Exercise III (15 + 5 = 20 points) Let S(p) denote the number of units of a particular commodity supplied to the market at a price of p dollars per unit, and D(p) denote the corresponding number of units demanded by the market at the same price. In static circumstances, market equilibrium occurs at the price where demand equals supply (as seen in this class and in MFE I). However, certain economic models consider a more dynamic kind of economy in which price, supply, and demand are assumed to vary with time. One of these models is known as the Evans price adjustment model I which assumes that the rate of change of price with respect to time t is proportional to the shortage D - 8, so that we have the relation below (where k > 0 is constant): dp _ k(D - S) Suppose the price p(t) of an item varies as described above, where D(p) = 7 -3p and S(p) = 2 + p. 1. If the price is $4 when t =0 and $2 when { = 3, find p(t). 2. Find and interpret the meaning of lim p(t) in this context