# Economics math

• Aug 31st 2009, 02:35 PM
brumby_3
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.
• Aug 31st 2009, 06:01 PM
Robb
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?
• Aug 31st 2009, 06:02 PM
brumby_3
It's a 1st year university econometrics class
Thanks for your help by the way!
• Aug 31st 2009, 06:08 PM
Robb
No problem, good luck with it. I remember failing/dropping out of first year econometrics (Doh)
ANU?
• Aug 31st 2009, 06:12 PM
brumby_3
Nah I'm in Sydney.... wanted to go to ANU though!