Help Finding elasticity of demand!!

Jan 2010
17
0
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.
thanks in advance
 
May 2010
1,034
272
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:
\(\displaystyle \frac{dQ}{dP} = -2\)
\(\displaystyle e = \frac{P}{Q(P)} *-2\)
\(\displaystyle e = \frac{-2P}{30-2P}\)
 
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