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vf321Best ResponseYou've already chosen the best response.1
What specifically? I know a bit...
 one year ago

TedGBest 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...
 one year ago

TedGBest 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 \[p_{n}\]
 one year ago

vf321Best ResponseYou've already chosen the best response.1
Well hang onwhat is the relation between \(d_n\) and \(s_n\)?
 one year ago

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

vf321Best ResponseYou've already chosen the best response.1
OK then. Well, then what's the problem?\[s_{n+1} = d_{n+1} = 2 p_{n+1}+3\]
 one year ago

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

vf321Best ResponseYou've already chosen the best response.1
Yes, but that's the point of difference equations  they're true for all integral \(n > 0\)
 one year ago

vf321Best ResponseYou've already chosen the best response.1
Or, depending on your definitions, \(n = 0\) may be valid too.
 one year ago

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

vf321Best ResponseYou've already chosen the best response.1
yeah. Given that, can you replace \(s_{n+1}\) in the other equation?
 one year ago

vf321Best ResponseYou've already chosen the best response.1
BTW, for inline latex surround your formula in \.(formula\.) ( without the periods)
 one year ago

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

vf321Best ResponseYou've already chosen the best response.1
Correct. Do you have Mathematica?
 one year ago

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

vf321Best ResponseYou've already chosen the best response.1
Yes, it would let you solve the difference equation if you needed to.
 one year ago

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

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

vf321Best ResponseYou've already chosen the best response.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.
 one year ago

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

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

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

vf321Best ResponseYou've already chosen the best response.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.
 one year ago

vf321Best ResponseYou've already chosen the best response.1
And you already have a formula for \(p_{n+1}\), so I would just plug it in and solve.
 one year ago

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