Assertion (A) : The average fixed cost curve is a rectangular hyperbola.
Reason (R) : Multiplication of average fixed cost with the quantity of output produced, always yields a fixed value.
In the light of the above statements, choose the most appropriate answer from the options given below :
Analyzing Average Fixed Cost Curve Properties
Assertion (A) Analysis: AFC as a Rectangular Hyperbola
The statement asserts that the Average Fixed Cost (AFC) curve is a rectangular hyperbola.
In economics, Average Fixed Cost is calculated as:
$ \text{AFC} = \frac{\text{Total Fixed Cost (TFC)}}{\text{Quantity of Output (Q)}} $
Since Total Fixed Cost (TFC) is constant in the short run, as the quantity of output (Q) increases, the AFC decreases. The product of AFC and Q always equals TFC:
$ \text{AFC} \times \text{Q} = \text{TFC} $
A curve where the product of the two variables (AFC and Q) is constant represents a rectangular hyperbola. Therefore, Assertion (A) is correct.
Reason (R) Analysis: TFC Multiplication Property
The statement explains that multiplying average fixed cost by the quantity of output produced always yields a fixed value. As shown above, this product equals Total Fixed Cost (TFC), which is indeed a fixed value in the short run.
This mathematical relationship is the defining characteristic of a rectangular hyperbola when plotted on a graph with quantity on one axis and cost per unit on the other. Thus, Reason (R) is correct.
Connecting Assertion and Reason
Reason (R) directly explains the mathematical property that causes the AFC curve to take the shape of a rectangular hyperbola, as stated in Assertion (A). The constant product (TFC) is the fundamental reason for the hyperbolic shape.
Therefore, both (A) and (R) are correct, and (R) provides the correct explanation for (A).
Conclusion
The most appropriate answer is that both statements are correct, and Reason (R) correctly explains Assertion (A).
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