Rational inattention, multi-product firms and the neutrality of money

In a model where firms set prices under rational inattention we allow them to produce multiple goods. In addition to monetary shocks and firm-specific shocks, good-specific shocks affect firms, consistent with micro price data. When per-good expected losses in profits from inattention are held constant, monetary non-neutrality quickly vanishes as the number of goods per firm rises. This result is due to (1) economies of scope that arise naturally in the multi-product setting, where processing information is costly but using already internalized information is free, and (2) good-specific shocks.