Compound Markups: A Theory of Price Amplification in Production Networks

This paper introduces compound markups in production networks: the wedge between observed prices and the pure-cost prices that would prevail if all output markups were set to one, holding technology and primary-factor prices fixed. The main contribution is a representation theorem showing that, in a Cobb-Douglas network, compound markups are obtained by applying the Leontief inverse of the intermediate-share matrix to any vector of direct markups measured at market input prices. The paper provides a walk decomposition for upstream attribution, a strongly connected component decomposition that isolates feedback loops, and bounds on amplification and truncation error. Extensions relate the approach to the classic input-output price model and to local results for general unit-cost functions. A short illustration shows how loops raise price-to-resource-cost wedges. The framework enables IO-implementable attribution of final-price wedges to upstream market power and supports applications to cost-of-living measurement, inflation pass-through, and policy incidence.