Title: Taxes and Market Power: A Principal Components Approach
Abstract:
Suppliers of differentiated goods strategically make simultaneous pricing decisions. We analyze which cost changes (e.g., shocks to commodity prices) are most amplified by strategic behavior. We also investigate the policy question of designing welfare-improving deliberate cost changes—marginal taxes and subsidies. A key tool simplifying the problem is a certain ordered basis for the goods space, determined by the network of interactions among suppliers. Costs and prices are decomposed into principal components, which can be thought of as independent fictitious goods. Volatility analysis is very simple in this basis. The ordered basis also permits a simple cutoff characterization of optimal tax-and-subsidy interventions, which subsidizes the first principal components and taxes the last ones. The gain in welfare achievable by an optimal tax scheme is increasing in a measure of the intensity of strategic interactions. The results permit us to leverage the theory of spectral approximation to design optimal interventions even when the demand system is observed with considerable noise.