Discuss the below:
Q: The Evans Price Adjustment model is a dynamic model in which price p denote the price of a particular commodity, S(p) and D(p) denote the supply and demand functions of that commodity respectively. These 3 parameters are regarded as function of time t. The time rate of change of price is assumed to be proportional to the shortage D - S, so that
where k is a positive constant.
Suppose the price p(t) of a particular commodity varies in such a way that its rate of change with respect to time is proportional to the shortage D - S, where D(p) and S(p) are the linear demand and supply functions D = 8 - 2p and S = 2 + p.
Problems
a) If the price is $5 when t = 0 and $3 when t = 2, find p(t)
b) Determine what happen to p(t) in the long run ( as t → ∞).