The demand function for a certain brand of compact disc is where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Compute the elasticity of demand and determine whether the demand is inelastic, unitary, or elastic when x = 10.
A) elastic
B) inelastic
C) unitary

Question

The demand function for a certain brand of compact disc is  where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Compute the elasticity of demand and determine whether the demand is inelastic, unitary, or elastic when x = 10. ​
A) elastic 
B) inelastic 
C) unitary

Quizplus · Accepted Answer

To calculate the elasticity of demand, we need to use the formula:

E = (p/x) * (dx/dp)

Where:
- E = elasticity of demand
- p = wholesale unit price
- x = quantity demanded
- dx/dp = derivative of x with respect to p

Taking the derivative of the demand function, we get:

dx/dp = -11e^(-0.0005p)

Substituting p = 10, we get:

dx/dp = -11e^(-0.005) = -10.487

Substituting p = 10 and x = 10, we get:

E = (10/10) * (-10.487) = -10.487

Since the elasticity of demand is negative, the demand is inelastic. Therefore, the best choice is B.

The Demand Function for a Certain Brand of Compact Disc