We are interested in the price of a commodity which is traded at regular intervals. We let Qk denote the supply of the commodity, Dk the demand for the commodity, and pk the price at the kth time. The demand depends on the current price, Dk= a + b p_k and the supply depends on the previous price, Qk = c + d p_k-1. (a,c,d>0 and b<0) . We know that p_k = (dp_k-1 a+ c)/b and the sequence {pk} converges to a limiting price p ( p=(-a+c)/ (b-d))

(d) Find a condition on the coefficients so that you can prove that pk -> p. (Show that pk converges to p by using Cauchy argument, epsilon-delta, epsilon-N, epsilon-M etc ) Why is it reasonable that the conditions depend on d and b? you can use reasonable number for a,b,c,d.