If the demand function for orange juice is expressed as Q = 2000 - 500p,where Q is quantity in gallons and p is price per gallon measured in dollars,then the demand for orange juice has a unitary elasticity when price equals
A) $0.
B) $1.
C) $2.
D) $4.

Question

Quizplus · Accepted Answer

To find the price at which demand has unitary elasticity, we need to find the price at which the absolute value of the elasticity of demand is equal to 1. The formula for elasticity of demand is:

E = (% Change in Quantity Demanded) / (% Change in Price)

We can express this in terms of Q and p as:

E = (dp/p) / (dQ/Q)

Using the demand function Q = 2000 - 500p, we can calculate the derivative of Q with respect to p as:

dQ/dp = -500

Substituting these values into the formula for elasticity, we have:

E = (-500p / Q) * (Q / 2000) = -0.25p

To find the absolute value of elasticity equal to 1, we solve:

| -0.25p | = 1

p = 4

Therefore, the demand for orange juice has a unitary elasticity when the price is $2, as shown by the answer choice C).

If the Demand Function for Orange Juice Is Expressed as Q