# Help Finding elasticity of demand!!

• Jun 18th 2010, 06:24 PM
ihatemath09
Help Finding elasticity of demand!!
Find the elasticity of demand for each of the following demand functions. Ineach case determine how elasticity varies as price varies.

a) q = 30 - 2p , 0 < p < 15
b) q = p^-a , a > 0
c) q = 100 - 2p^2 , 0 < p < sqrt(20)
d) q = 1/ln(3p) , p>1/3

so (a) is pretty simple as it is linear, its -2, but i'm not sure how to calculate the other ones.
For example, (c) is a parabola, so how would i calculate overall elasticity of demand?

Help with b, c , or d is much appreciated.
• Jun 19th 2010, 03:41 AM
SpringFan25
Be careful, the elasticity of demand is not the slope of the curve. it is:

$\displaystyle e = \frac{% \Delta Q}{% \Delta P}$

If you have a differentiable demand function Q(p) then the instantaneous Price elasticity of demand normally defined as
$\displaystyle e = \frac{P}{Q(P)} * \frac{dQ}{dP}$

So for part a:
$\displaystyle \frac{dQ}{dP} = -2$
$\displaystyle e = \frac{P}{Q(P)} *-2$
$\displaystyle e = \frac{-2P}{30-2P}$