Assertion:The short run marginal cost (SMC) is defined as the change…

The correct answer is option 1: Both Assertion (A) and reasoning (R) are correct and R is the correct explanation of A.

Assertion:The short run marginal cost (SMC) is defined as the change in total variable cost per unit of change in output. This is correct. The short run marginal cost (SMC) is defined as the change in total cost per unit of change in output (SMC = change in total cost/ change in output i.e. ΔTC/ΔQ ). But in the short run, total cost is the sum of total fixed cost and total variable cost. Since fixed cost remains constant, any change in total cost comes only from change in total variable cost.

Therefore: change in total cost = change in total variable cost

So, both expressions give the same value

SMC = change in total cost divided by change in output = change in total variable cost divided by change in output

Therefore, SMC can also be expressed as the change in total variable cost per unit change in output.

Reasoning: When we change the level of output in short term, whatever change occurs to total cost is entirely due to the change in total variable cost because fixed cost cannot be changed in the short run. This is correct. In the short run, total cost (TC) is the sum of total fixed cost (TFC) and total variable cost (TVC). Fixed cost does not change with output, so TFC remains constant. When output changes, only TVC changes. Hence, any change in total cost is entirely due to change in total variable cost.

Thus: Change in TC = Change in TVC

Therefore: SMC = Change in TC ÷ Change in Output = Change in TVC ÷ Change in Output

Evaluating the Relationship: The reason $SMC$ is effectively the change in $TVC$ is precisely because $TFC$ is constant in the short run. Since the Reasoning provides the logical foundation for why the Assertion is true, it is the correct explanation.