Check My Work (2 remaining) Suppose that at a price of \( \$ 30 \) per month, there are 30,000 subscribers to Small Town Streaming Service. If Small Town Streaming Service raises its price to \( \$ 40 \) per month, the number of subscribers will fall to 20,000 . Using the midpoint method for calculating the elasticity, what is the price elasticity of demand for this company's streaming service? a. 0.75 b. 0.66 c. 2.0 d. 1.4 e. 1.0

To calculate the **price elasticity of demand** using the **midpoint method**, follow these steps: ### Given: - **Initial price (\( P_1 \))**: \$30 per month - **Initial quantity (\( Q_1 \))**: 30,000 subscribers - **New price (\( P_2 \))**: \$40 per month - **New quantity (\( Q_2 \))**: 20,000 subscribers ### Step 1: Calculate the Change in Quantity and Price \[ \Delta Q = Q_2 - Q_1 = 20,000 - 30,000 = -10,000 \] \[ \Delta P = P_2 - P_1 = 40 - 30 = 10 \] ### Step 2: Calculate the Midpoints \[ \text{Average Quantity} = \frac{Q_1 + Q_2}{2} = \frac{30,000 + 20,000}{2} = 25,000 \] \[ \text{Average Price} = \frac{P_1 + P_2}{2} = \frac{30 + 40}{2} = 35 \] ### Step 3: Apply the Midpoint Formula for Elasticity \[ \text{Elasticity} (E) = \frac{\frac{\Delta Q}{\text{Average Quantity}}}{\frac{\Delta P}{\text{Average Price}}} \] \[ E = \frac{\frac{-10,000}{25,000}}{\frac{10}{35}} = \frac{-0.4}{0.2857} \approx -1.4 \] ### Interpretation: The **absolute value** of the elasticity is **1.4**, indicating that the demand is **elastic**. This means that the quantity demanded is relatively responsive to price changes. ### **Answer:** **d. 1.4**