1. ## 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.

2. 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?

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

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

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