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Math Help - Economics math

  1. #1
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    Talking Economics math

    Let y be the price per unit of a good. The price a consumer is willing to pay for different quantities (x) of the good is given by the relation y = 30 - x^2. So a quantity of 4 units of the good will be bought at a price of $14, i.e. for a total payment of $56. However, the total amount the consumer was willing to pay is given by the area between the graph of y = 30 - x^2 and the x-axis from x = 0 to x = 4. Find this value. How much larger is it than the actual payment of $56? What is this difference called in economics?


    I've got the x intercepts - and +squareroot30
    and the y intercept 30

    so it's an upside down parabola but not sure where to go from here.
    Last edited by brumby_3; August 31st 2009 at 05:33 PM. Reason: more info
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  2. #2
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    The area is Consumer Surplus.

    Its equal to the total area under the curve between x=0 and x=4 less the cost which is equal to \$14\cdot4=\$56

    In order to work out the total area under the curve, you need to integrate;

     \int^{4}_{0}30-x^2=\left[ 30x-\frac{x^3}{3}\right]^{4}_{0} =30\cdot(4)-\frac{4^3}{3}=98.66667
    therefore CS = 98.667-56=\$42.667

    What year level is this question for?
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  3. #3
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    It's a 1st year university econometrics class
    Thanks for your help by the way!
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  4. #4
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    No problem, good luck with it. I remember failing/dropping out of first year econometrics
    ANU?
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  5. #5
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    Nah I'm in Sydney.... wanted to go to ANU though!
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