When calculating percentage change using the midpoint (arc elasticity) method, is the percent increase from 50 to 70 equal to the percent decrease from 70 to 50? Which statement is correct?

• A. No, the percent increase is always greater than the percent decrease, regardless of the method used.
• B. The percent increase and decrease are never equal, even with the midpoint method.
• C. No, the percent decrease is always greater than the percent increase, regardless of the method used.
• D. Yes, the percent increase and percent decrease are equal when using the midpoint method.

Answer: (D)

Verified step by step guidance

1. Understand that the midpoint (arc elasticity) method calculates percentage changes by using the average of the initial and final values as the base, rather than just the initial value.
2. Calculate the percentage change from 50 to 70 using the midpoint formula: \(\text{Percentage Change} = \frac{70 - 50}{\frac{70 + 50}{2}} \times 100\).
3. Calculate the percentage change from 70 to 50 using the same midpoint formula: \(\text{Percentage Change} = \frac{50 - 70}{\frac{70 + 50}{2}} \times 100\).
4. Observe that because the denominator (the average of 50 and 70) is the same in both calculations, the magnitude of the percentage increase and decrease will be equal but with opposite signs.
5. Conclude that the midpoint method ensures the percent increase from 50 to 70 is equal in magnitude to the percent decrease from 70 to 50, making the correct statement: 'Yes, the percent increase and percent decrease are equal when using the midpoint method.'