This paper reviews prior research by agricultural economists on the demand for food products using scanner data. Thereafter, a differentiated product's oligopoly model with Bertrand price competition is developed and used to specify brand level demand and oligopoly price reaction equations. The model has sufficient detail to estimate brand level price elasticities and price response elasticities which in turn can be used to estimate three indices of market power. The first index estimated is the familiar Rothschild Index. The paper develops estimates two new indexes, the observed index and the Chamberlin quotient for tacit collusion. It concludes with comments on how the proposed method for the measurement of market power in a differentiated oligopoly can be improved.