Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 years ago

Elasticity of demand problem (calculus)?

Use the price-demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p.

x=f(p)=2005-p^2; p=13

Thanks SO much :))

Update:

BTW, E(p)=-(pf'(p))/(f(p) Thanks!

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  • 6 years ago
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    Equation for Elasticity of Demand:

    E(P) = (dQ/dP)*(P/Q)

    Where:

    (dQ/dP) = derivative of the demand function

    P = Price

    Q = Quantity

    The demand function we're given is:

    x = 2005 - P²

    And the question is asking us to determine whether demand is elastic, inelastic, or is unit elastic when the price is $13.

    We first start by taking the derivative of the demand function, which we can easily do by applying the power rule. Taking the derivative of the demand function will give us:

    x = 2005 - P²

    dx/dP = -2P

    Plugging in what we know into the Elasticity of Demand equation will give us:

    E(P) = (dx/dP)*(P/x)

    E(P) = (-2P)*(P/x)

    Since we're told that x = 2005 - P², we can substitute 2005 - P², for x, in the Elasticity of Demand equation. Doing so will give us:

    E(P) = (-2P)*(P / 2005 - P²)

    Multiplying through by P will give us:

    E(P) = (-2P²) / (2005 - P²)

    Plugging 13 in for all values of P will give us:

    E(13) = (-2(13)²) / (2005 - (13)²)

    E(13) = -338 / 1836

    E(13) = -169 / 918 = -.184096

    Because -.184096 is greater than -1 but less than 0, demand is therefore inelastic when P = 13

    Final Answer:

    Demand is Price Inelastic when P = 13

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  • 6 years ago

    When a firm produces a total distinct product that is not a substitute for the existing products in the market this situation is called as ...........?????

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