Effects of monetary shocks on the distribution of prices

We develop a model economy in which the distribution of prices exhibits two forms of temporary monetary non-neutrality. Monetary shocks produce an increase in the dispersion of prices and some prices change in the `wrong' direction: positive monetary shocks produce a decrease in some prices. These features are derived in a framework in which all firms exhibit optimizing behavior, charge market-clearing price, and do not suffer from money illusion. Our model is built on the standard model of monopolistic competition in the market for intermediate goods (Dixit & Stiglitz 1977). Firms are related to each other through a production network in which each firm buys inputs and sells output to a subset of firms (Gualdi & Mandel 2015). Each firm minimizes cost to determine the proportions in which to buy inputs from its suppliers. A representative household buys goods and sells labor. Once the model economy converges to a steady state, we study how the distribution of prices responds to monetary shocks.  A monetary shock occurs through a change in the nominal wealth of a subset of firms. Firms change prices sequentially as the shock propagates through the economy via demand and supply relations of the production network. In the short run, price dispersion increases because different firms change prices at different rates and at different times. In the long run, price dispersion returns to the pre-shock level as all firms change prices equiproportionally to the change in the economy's stock of money.  Some prices temporarily change in the `wrong' direction because some firms experience a negative demand shock as a consequence of a positive monetary shock to the economy.  The reason for why a monetary shock can produce demand shocks of the opposite sign has to do with the how of money in the production network. After a positive monetary shock, prices change sequentially as new money flows through the production network. Some firms are hurt because their input prices rise before their output price. These firms lower demand for inputs, their suppliers experience a negative demand shock and consequently decrease prices. An injection of money in a subset of firms can lead to a temporary decrease of prices in another subset of firms because of the network of relations between the two sets of firms.