anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
consumer surplus is everything above the equilibrium line; but whats the equation for supply?
amistre64
  • amistre64
helps if I read the qwestun all the way to the end :)
amistre64
  • amistre64
is that x^2?

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amistre64
  • amistre64
its the area under the curve..... i see that much :)
amistre64
  • amistre64
y = 36 when x = 6; so we need the area under the curve from [0,6] of the equation 36-x^2
anonymous
  • anonymous
so how do we find the area
amistre64
  • amistre64
36x - (x^3)/3; at x=0 we get 0 at x = 6 we get... 36(6) - (6^3)/3 as the ansswer
amistre64
  • amistre64
its taking the antiderivative/indegral of the equation with the bounds established...
anonymous
  • anonymous
Ohhh ok thanksx:D
amistre64
  • amistre64
I get 144 as my answer
anonymous
  • anonymous
OK i got 2268??
amistre64
  • amistre64
at x = 6; the y(equilib line) = 36 right?
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amistre64
  • amistre64
so we just want the area under the top part for our consumer surplus
amistre64
  • amistre64
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
  • anonymous
ook i know wat i did wrong
amistre64
  • amistre64
if you dont drop it; then you have to subtract the bottom part :)
anonymous
  • anonymous
gotcha! :D
amistre64
  • amistre64
:) this is the graphical representation ;)
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anonymous
  • anonymous
ok thanx

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