Monetary policy analysis in a new keynesian model

The present paper is an initiation to research, in which the aim is to learn about the basic methodologies for the business cycle and monetary policy analysis in a dynamic macroeconomic model. First, the equations of a New Keynesian (sticky-price) model are presented, based on the rational behavior of households, firms and the Central Bank. All the equations undergo a log-linearization process, allowing to solve and simulate the initially nonlinear model through Matlab and Dynare. Once the model is solved, the effects of three different shocks to technology, household preferences and inflation are examined by displaying the corresponding impulse-response functions. The work ends with a proposal for an optimal monetary policy for the Central Bank and a comparative analysis of its economic consequences. The criterion of optimality chosen is that of maximizing household welfare.