1. Consider the discrete model for price pn of a certain product: pn+1=f(pn)=pn+pnabpnc where a and c are non-negative constants and b1. (a) Interpret this model in terms of price-dependent demand and supply of the product and describe each term and parameter in the model. For the rest of the problems, assume a=9 and b=21. (b) Find the 1-period fixed point(s) and determine the values of c for which the fixed point(s) are stable. (c) The 2-period fixed points are obtained by solving the equation p=g(p)=f(f(p)). Solve equation (1) using the fact that the 1-period fixed points also satisfy the 2-period fixed point equation. Show that there are two 2-period fixed points if c>6. (d) Using the chain rule show that the two 2-period fixed points become unstable at the same value of c which satisfies the equation, (dpdfp=p1)(dpdfp=p2)=1 where p1 and p2 denote the 2-period fixed points. (e) Using equation 3 find the value of c at which the two 2-period fixed points become unstable (ie. the bifurcation point for 2-period fixed points). 1. Consider the discrete model for price pn of a certain product: pn+1=f(pn)=pn+pnabpnc where a and c are non-negative constants and b1. (a) Interpret this model in terms of price-dependent demand and supply of the product and describe each term and parameter in the model. For the rest of the problems, assume a=9 and b=21. (b) Find the 1-period fixed point(s) and determine the values of c for which the fixed point(s) are stable. (c) The 2-period fixed points are obtained by solving the equation p=g(p)=f(f(p)). Solve equation (1) using the fact that the 1-period fixed points also satisfy the 2-period fixed point equation. Show that there are two 2-period fixed points if c>6. (d) Using the chain rule show that the two 2-period fixed points become unstable at the same value of c which satisfies the equation, (dpdfp=p1)(dpdfp=p2)=1 where p1 and p2 denote the 2-period fixed points. (e) Using equation 3 find the value of c at which the two 2-period fixed points become unstable (ie. the bifurcation point for 2-period fixed points)