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Math Help - economics with integral

  1. #1
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    economics with integral

    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 - x2. Hence, a quantity of 4 units of the good will be bought at a price of $9, i.e. for a total payment of $36. However, the total amount the consumer was willing to pay is given by the area between the graph of y =30 - x2 and the x-axis from x = 0 to x = 4. Find this value. How much does it differ from the actual payment of $36? This difference is known as ‘consumer surplus’.
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  2. #2
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    Hello,

    Translating the text, the total price the consumer is willing to pay for 4 units is :

    \int_0^4 y ~dx=\int_0^4 (30-x^2) ~dx=\left[30x-\frac{x^3}{3}\right]_0^4=\dots

    Compare it to 36$ and that's all
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