The Great Recession led to a large reduction in investment. Explain mathematically why this corresponds to a negative aggregate demand shock in the IS-model. The Federal Reserve (Fed) responded to the Great Recession by reducing the federal funds rate (that is, the nominal interest rate determined by the Fed). Use the three parts of the short-run model (that is, the IS-curve, the MP-curve, and the Phillips curve (PC)) to explain what would happen to short-run output, the real interest rate, and the change in the inflation rate according to economic theory. Explain this mathematically (that is, by using the equations for the IS-curve, MP-curve, and PC-curve) and graphically (that is, by drawing the IS-MP diagram and the PC-diagram and showing how the investment shock will lead to movements and/or shifts in these curves).