Calculus

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Given the demand function q=173-5p, determine the price where demand has unit elasticity.

  • Calculus -

    Since the p-q curve has negative slope (which is normal), unit elasticity means -1.

    Elasticity = (ΔQ/Q) / (ΔP/P)
    =(ΔQ/ΔP) / (P/Q)
    =(dQ/dP)*(P/Q)
    =-1

    dQ/dP = d(173-5P)/dP = -5

    Therefore
    -5*(P/Q) = -1
    -5P = -1(173-5P)
    Solve for P to get P=17.3

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