This thesis is separated in two chapters. In the first chapter I develop a multi-sector model with price frictions, production networks, trend inflation and different types of shocks to study how these conditions affect the properties of inflation and their implications for monetary policy. Calibrating the model to the U.S. economy my results show that in this setting inflation becomes 30\% less sensitive to the output-gap compared to a standard one-sector model. Furthermore, in the multi-sector model inflation is affected by sectoral variables linked to between-sector and within-sector price distortions. This fact adds inertia to the inflationary process and makes monetary policy less effective. Additionally, the welfare costs of trend inflation increase by one order of magnitude in the multi-sector model compared to the standard one-sector model. The amplification is quantitatively explained by between-sector rather than within-sector price distortions. This suggests that one-sector models and models without heterogeneity underestimate the costs of long-run inflation and the efficacy of monetary policy to fight inflation. The second chapter is based on a paper jointly written with Francesca Loria. We construct a New Keynesian model with production networks to study how aggregate productivity, measured as the Solow residual, depends on sectoral markups and on the production network itself. The model also allows us to study the dynamic behavior of aggregate productivity facing different types of aggregate and sectoral shocks. The introduction of price stickiness allows us to shed a light on monetary-induced short run productivity changes. We calibrate a 14-sectors economy using the I-O tables from the Bureau of Economic Analysis. For the U.S. economy, aggregate productivity is quite sensitive to average markups. A relatively small average price markup of 15\% over marginal cost can reduce the steady state level of productivity by 25\% relative to a perfect competition case. On the dynamic dimension, we find that a 1\% contractionary monetary policy shock and a 1\% positive markup shocks contract total factor productivity by 3.5\% and 0.1\% respectively on an annual basis. Idiosyncratic shocks can have a large impact on changes in productivity depending on the centrality of the sector in the network.