John Taylor of Stanford University proposed the following monetary policy rule: R -7 = m(TI, - TT) + ny. . That is, Taylor suggests that monetary policy should change the real interest rate not only when inflation exceeds the target, but also when output exceeds potential. The IS curve is described by y. = a - b (R, -7 ), and the Phillips curve by 1 = T _ 1 + VY, + . Answer the following questions. i. Derive the AD curve. Show your work. ii. How is the AD when the Federal Reserve does not respond to inflation (m = () different from when it does? iii. How does the output gap respond to demand shocks, , when the Federal Reserve reacts to inflation relative to when it does not (m = 0)? iv . How does the output gap respond to inflation shocks, , when the Federal Reserve reacts to inflation relative to when it does not (m = 0)? V. Derive expressions for the equilibrium output gap and inflation in the AD-AS framework. In other words, find an expression for the output gap and inflation that depend only on the parameters of the model. Hint: The equilibrium of the AD-AS framework occurs at the points where the AD intersects the AS. Solving the equilibrium is equivalent to solving a system of 2 equations (AD and AS) in two unknowns (output gap and current inflation)