Abstract
Suppliers of differentiated goods make simultaneous pricing decisions, which are strategically linked because the goods are substitutes or complements in consumption. We study how changes in producers' costs pass through to two key outcomes: prices and welfare. We consider the positive question of which cost changes (e.g., shocks to commodity prices) are most amplified by strategic behavior. We also investigate the policy question of which marginal taxes and subsidies are best for welfare. A key tool is a certain basis for the goods space, determined by the network of interactions among suppliers. It consists of principal components in the goods space, independent in the sense that a cost change incident on any component passes through to the price only of that component. Pass-through coefficients are determined by associated eigenvalues of a demand matrix and yield an ordering of principal components. The ordered basis permits a simple cutoff characterization of optimal tax-and-subsidy interventions, which subsidizes principal components, with high pass-through, and taxes ones with low pass-through. The gain in welfare achievable by an optimal tax scheme is increasing in a suitable measure of eigenvalue dispersion. The results permit us to leverage the theory of spectral approximation to design optimal interventions even when the demand system is observed with a lot of noise.