PDA

View Full Version : Derivative


rusticoroad
Mar 9, 2011, 07:10 AM
I have a derivative question.
If "p" is price and "q" is quantity, and the demand for a product is q = 5000e(-0.08p) (exponential function), what is the derivative of demand with respect to price when p=$10. Interpret answer in terms of demand.

ebaines
Mar 9, 2011, 07:26 AM
The derivative of a function like


y = Ae^{bx}


is:


\frac { dy} {dx}= Abe^{bx} = by


For your function you have p as the independent variable rather than x, A = 5000 and b = -0.08. Can you finish it from here?

rusticoroad
Mar 9, 2011, 08:03 AM
I thought that the answer might be: q'= -400e (-.08 x 10) = -179.73. Am I doing the derivative wrong?

ebaines
Mar 9, 2011, 08:16 AM
Please do not use the comment feature of the web site to ask follow-up questions, but rather use the "answer" box.

You have it correct: the derivative at p = 10 is indeed dp/dq = -179.73 units/dollar.