# Finding Price Elasticity through differentiation

• Mar 2nd 2010, 06:03 PM
ihatemath09
Finding Price Elasticity through differentiation

Suppose the demand function for a particular graphing calculator is
D( p) = 1000 e - 0.02 p

a. Find the price elasticity of demand, the revenue function, and how revenue changes with price (dR/dp).

b. Determine the range of prices for which this demand function is elastic (, > 1) and inelastic (, < 1).

c. Determine how the elasticity of demand is related to the way that revenue responds to price increases (i.e., how does the sign of dR/dp relate to whether the function is elastic or inelastic?).
• Mar 7th 2010, 06:39 PM
jass10816
Quote:

Originally Posted by ihatemath09
It is hard to tell, but i'm assuming your equation is $D(p)=1000e^{-0.02p}$
Then the price elasticity of demand is $\frac{p}{q}*\frac{dq}{dp}=\frac{p}{q}*-20e^{-0.02p}=\frac{p}{1000e^{-0.02p}}*-20e^{-0.02p}=-0.02p$
Revenue is price times quantity so $R(p)=1000pe^{-0.02p}$
and $\frac{dR}{dp}=1000 e^{-0.02 p}-20. e^{-0.02 p} p$