Expert: Ahmed Salami - 12/6/2009

Question
Question #1 - Given the demand function D(p)=415-4p, calculate the elasticity of demand for p=53.


Question #2 - Find dy/dx USING IMPLICIT DIFFERENTIATION:   12x^3-x^2y^3=7

Answer
Hi Melissa,
1) D = 415 - 4p
dD/dp = -4
Price elasticity of demand
PED = (dD/dp)(p/D)
   = (-4)[p/(415 - 4p)]
   = 4p/(4p - 415)
at p = 53
PED = 212/(212 - 415)
   = 212/(-203)
   = -1.0443

2) 12x³ - x²y³ = 7
The thing to remember in implicit differentiation is that you always add dy/dx when you differentiate anything in y. And so,
36x² - [x².(3y²)(dy/dx) + 2x.y³] = 0
36x² - 3x²y²(dy/dx) - 2xy³ = 0
36x² - 2xy³ = 3x²y²(dy/dx)
dy/dx = (36x² - 2xy³)/3x²y²
     = 2(18x - y³)/3xy²

Regards