Fill in the missing mathematical steps in the derivation of the optimal government expenditure rule shown in lecture 22 (i.e., beginning with the equations on slide 7, derive the equations on slide 8).

Fiscal Policy: Fiscal Policy Rules So we now have an IS curve yt+1 = YP(1-mpc ) 1 Gt - Gt) the Phillips curve "t+ 1 = Tit + Vyt+1 and the loss function L = y+ + BT?. Lecture 22 - Fiscal Policy II: R. J. Hawkins Econ 100B: Macroeconomics 7/ 26Fiscal Policy: Fiscal Policy Rules Minimizing the loss function with respect to )7} as before we have the same optimal path Vt 2\" _67%t and the optimal expenditure rule a EtMlt'l' Lecture 22 7 Fiscal Policy II: R. J. Hawkins Econ 1008: Macroeconomics