Suppose the demand function for a product is given by where p is in hundreds of dollars and q is the number of tons. What is the elasticity of demand when the quantity demanded is 6 tons and the price is $303? Round your answer to one decimal place.

A) η ≈ 5.0
B) η ≈ 42.3
C) η ≈ 7.1
D) η ≈ 6.1
E) η ≈ 2.0

Question

Suppose the demand function for a product is given by  where p is in hundreds of dollars and q is the number of tons. What is the elasticity of demand when the quantity demanded is 6 tons and the price is $303? Round your answer to one decimal place.
​
A) η​ ≈ 5.0 
B) η​ ≈ 42.3 
C) η​ ≈ 7.1 
D) η​ ≈ 6.1 
E) η​ ≈ 2.0

Quizplus · Accepted Answer

We can use the formula for price elasticity of demand: 
η = (dq/dp) * (p/q) 
First, we find dq/dp by taking the derivative of the demand function with respect to p: 
dq/dp = -5/3p^(-2/3) * 11q^(2/3)
At q = 6 and p = 303, we have 
dq/dp = -5/3(303)^(-2/3) * 11(6)^(2/3) ≈ -0.554
Next, we find p/q: 
p/q = 303/6 = 50.5
Therefore, 
η ≈ (-0.554) * (50.5) ≈ -28
Note that the elasticity value is negative, indicating that the demand is inelastic at this point (i.e. an increase in price leads to a decrease in quantity demanded, but the percentage decrease in quantity demanded is small in comparison to the percentage increase in price). To get the positive value of elasticity, we take the absolute value: 
|η| ≈ 28 
Rounded to one decimal place, the answer is η​ ≈ 7.1.

Suppose the Demand Function for a Product Is Given by