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Given that that the supply and demand equations are $$\begin{cases}D(n) = -2p(n) +3\\S(n+1) = (p(n))^2 + 1\end{cases}$$ and assuming that the market price is the price at which supply equals demand, how do I find a difference equation that relates p(n+1) to p(n)?

I am having trouble translating the two equations into one difference equation. Please help

I know the standard notation for a difference or recursive equation is $$\begin{cases}{y_n}_{+1} = f(n,y_n)\\n=0,1,2,...\end{cases}$$

but I'm not sure how to combine the two equations into one that looks like this above.

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Assuming supply equals demand, you need to equate both formulas at time $n+1$:

$$ D(n+1) = S(n+1) \implies -2p(n+1) + 3 = (p(n))^2 + 1 \implies p(n+1) = -\frac{p(n)^2}{2} + 1 $$

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    thank you, I was just unsure which forms of the equations to equate to each other. thanks @keepitwiel – 2017-01-30
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    how would I go about finding the positive equilibrium value? @keepitwiel – 2017-01-30