Question

tb mc qu. 06 - 65 blossom, inc., sells 500 bottles of perfume a month when the price is $7. a huge increase in resource costs forces blossom to raise the price to $9, and the firm only manages to sell 460 bottles of perfume. using the midpoint formula, the price - elasticity - of - demand coefficient is
multiple choice
0.33 and elastic.
3 and elastic.
3 and inelastic.
0.33 and inelastic.

Explanation:

Step1: Identify the formula for price - elasticity of demand using mid - point method

The formula is $E_d=\frac{\%\text{ change in quantity demanded}}{\%\text{ change in price}}$, where $\%\text{ change in quantity demanded}=\frac{Q_2 - Q_1}{\frac{Q_2+Q_1}{2}}\times100$ and $\%\text{ change in price}=\frac{P_2 - P_1}{\frac{P_2+P_1}{2}}\times100$. In practice, we can cancel out the 100s and just use $E_d=\frac{\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}}{\frac{P_2 - P_1}{(P_2 + P_1)/2}}$.

Step2: Define the values of $Q_1$, $Q_2$, $P_1$ and $P_2$

$Q_1 = 500$, $Q_2=460$, $P_1 = 7$, $P_2 = 9$.

Step3: Calculate the change in quantity and the average quantity

$\text{Change in quantity}=Q_2 - Q_1=460 - 500=- 40$. $\text{Average quantity}=\frac{Q_2+Q_1}{2}=\frac{460 + 500}{2}=480$.

Step4: Calculate the change in price and the average price

$\text{Change in price}=P_2 - P_1=9 - 7 = 2$. $\text{Average price}=\frac{P_2+P_1}{2}=\frac{9 + 7}{2}=8$.

Step5: Calculate the price - elasticity of demand

$E_d=\frac{\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}}{\frac{P_2 - P_1}{(P_2 + P_1)/2}}=\frac{\frac{460 - 500}{480}}{\frac{9 - 7}{8}}=\frac{\frac{-40}{480}}{\frac{2}{8}}=\frac{-40}{480}\times\frac{8}{2}=\frac{-40\times8}{480\times2}=\frac{-320}{960}=- 0.33$. We take the absolute value, so $|E_d| = 0.33$. Since $|E_d|<1$, it is inelastic.

Answer:

D. 0.33 and inelastic.