The Taylor Principle says that monetary policy ought to respond more than proportionately toincreases in inflation. The New-Keynesian model describes an economy where expectations of the future influence the current state. Consider the following simplified 3-equation model plus theFisherequation:

=

=+1++

= + + +

= +1

Notice how we dropped the expected output gap from the IS curve (to reduce thedimensionality of the problem) and in Phillips Curve, future inflation has a one-to-one impact oncurrent inflation. We also simplified the central bank reaction function by restricting the rule to onlyrespondtodeviationsof inflation fromtarget inflation. Furthermore,tosimplifythe math/notation,assumethatand =0.

1. Show that inflation is explosive if< 1. Can you provide an economic intuition why this isso?
   1. SubstitutetheFisherequationintheMonetarypolicyrule
   2. Plug in the monetary policy rule into the IS equation to generate the AggregateDemandequation.
   3. Introduce the aggregate demand equation into the Aggregate Supply one and solvefor current period inflation. Analyze whether current inflation will converge ordiverge fordifferentparametervaluesofasexpectedfutureinflationchanges.

2. Without engaging in complicated derivations, provide an intuitive response about what youexpecthappens toeconomicactivityandinflationwhenthereisapositiveshock

("bottleneckseverywhere"asmanyanalystsdubbedtheincrease ininflation).