Expert: Dr. Nyayapati Swami - 9/18/2009

Question
Sorry if this question is not in your area of expertise but I could not find a place to as an economics question.  I have no problem figuring for price with the demand equation when I get both Qs and Qd but when I only get one side of the equation I am not sure how to get started.  The question is;
The point price elasticity of demand for red herring is $-4.  The demand curve for red herring is  Q = 120 - P.  What is the price of red herring.  I know that the answer is $96 I just don't understand how to get there.  Thanks for any help.


Answer
This requires the knowledge of derivatives.
Point elasticity of demand = (P/Q) dQ/dP
Since your demand is Q = 120 - P, you have dQ/dP = -1
Therefore, point elasticiy = (P/Q)(-1) = -P/Q
You are given point elasticity is -4, therefore
-P/Q = -4
or P = 4Q
Substituting this into your demand
Q = 120 - P
Q = 120 - 4Q
5Q = 120
Q = 120/5 = 24
Hence P = 120 - P = 120 - 24 = 96.