Why does the SMC curve cut the AVC curve at the minimum point of the AVC curve?
The SMC and AVC curves start from the same point because, for the first unit of output, SMC and AVC are the same value. As output increases, SMC initially falls. Since AVC is the average of marginal costs, it also falls, but it falls less than the SMC. The AVC curve is therefore ‘U’-shaped.
After a point, SMC starts rising. However, AVC continues to fall as long as the value of SMC remains less than the prevailing value of AVC. This is because the lower marginal cost pulls the average down.
Once SMC has risen sufficiently, its value becomes greater than the value of AVC. At this stage, AVC starts rising because the higher marginal cost pulls the average up.
Therefore, the relationship is clear: as long as AVC is falling, SMC must be less than AVC, and when AVC rises, SMC must be greater than AVC. It follows that the SMC curve must cut the AVC curve from below at the minimum point of the AVC curve.
Explanation
The answer is derived directly from the relationship between marginal and average values described in the context. The textbook explains that when a marginal value is below the average, it pulls the average down, and when it is above, it pulls the average up. Consequently, the marginal cost curve can only intersect the average variable cost curve when the average stops falling and starts rising—precisely at the minimum point.
Solution Steps
Step 1: Establish that SMC and AVC start from the same point at the first unit of output.
Step 2: Explain that as output increases, SMC falls. AVC also falls but less than SMC because it is an average.
Step 3: Describe that when SMC starts rising, AVC continues to fall as long as SMC is less than AVC.
Step 4: State that once SMC becomes greater than AVC, the AVC starts rising.
Step 5: Conclude that since SMC < AVC when AVC falls and SMC > AVC when AVC rises, SMC must cut AVC from below at its minimum point.