Question: An item is initially sold at a price of $p per unit. Over time, market forces push the price toward the equilibrium price, $p∗, at which supply balances demand. The Evans Price Adjustment model says that the rate of change in the market price, $p, is proportional to the difference between the market price and the equilibrium price.
(a) Write a differential equation for p as a function of t.
(b) Solve for p.
(c) Sketch solutions for various different initial prices, both above and below the equilibrium price.
(d) What happens to p as t → ∞?