(36 pts) Consider a stochastic version of the traditional cobweb model. The model was orig inally developed to explain the volatility in agricultural prices, let the market for a product. dt=Gz')'Pt S=b+p:+ (1) St=dt (a) (4 pts) Please explain the meaning of each equation in the model? What is sign of 7 and ,8? Why? How do you assume pf? What is meaning of your assumption for p; in this model. (b) (4 pts) What is price and quantity of the agricultural product in the longrum equilib- rium. (c) (4 pts) Please draw a graph to show how does some point converge to the long-run equilibrium point and explain it. What is the condition of converge in the model? (d) (4 pts) Please derive the stability condition in the model. (e) (4 pts) What is the homogenous equation of Pt? Please nd a homogenous solution of the equation of p; and show the details. (f) What is the particular solution of pt ? How do you nd it? (Show the process). (g) (8 pts) Following the procedure, how do you nd the genneral solution for 3):. Assume that 10;) is known. (h) (4 pts) If assume that all shocks are zero in each period and p0 = (a b) / (7 + ,8), what is 3),? If pg is the initial price of the model, how does the model work in the system? (i) (4 pts) What is impact multiplier, one-period multiplier and impact response function in the model? If gap between the periods of the shock and price increases, how does impact response function change? Why do we need th econdition of converge in this model for the impact response function