We develop a tractable model of price dynamics in a general equilibrium economy with cash-in-advance constraints. The dynamics emerge from local interactions between firms that are governed by the production network underlying the economy. We analytically characterise the influence of network structure on the propagation of monetary shocks. In the long run, the model converges to general equilibrium and the quantity theory of money holds. In the short run, monetary shocks propagate upstream via nominal changes in demand and downstream via real changes in supply. Lags in the evolution of supply and demand at the micro level can give rise to arbitrary dynamics of the distribution of prices. Our model provides an explanation of the price puzzle: a temporary rise in the price level in response to monetary contractions. In our setting, the puzzle emerges under two assumptions about downstream firms: they are disproportionally affected by monetary contractions and they account for a sufficiently small share of the wage bill. Empirical evidence supports the two assumptions for the US economy. Our model calibrated to the US economy using a data set of more than fifty thousand firms generates the empirically observed magnitude of the price level rise after monetary contractions.