Finding Price Elasticity through differentiation

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March 2nd 2010, 06:03 PM
ihatemath09

Finding Price Elasticity through differentiation

help please...

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?).
March 7th 2010, 06:39 PM
jass10816

Quote:

Originally Posted by ihatemath09

help please...

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).

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 $\frac{dR}{dp}=1000 e^{-0.02 p}-20. e^{-0.02 p} p$

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