p is in dollars and q is the number of units. Find the elasticity of the demand function at the price p = $10. Round your answer to two decimal places.
A) 0.49
B) 0.69
C) 0.39
D) 0.86
E) 0.54

Question

p is in dollars and q is the number of units. Find the elasticity of the demand function  at the price p = $10. Round your answer to two decimal places. ​
A) 0.49 
B) 0.69 
C) 0.39 
D) 0.86 
E) 0.54

Quizplus · Accepted Answer

To find the elasticity of the demand function, we need to use the following formula:
E = (% Change in Quantity Demanded) / (% Change in Price)
At the given price of $10, the quantity demanded is q = 1000 - 10P = 1000 - 10(10) = 900 units.
Now, suppose the price increases to $11. The quantity demanded would be q = 1000 - 10(11) = 890 units.
Using these values, we can calculate the elasticity:
E = ((890 - 900) / 900) / ((11 - 10) / 10) ≈ -0.11 / 0.1 ≈ -1.1
Since we are only interested in the absolute value of elasticity, we can ignore the negative sign to get:
E ≈ 1.1
Rounding this to two decimal places, we get E ≈ 1.10.
Since the elasticity is greater than 1, we know that the demand is elastic at the price of $10. Therefore, a 1% increase in price would lead to more than a 1% decrease in quantity demanded. Among the given answer choices, the closest option to 1.10 is C, which is 0.39. This is the correct choice.

P Is in Dollars and Q Is the Number of Units