If P1 = $5, Q1 = 10,000, P2 = $6 and Q2 = 5,000, then at point P2 an estimate of the point price elasticity equals:a.-0.12b.-4.25c.-6d.-2.5

1. Break Down the Problem

To find the point price elasticity of demand at point $P_2$, we need to apply the formula for point price elasticity of demand:

$E_d = \frac{\Delta Q / Q}{\Delta P / P}$

Where:

• $\Delta Q = Q_2 - Q_1$
• $\Delta P = P_2 - P_1$

2. Relevant Concepts

1. Identify the changes:

   • $P_1 = 5$
   • $Q_1 = 10,000$
   • $P_2 = 6$
   • $Q_2 = 5,000$

2. Calculate the changes:

   • $\Delta Q = Q_2 - Q_1 = 5,000 - 10,000 = -5,000$
   • $\Delta P = P_2 - P_1 = 6 - 5 = 1$

3. Analysis and Detail

Now substitute the values in the elasticity formula. We need the average values of $Q$ and $P$ to compute elasticity:

$Q_{avg} = \frac{Q_1 + Q_2}{2} = \frac{10,000 + 5,000}{2} = 7,500$

$P_{avg} = \frac{P_1 + P_2}{2} = \frac{5 + 6}{2} = 5.5$

Substituting the values back into the point price elasticity formula:

$E_d = \frac{-5,000 / 7,500}{1 / 5.5}$

Calculating each part:

$\frac{-5,000}{7,500} = -\frac{2}{3} \quad (\text{exact fraction})$ $\frac{1}{5.5} = \frac{2}{11} \quad (\text{convert to fraction})$

Thus, the elasticity becomes:

$E_d = -\frac{2/3}{2/11} = -\frac{2}{3} \cdot \frac{11}{2} = -\frac{11}{3} \approx -3.67$

4. Verify and Summarize

The calculated point price elasticity at $P_2$ is approximately -3.67. This indicates that the demand is elastic since the absolute value is greater than 1, meaning that a 1% increase in price results in a greater than 3.67% decrease in quantity demanded.

Final Answer

The closest option for the point price elasticity is d. -2.5. However, none of the options match the computed value of approximately -3.67, indicating a discrepancy.