Question

Calculate the consumers' surplus at the indicated unit price (P with a bar over it) for the demand equation.
q=20-0.05p^2; (P with bar over it) = 2

Answer 1

nobody knows if they can help you if you don't post your actual question ;)

Answer 2

good point haha my first question is

Calculate the consumers' surplus at the indicated unit price (P with a bar over it) for the demand equation.
q=20-0.05p^2; (P with bar over it) = 2

Answer 3

I can send you some examples if you need them to get your bearings

Answer 4

maybe that would help, this seems to require some context

just so you know, it's better to post the question like that in the original post

the problem here though is terminology... p is your "unit price"
if so I would think you just plug in the number 2 for p and get your answer q, but you say this is a calculus problem?

Answer 5

Yeah its considered calculus in my book the chapter is labeled "Further integration techniques and Applications of the integral"

Answer 6

let me find you an example one moment

Answer 7

so then you must be integrating with respect to p over some interval?

Answer 8

Yes exactly! :D

Answer 9

ok just a few seconds more waiting for picture of example to save

Answer 10

there is a button that says "equation" below on most browsers that lets you type the equation in

Answer 11

\[\int_a^b f(x)dx\]

Answer 12

its backwards but the answer is 40.5

Answer 13

the issues I am having with the current problem however though is q equals the equation instead of p which is what i'm used to doing.

Answer 14

in this case the "unit price" went from 0 to 27 or what?
where did the bounds come from?

Answer 15

all this depends on what these variables represent; we need more context here...

Answer 16

yes the unit price goes from 0 to 27 which is why we use the interval 0 to 27

Answer 17

and what are you calculating in that paper?

Answer 18

The consumers' surplus which is basically how much a customer is willing to pay for a given item

Answer 19

and where does the 4 come from?

Answer 20

you say p=4 in the paper?
is that like p=2 in this question?

Answer 21

exactly!

Answer 22

you take the p bar value and substitute it in for the value of p

Answer 23

ok, so this problem is the exact same as the other one, but with p=2, and you don't know the bounds?
you are calculating the same thing you say; the consumer price... thing

Answer 24

oh I see

Answer 25

so if I were to do it my q would end up equalling 79.8 but thats just the first part

Answer 26

after obtaining the q value we still have to integrate it

Answer 27

but in your example, the integration you do results in q?

Answer 28

so I know we would use the integral \[\int\limits_{0}^{27}\]

Answer 29

but I am not sure what we would use as the equation to put inside that integral

Answer 30

if you look closely at the example our original equation is p=10-2q^(1/3) after substituting in 4 for p and subtracting 10 from either side we are left with -6=-2q^1/3

Answer 31

oh man I really wish that paper hadn't been backwards, I didn't realize there were q's in there the whole time :P

Answer 32

which we then later use in our interval as \[\int\limits_{0}^{27}(6-2q^(1/3)-4dq\]

Answer 33

hahaha Its all good that one is on me xD

Answer 34

after integrating we write (6-2q^(4/3))-4q) still using the interval 0 to 27

Answer 35

I don't really knw what you're doing, or where you get 27 from again, but if I had to guess I would think you'd just turn it around\[q=20-0.5p^2\implies p=\sqrt{40-2q}\]

Answer 36

and integrate that

Answer 37

I'm sorry, for one thing this is talking about I subject I don't know. math yes, business or econ or whatever this is, no....
another is I'd really like to at least have that pic not reversed.

Answer 38

so the 27 comes from us taking -6=2q^(1/3) which we got from substituting in 4 for p in the original equation. We then have to isolate the q in -6=-2q^(1/3) we do that by dividing each side by -2

Answer 39

give me one moment and I'll have a non-reversed version for you :)

Answer 40

actually I have to go, but I suggest you repost your question along with this prior explanation (not reversed of course) and someone will be able to help you.
Good luck

Answer 41

Thank you have a good evening:)