This paper evaluates how firms change their prices in response to cost shocks and other price changes in their environment. We first document three new facts on the heterogeneity of firm-level producer prices and their relation-ship to buyers and suppliers in a production network. We then develop a non-parametric framework of how producers update their prices, taking into account this production network. The framework is very general, and accounts for the heterogeneity in price changes and the production network from the stylized facts. Moreover, the framework is consistent with various price setting mechanisms, and does not impose a particular market structure or demand func-tional form. Exploiting rich data on producer prices and the network structure of production in Belgium, we estimate the model to evaluate the importance of both channels in the data. We find that, on average, input price pass-through is incomplete and very much below one, while firms also strongly react to other prices in their environment. This implies that firms can adjust their markups in response to both cost shocks and prices of other firms. Furthermore, firms react differently to common shocks than to idiosyncratic shocks, on average completely passing through common shocks, but much less idiosyncratic shocks.