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 start by finding the derivative of the demand function with respect to price:

q(p) = 11eb0d3b_9885_0d41_9790_33a460067789_TB1243_11

q'(p) = 11eb0d3b_9885_0d41_9790_33a460067789_TB1243_11 * (-1/p)

Next, we can calculate the elasticity of demand using the formula:

η = (p/q) * (dq/dp)

At the given price and quantity, we have:

p = 303 (in hundreds of dollars)
q = 6 (in tons)
dq/dp = q'(p) / 100

Plugging in the numbers, we get:

dq/dp = q'(303) / 100 = 11eb0d3b_9885_0d41_9790_33a460067789_TB1243_11 * (-1/303) / 100 ≈ -0.000361

η = (303/6) * (-0.000361) ≈ -7.1

Note that the elasticity is negative, which means that demand is inelastic at this point (i.e. a price increase would result in a decrease in revenue). We can take the absolute value to get the elasticity as a positive number:

η ≈ 7.1

Suppose the Demand Function for a Product Is Given by