Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

TedG

  • 2 years ago

anyone able to help me with difference equations?

  • This Question is Closed
  1. vf321
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What specifically? I know a bit...

  2. TedG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @vf321 sorry was watching the rugby :D. how do you take two recurrance equations ( i think thats correct term) and create a difference equation that relates the two. More specifically...

  3. TedG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[d _{n}=-2p_{n}+3 \] and \[s _{n+1}=p^{2}_{n}+1\] need a difference equation that relates \[p_{n+1}\] to \[p_{n}\]

  4. vf321
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well hang on-what is the relation between \(d_n\) and \(s_n\)?

  5. TedG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you may need the information that P_{n} represents price per unit in period n. s_{n}, d_{n} represents supply and demand respectively. the question says asumming market price is price at which supply equals demand... i think that is answering what you have just asked.

  6. vf321
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    OK then. Well, then what's the problem?\[s_{n+1} = d_{n+1} = -2 p_{n+1}+3\]

  7. TedG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but d_{n} is given, not d_{n+1}

  8. vf321
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes, but that's the point of difference equations - they're true for all integral \(n > 0\)

  9. vf321
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Or, depending on your definitions, \(n = 0\) may be valid too.

  10. TedG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so, d_{n+1} is simply -2p_{n+1}+3

  11. vf321
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah. Given that, can you replace \(s_{n+1}\) in the other equation?

  12. vf321
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    BTW, for inline latex surround your formula in \.(formula\.) ( without the periods)

  13. TedG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so the difference equation would be -2p_{n+1}+3=p^{2}_{n}+1, and rearranged?

  14. vf321
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Correct. Do you have Mathematica?

  15. TedG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Mathematica, no. is it software?

  16. vf321
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes, it would let you solve the difference equation if you needed to.

  17. TedG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh... I use maple. pretty sure that will help solve it. also thanks for the tip on the inline latex. been wandering how to do that for ages.

  18. vf321
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yup. np.

  19. TedG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do you know about steady states? because thats what i am asked to find.

  20. vf321
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Hmm. If I had to guess (so, no, I haven't really done them before), then I would say that steady states are situations where the price has asymptotic behavior, so as \(n\) goes up, \(p_n\) continually gets closer to a certain value.

  21. TedG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm ok. Well I think the steady states are a diferrent way of saying stationary points. as we were taught them with an example using dx/dt=f(x*) and the steady states were solutions of f(x*)=0.

  22. TedG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    not sure if that will change the way you think about it.

  23. TedG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh ok. so do you have an idea on how you would approach finding steady states of a difference equation?

  24. vf321
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, (and again I dont know for sure), being in a steady state for something discrete like a difference equation probably means solving \(p_{n+1}-p_{n} = 0\), because the difference between the two steps is 0 means it's in a steady state.

  25. vf321
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    And you already have a formula for \(p_{n+1}\), so I would just plug it in and solve.

  26. TedG
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh ok. that makes sense. well anyway i guess that is everything. thanks for the help.

  27. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.