c) Lastly, let E[P] be given by a current period "rational" expectation of the future price level, i.e., E[P] - Et[piti]. Show that each of pe, Mt, and Ry can be solved for in terms of current and expected future values of the money supply. (5 marks) 3) Consider the following dynamic "rational expectations" model of an ag- gregate economy. yi - Po+ Pitme - Elpstill (1) (2) where up ~ i.id(0, 0;) me - me-1+ 710-1+ 7251-1 + Et (3) where Et ~ i.i.d(0, a?) Equation 1 is a version of a "Lucas Supply" function where current output supply responds positively to a current price that is high relative to expected future prices. Equation 2 is an "aggregate demand" equation where aggregate demand responds positively to a current money supply that is high relative to expected future money (a liquidity effect), but responds negatively to current prices that are high relative to expected future prices. Aggregate demand is also subject to random disturbances or shocks given by 14 in each period t. Lastly, equation 3 specifies the money supply process. Current money supply is equal to the previous periods money supply plus "policy responses" to past demand and monetary shocks (accomodating monetary policy). a) Solve this model for the "rational expectations" equilibrium output and show that in this framework systematic monetary policy variables can have an effect on output and thus that the assumption of rational expectations alone is not sufficient to produce the "policy irrelevance" results discussed in class. (5 marks) b) What policy parameter choices for y and for 2 would minimize the variance of output (stabilization) in this model economy