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Math Help - Finding Price Elasticity through differentiation

  1. #1
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    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?).
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  2. #2
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    Quote Originally Posted by ihatemath09 View Post
    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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