Assertion A Verification

We are given the demand function $P = 60 - Q^2$ and a specific price $P = 44$. First, we need to find the corresponding quantity $Q$.

• Substitute $P = 44$ into the demand function:

  $44 = 60 - Q^2$

• Solve for $Q^2$:

  $Q^2 = 60 - 44$

  $Q^2 = 16$

• Find $Q$ (assuming quantity is positive):

  $Q = \sqrt{16} = 4$

Next, we calculate the point elasticity of demand ($E_d$). The formula is:

$E_d = \frac{dQ}{dP} \times \frac{P}{Q}$

First, find the derivative of $P$ with respect to $Q$:

$P = 60 - Q^2 \implies \frac{dP}{dQ} = -2Q$

Now, find the derivative of $Q$ with respect to $P$:

$\frac{dQ}{dP} = \frac{1}{\frac{dP}{dQ}} = \frac{1}{-2Q}$

Substitute $Q=4$ into the expression for $\frac{dQ}{dP}$:

$\frac{dQ}{dP} = \frac{1}{-2(4)} = -\frac{1}{8}$

Finally, calculate the point elasticity of demand using $P=44$, $Q=4$, and $\frac{dQ}{dP} = -\frac{1}{8}$:

$E_d = \left(-\frac{1}{8}\right) \times \left(\frac{44}{4}\right)$

$E_d = -\frac{1}{8} \times 11 = -\frac{11}{8}$

Convert the fraction to a decimal:

$E_d = -1.375$

Conclusion for Assertion A: The calculated point elasticity is $-1.375$, which matches the value stated in Assertion A. Therefore, Assertion A is correct.

Reason R Verification

Reason R states that demand is inelastic. To determine if demand is elastic or inelastic, we look at the absolute value of the price elasticity of demand ($|E_d|$).

• Calculated elasticity: $E_d = -1.375$.
• Absolute value: $|E_d| = |-1.375| = 1.375$.

The interpretation of elasticity is as follows:

• If $|E_d| > 1$, demand is elastic.
• If $|E_d| < 1$, demand is inelastic.
• If $|E_d| = 1$, demand is unit elastic.

Since $|E_d| = 1.375$, which is greater than 1, the demand is elastic at the given price point, not inelastic.

Conclusion for Reason R: Reason R is incorrect.

Final Answer Derivation

Based on the analysis:

• Assertion A is correct.
• Reason R is incorrect.

This corresponds to Option C.