Find the consumer's surplus if the demand for an item is given by D(x)=72-x2, assuming supply and demand are in equilibrium at x=6

Question

Find the consumer's surplus  if the demand for an item is given  by D(x)=72-x2, assuming supply and demand are in equilibrium at x=6

amistre64 · Answer

consumer surplus is everything above the equilibrium line; but whats the equation for supply?

amistre64 · Answer

helps if I read the qwestun all the way to the end :)

amistre64 · Answer

is that x^2?

amistre64 · Answer

its the area under the curve..... i see that much :)

amistre64 · Answer

y = 36 when x = 6; so we need the area under the curve from [0,6] of the equation 36-x^2

anonymous · Answer

so how do we find the area

amistre64 · Answer

36x - (x^3)/3; at x=0 we get 0

at x = 6 we get...

36(6) - (6^3)/3 as the ansswer

amistre64 · Answer

its taking the antiderivative/indegral of the equation with the bounds established...

anonymous · Answer

Ohhh ok thanksx:D

amistre64 · Answer

I get 144 as my answer

anonymous · Answer

OK i got 2268??

amistre64 · Answer

at x = 6; the y(equilib line) = 36 right?

amistre64 · Answer

so we just want the area under the top part for our consumer surplus

amistre64 · Answer

drop your equation by 36 to get it to the x axis:

72-36 -x^2 = 36 - x^2

integrate 36 - x^2 to get;  36x - (x^3)/3; and solve for x at 0 and 6

anonymous · Answer

ook i know wat i did wrong

amistre64 · Answer

if you dont drop it; then you have to subtract the bottom part :)

anonymous · Answer

gotcha! :D

amistre64 · Answer

:)  this is the graphical representation ;)

anonymous · Answer

ok thanx