Consider an economy where rational expectations hold. Let y, m, and p be the logs of real output, money stock and price level in period t respectively. Suppose that the following relationships hold: yt = mt Pt yt = y'+ B(Pt - Et-1(P:)) + ut mt = m ONE where y' is the level of output under perfect information and flexible wages, B> 0 and ut is a random variable with zero mean and variance ou A. Calculate the reduced forms for p: and y. Interpret the determinants of these reduced forms. Can the monetary authority affect the equilibrium by your results. changing the parameter(s) of the monetary policy? Provide an explanation for [15 marks] Now suppose that the monetary policy takes the following form: m. = m + a(P. P ) where p=my is the level of prices under perfect information and flexible wages and a 1 [0, 1]. B. Calculate the reduced forms for p: and y in this setup. Estimate the value of a the monetary authority could set in order to close the gap between y and y*. Provide intuition for your results. I [15 marks]