  Suppliers of differentiated goods make simultaneous pricing decisions, which
are strategically linked. Because of market power, the equilibrium is
inefficient. We study how a policymaker should target a budget-balanced
tax-and-subsidy policy to increase welfare. A key tool is a certain basis for
the goods space, determined by the network of interactions among suppliers. It
consists of eigenbundles -- orthogonal in the sense that a tax on any
eigenbundle passes through only to its own price -- with pass-through
coefficients determined by associated eigenvalues. Our basis permits a simple
characterization of optimal interventions. A planner maximizing consumer
surplus should tax eigenbundles with low pass-through and subsidize ones with
high pass-through. The Pigouvian leverage of the system -- the gain in consumer
surplus achievable by an optimal tax scheme -- depends only on the dispersion
of the eigenvalues of the matrix of strategic interactions. We interpret these
results in terms of the network structure of the market.
