
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 xaxis 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.

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The area is Consumer Surplus.
Its equal to the total area under the curve between $\displaystyle x=0$ and $\displaystyle x=4$ less the cost which is equal to $\displaystyle \$14\cdot4=\$56$
In order to work out the total area under the curve, you need to integrate;
$\displaystyle \int^{4}_{0}30x^2=\left[ 30x\frac{x^3}{3}\right]^{4}_{0} =30\cdot(4)\frac{4^3}{3}=98.66667$
therefore $\displaystyle CS = 98.66756=\$42.667$
What year level is this question for?

It's a 1st year university econometrics class
Thanks for your help by the way!

No problem, good luck with it. I remember failing/dropping out of first year econometrics (Doh)
ANU?

Nah I'm in Sydney.... wanted to go to ANU though!