Suppose that the demand at timetfor an agricultural product isDt=abPt;

wherePtis the price andP0>0is given. The supply at timetisSt=cPt-1;

because the producer bases his supply on the price of the product one year before. Assume all constantsa; b;andcto be positive.

1. (a)(5 marks) Derive the difference equation about price based on the equilibrium condi- tionDt=St.
2. (b)(7 marks) Solve forPtfrom the dierence equation derived in part (a).
3. (c)(3 marks) What will happen to the equilibrium price in the long run ifc < b?That is, limPt=?t tends to infinity