Question 8

Consider a competitive market in which price adjusts to excess demand or supply and rms enter and exit the industry if profits or losses are being made. Price adjusts to excess demand according to dp _ D 3 dt 0.501 q ) Where (1\" = 30 2p is the demand function, (15 = 2N is the supply function, p is price, N is the number of firms in the industry and a is the speed of adjustment coefficient. The number of rms adjust according to dN _ 5 ( 10) (it _ 4 p (i) Derive the linear second-order differential equation implied by this model. (ii) Solve the second-order differential equation. [iii] Derive a system of differential equation to represent this information. [iv] Solve the system