In one week, an appliance store sells 90 DVD players at $100 each. It then lowers its price to $90 and it sells 100 DVD players. After calculating the elasticity coefficient using the midpoint formula __________.

Question

They find that demand is elastic.

They find that demand is inelastic.

The elasticity coefficient is equal to 1.

The elasticity coefficient is equal to 1.5.

Answer 1

To calculate the price elasticity of demand using the midpoint formula, we will first apply the following formula:

\[ E_d = \frac{Q_2 - Q_1}{(Q_1 + Q_2) / 2} \div \frac{P_2 - P_1}{(P_1 + P_2) / 2} \]

Where:

• \(Q_1 = 90\) (original quantity sold at original price)
• \(P_1 = 100\) (original price)
• \(Q_2 = 100\) (new quantity sold at new price)
• \(P_2 = 90\) (new price)

Step 1: Calculate the change in quantity (Q) and average quantity \[ Q_2 - Q_1 = 100 - 90 = 10 \] \[ \frac{Q_1 + Q_2}{2} = \frac{90 + 100}{2} = 95 \]

Step 2: Calculate the change in price (P) and average price \[ P_2 - P_1 = 90 - 100 = -10 \] \[ \frac{P_1 + P_2}{2} = \frac{100 + 90}{2} = 95 \]

Step 3: Plug the values into the elasticity formula \[ E_d = \frac{10}{95} \div \frac{-10}{95} \]

This simplifies to: \[ E_d = \frac{10}{95} \times \frac{95}{-10} = \frac{10}{-10} = -1 \]

Step 4: Interpret the coefficient Since we are interested in the absolute value of elasticity, we will take the positive value: \[ |E_d| = 1 \]

Since the coefficient equals 1, we interpret that the demand is unit elastic.

So the correct answer is:

The elasticity coefficient is equal to 1.