Aggregate Demand, Inflation and monetary policy reaction function

Aggregate Demand and Inflation:

Previously we combined the IS curve with this Taylor rule for setting monetary policy and produced an aggregate demand function that showed how real GDP depended on the inflation rate. This MPRF (monetary policy reaction function) was:

Y = Yo - Φ x (Π - Π')

Nevertheless we would prefer an aggregate demand equation with the unemployment rate on the left-hand side therefore we can use it along with the Phillips curve. Therefore we use Okun’s law to replace real GDP by the unemployment rate on the left-hand side:

u = uo + Φ x (Π - Π')

where the parameter Φ is the product of three varied things:

•    How much the central bank elevates the real interest rate in response to a rise in inflation
•    The slope of the IS curve—how greatly real GDP changes in response to a change in the real interest rate.
•    And the Okun’s law coefficient—how big a change in unemployment is produced by a change in real GDP.

Mutually this unemployment form of the aggregate demand relationship and the Phillips curve equation:

Π = Πe - β (u - u*) + εs

Permit us to determine what the inflation and unemployment rates will be in the economy. (As well as when we have determined the unemployment rate Okun’s law allows us to immediately calculate real GDP as well.) Once more the economy’s equilibrium is where the curves cross: the Phillips curve concludes inflation as a function of the unemployment rate, the monetary policy reaction function [MPRF] determines the unemployment rate as a function of the inflation rate and the two must be consistent.

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