Monetary policy as an optimal control problem

This paper analyses the monetary policy of a central bank in a simple deterministic and continuous dynamic non-linear New-Keynesian model with an active central bank conducting monetary policy within inflation targeting framework. To meet this purpose, first we derive two differential equations capturing the dynamics in the economy: the dynamic IS curve representing the commodity market and the Phillips curve capturing the connection between the real and nominal sectors of the economy in a continuous form. By introducing a quadratic loss function commonly used in New Keynesian Economics we get optimal control problem which solution will be analysed with the use of fuzzy control. Then we introduce a modified form of the Taylor rule and analyse the solution of the same differential equations capturing the dynamics of the economy using Taylor rule instead of loss function. The comparison of the solutions of both models will be demonstrated in examples in which the main characteristic of dynamics of production and inflation are displayed.