In contrast to single-equation cross-sectional studies of private label share, developing a complete understanding of the nature of the competitive interaction between national brands and private labels requires an understanding of the determinants of both demand and strategic pricing decisions by firms. Consequently, we estimate a simultaneous system of share and price for private labels and national brands. From the empirical results, two measures of market response are derived. The unilateral demand elasticity measures the pure "own" demand response, while the residual (or "total") elasticity also captures the impact of competitive price reaction (Baker and Bresnahan 1985). When taken together, these provide important strategic insights into the pricing interaction between national brands and private labels. In our empirical analysis, we employ a flexible, non-linear demand specification, the Linear Approximate Almost Ideal Demand System (LA/AIDS, Deaton and Muellbauer 1980a), and specify the price reaction equations derived under the LA/AIDS demand specification. Incorporating LA/AIDS demands into a structural equation framework represents an important departure from previous demand specifications in competitive analysis. Using the proposed LA/AIDS framework, we perform a detailed intra-category analysis using data on six individual categories: bread, milk, pasta, instant coffee, butter and margarine. In addition, in an attempt to generalize the results to a broader set of categories and in order to enable us to compare our results to previous cross-section studies, we also estimate using a sample pooled across 125 categories and 59 geographic markets. Consistent with our objectives, we find that consumer response to price and promotion decisions (demand) and the factors influencing firm pricing behavior (supply) jointly determine observed market prices and market shares. Further, estimates of residual demand elasticities suggest that examination of partial demand elasticities alone may provide an incomplete picture of the ability of brands to raise price. Managerial implications, limitations and suggestion for future research are discussed.