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anonymous

  • 5 years ago

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

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  1. amistre64
    • 5 years ago
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    consumer surplus is everything above the equilibrium line; but whats the equation for supply?

  2. amistre64
    • 5 years ago
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    helps if I read the qwestun all the way to the end :)

  3. amistre64
    • 5 years ago
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    is that x^2?

  4. amistre64
    • 5 years ago
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    its the area under the curve..... i see that much :)

  5. amistre64
    • 5 years ago
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    y = 36 when x = 6; so we need the area under the curve from [0,6] of the equation 36-x^2

  6. anonymous
    • 5 years ago
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    so how do we find the area

  7. amistre64
    • 5 years ago
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    36x - (x^3)/3; at x=0 we get 0 at x = 6 we get... 36(6) - (6^3)/3 as the ansswer

  8. amistre64
    • 5 years ago
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    its taking the antiderivative/indegral of the equation with the bounds established...

  9. anonymous
    • 5 years ago
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    Ohhh ok thanksx:D

  10. amistre64
    • 5 years ago
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    I get 144 as my answer

  11. anonymous
    • 5 years ago
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    OK i got 2268??

  12. amistre64
    • 5 years ago
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    at x = 6; the y(equilib line) = 36 right?

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  13. amistre64
    • 5 years ago
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    so we just want the area under the top part for our consumer surplus

  14. amistre64
    • 5 years ago
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    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

  15. anonymous
    • 5 years ago
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    ook i know wat i did wrong

  16. amistre64
    • 5 years ago
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    if you dont drop it; then you have to subtract the bottom part :)

  17. anonymous
    • 5 years ago
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    gotcha! :D

  18. amistre64
    • 5 years ago
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    :) this is the graphical representation ;)

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  19. anonymous
    • 5 years ago
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    ok thanx

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