(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 = a - YPt St = b + Bpt te (1) St = at (a) (4 pts) Please explain the meaning of each equation in the model? What is sign of y and ? Why? How do you assume pt? 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 long-rum 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 p? Please find a homogenous solution of the equation of pt and show the details. (f) What is the particular solution of p ? How do you find it? (Show the process). (g) (8 pts) Following the procedure, how do you find the genneral solution for pt. Assume that po is known. (h) (4 pts) If assume that all shocks are zero in each period and po = (a - b)/(7 + 3), what is pt? If po 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