Let the demand and supply functions for a given commodity be

Qd = a - Bp

Qs = - γ + dp where (α, β, δ, γ > 0) and Qd and Qs are quantity demanded and quantity supplied

(i) Assuming that the market is cleared at every point of time, find the general and definite time path of price P(t) - assume the initial price P(0)=6

(ii) Explain which component of the price path determines the dynamic stability of the price 

(iii) Does this market have a dynamically stable intertemporal equilibrium price? Explain

(iv) What is the market clearing equilibrium price

(v) Given the demand and supply functions, determine the price elasticity of demand and price elasticity of supply at the equilibrium, given that α=10, β=1/2, γ=-2, δ=2 and equilibrium price is 12 and equilibrium quantity is 4.