# Monetary policy reaction function

The monetary policy reaction function (MPRF) is the upward-sloping relationship between the inflation rate and the unemployment rate. When the inflation rate rises, a central bank wishing to fight inflation will raise interest rates to reduce output and thus increase the unemployment rate.

The MPRF is a function of the Taylor rule, the IS curve, and Okun's law.[citation needed]

The MPRF has the equation:

$u = u_{0} + \Phi(\pi - \pi_{t})$

Where $\Phi$ is a parameter that tells us how much unemployment rises when the central bank raises the real interest rate $r$ because it thinks that inflation is too high and needs to be reduced.

The Slope of the MPRF is: $\frac{1}{\Phi}$

The MPRF is used hand in hand with the Phillips Curve to determine the effects of economic policy. This framework illustrates equilibrium levels of the unemployment rate and the inflation rate in a sticky-price model.

## Alternative

Alternatively, in Ben Bernanke and Robert H. Frank's Principles of Economics textbook, the MPRF is a model of the Fed's interest rate behavior. In its most simple form, the MPRF is an upward-sloping relationship between the real interest rate and the inflation rate. The following is an example of an MPRF from the third edition of the textbook[full citation needed]:

r = r* + g(π - π*)

r = target real interest rate (or actual real interest rate)
r* = long-run target for the real interest rate
g = constant term (or the slope of the MPRF)
π = actual inflation rate
π* = long-run target for the inflation rate

Of course, the MPRF above is just one example, and there are other examples (such as the Taylor rule) that are more complex.