AVC at 7} = \frac{47}{7} = 6.71 \)
\( \displaystyle \text{SMC: 4th} = 5, \ \text{5th} = 4, \ \text{6th} = 6, \ \text{7th} = 8 \)
Assertion (A): The SMC of the 7th unit (Rs 8) is greater than the AVC at 6 units, so AVC rises from 6 to 7 units. — True. The 7th unit costs Rs 8, more than the average of 6.5, so it pulls the average up: AVC rises to 6.71.
Reason (R): Among these levels of output, SMC is the lowest at 6 units of output. — False. SMC is lowest at 5 units (Rs 4). At 6 units it is Rs 6.
NCERT (2026-27): “Shapes of the Short Run Cost Curves … Now, what does the AVC curve look like? For the first unit of output, it is easy to check that SMC and AVC are the same. So both SMC and AVC curves start from the same point. Then, as output increases, SMC falls. AVC being the average of marginal costs, also falls, but falls less than SMC. Then, after a point, SMC starts rising. AVC, however, continues to fall as long as the value of SMC remains less than the prevailing value of AVC. Once the SMC has risen sufficiently, its value becomes greater than the value of AVC. The AVC then starts rising. The AVC curve is therefore ‘U’-shaped. As long as AVC is falling, SMC must be less than the AVC. As AVC rises, SMC must be greater than the AVC. So the SMC curve cuts the AVC curve from below at the minimum point of AVC.”
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