The problem involves calculating the approximate change in demand based on a price elasticity of demand (E) and a price increase.

Given:

• Initial price $P = 78$ dollars
• Elasticity $E(78) = 3.1$
• Price increase $\Delta P = 9$ dollars

Solution:

The formula to approximate the percentage change in demand based on elasticity is:

$\text{Percentage change in demand} = E \times \frac{\Delta P}{P} \times 100\%$

Substitute the values: $= 3.1 \times \frac{9}{78} \times 100\%$

Calculating step-by-step:

1. $\frac{9}{78} \approx 0.1154$
2. $3.1 \times 0.1154 \approx 0.3577$
3. Multiply by 100 to get a percentage: $0.3577 \times 100 \approx 35.77\%$

Thus, the demand will decrease by approximately 35.77% when the price is increased by $9.

Would you like further details on this calculation?

1. What is the concept of price elasticity of demand?
2. How does a price increase generally affect demand with high elasticity?
3. What are other methods to calculate elasticity-related changes?
4. Why is elasticity important in pricing strategy?
5. How would a decrease in price affect demand in this scenario?

Tip: Remember, elasticity greater than 1 (like 3.1) indicates high sensitivity to price changes.