Economics

Consider the following problem, based on a simplied 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 Git + 'th (1) mt : mg + by: Cit + \"1% (2) where at and vi are independent random variables (i.e., Cov(u,v) : 0), with zero mean and variances, 0,2, and 03, respectively. yo and me are constant terms in the IS and LM curve respectively. Assume that the central bank wants to minimize the loss function, Lt : E (2%)2- (3) 1. Explain these equations [10 marks]; 2. Find analytically the minimum loss obtainable under an interest rate tar geting regime [25 marks]; 3. Find analytically the minimum loss obtainable under a monetary targeting regime [25 marks]; 4. Using your results in 1 and 2 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. [40 marks]. Particular attention must be given to the theoretical explanation and eco nomic intuition of all your equations and results. Please provide the full deriva- tion of your results, with explanations of all steps taken to arrive at each solu tion. Results Without evidence of their derivation, even if correct, will receive no credit