Consider the following problem, based on a simplified version of Poole (1970), (William Poole, 1970. Optimal choice of monetary policy instruments in a simple stochastic macro model, Quarterly Journal of Economics 84, 197-216): Yt = Yo air+u (1) my = mg+ by, ciy + vy (2) where u; and v, are independent random variables (i.e., Cov(u,v) = 0), with zero mean and variances, o2 and o2, respectively. yo and mg are constant terms in these two equations respectively. Assume that the central bank wants to minimize the loss function, L= B(w). 3) 1. Explain these equations [6 marks]; 2. Find analytically the minimum loss obtainable under an interest rate tar- geting regime [22 marks]; 3. Find analytically the minimum loss obtainable under a monetary targeting regime [22 marks|; 4. Using your results in 2 and 3 above, discuss how the choice of the optimal policy instrument depends on the nature of the shocks, and discuss the policy implications of these results. [50 marks]