Suppose that right now the AE schedule is:

Y=5000 - 200r (where r is the real rate stated in percentage terms). Both expected and actual inflation are zero. Potential output (Y*) is 4200.

1. What r must the Fed bring about in order to make output equal to potential output?
2. If spending collapses and AE becomes Y= 4000 -200r, what is the new natural rate? Can the Fed offset the spending shock and keep Y = Y*? How? If they cannot, why not?
3. If the Fed does the best they can do following the spending shock, what will the level of Y be?
4. Suppose that the Phillips curve implies that a fall in output of 200 below potential output causes inflation to fall by 1 percentage point below what it was expected to be, and that inflation expectations are adaptive. Next period, given that the Fed does the best it can do, what will the level of Y be? Why?