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vf321
 one year ago
Best ResponseYou've already chosen the best response.1What specifically? I know a bit...

TedG
 one year ago
Best ResponseYou've already chosen the best response.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...

TedG
 one year ago
Best ResponseYou've already chosen the best response.0\[d _{n}=2p_{n}+3 \] and \[s _{n+1}=p^{2}_{n}+1\] need a difference equation that relates \[p_{n+1}\] to \[p_{n}\]

vf321
 one year ago
Best ResponseYou've already chosen the best response.1Well hang onwhat is the relation between \(d_n\) and \(s_n\)?

TedG
 one year ago
Best ResponseYou've already chosen the best response.0you 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.

vf321
 one year ago
Best ResponseYou've already chosen the best response.1OK then. Well, then what's the problem?\[s_{n+1} = d_{n+1} = 2 p_{n+1}+3\]

TedG
 one year ago
Best ResponseYou've already chosen the best response.0but d_{n} is given, not d_{n+1}

vf321
 one year ago
Best ResponseYou've already chosen the best response.1Yes, but that's the point of difference equations  they're true for all integral \(n > 0\)

vf321
 one year ago
Best ResponseYou've already chosen the best response.1Or, depending on your definitions, \(n = 0\) may be valid too.

TedG
 one year ago
Best ResponseYou've already chosen the best response.0so, d_{n+1} is simply 2p_{n+1}+3

vf321
 one year ago
Best ResponseYou've already chosen the best response.1yeah. Given that, can you replace \(s_{n+1}\) in the other equation?

vf321
 one year ago
Best ResponseYou've already chosen the best response.1BTW, for inline latex surround your formula in \.(formula\.) ( without the periods)

TedG
 one year ago
Best ResponseYou've already chosen the best response.0so the difference equation would be 2p_{n+1}+3=p^{2}_{n}+1, and rearranged?

vf321
 one year ago
Best ResponseYou've already chosen the best response.1Correct. Do you have Mathematica?

TedG
 one year ago
Best ResponseYou've already chosen the best response.0Mathematica, no. is it software?

vf321
 one year ago
Best ResponseYou've already chosen the best response.1Yes, it would let you solve the difference equation if you needed to.

TedG
 one year ago
Best ResponseYou've already chosen the best response.0oh... 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.

TedG
 one year ago
Best ResponseYou've already chosen the best response.0do you know about steady states? because thats what i am asked to find.

vf321
 one year ago
Best ResponseYou've already chosen the best response.1Hmm. 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.

TedG
 one year ago
Best ResponseYou've already chosen the best response.0hmm 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.

TedG
 one year ago
Best ResponseYou've already chosen the best response.0not sure if that will change the way you think about it.

TedG
 one year ago
Best ResponseYou've already chosen the best response.0oh ok. so do you have an idea on how you would approach finding steady states of a difference equation?

vf321
 one year ago
Best ResponseYou've already chosen the best response.1Well, (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.

vf321
 one year ago
Best ResponseYou've already chosen the best response.1And you already have a formula for \(p_{n+1}\), so I would just plug it in and solve.

TedG
 one year ago
Best ResponseYou've already chosen the best response.0oh ok. that makes sense. well anyway i guess that is everything. thanks for the help.
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