We let $Q_k$ denote the supply of commodity, $D_k$ the demand for the commodity, and $p_k$ the price at $k$-th time. The demand depends on the current price, $D_k=a+bp_k$ and the supply depends on the previous price, $Q_k=c+dp_{k−1}$. (To get $\{p_k\}$ assume $D_k = Q_k$.)
Suppose that the sequence of prices $\{p_k\}$ converges to a limiting price $\bar p$. What must $\bar p$ be? Find a condition on the coefficients so that you can prove that $p_k \to\bar p$. Why is it reasonable that the conditions depend on $d$ and $b$?
I have calculated the sequence to be $\{p_k\} = c−a+dp_{k−1}b$, from here I was thinking that for number 1), $\bar p$ must be the average price that the supply and demand converges to, as for number 2) I'm lost as to what to do, possibly a Cauchy-$\epsilon$ argument?
Kyle, you're answer should be
, not {pk}=c−a+dpk−1b