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From its inception, demand estimation has faced the problem of "many prices." This paper provides estimators of average demand and associated bounds on exact consumer surplus when there are many prices in cross-section or panel data. For cross-section data we provide a debiased machine learner of consumer surplus bounds that allows for general heterogeneity and solves the "zeros problem" of demand. For panel data we provide bias corrected, ridge regularized estimators of average coefficients and consumer surplus bounds. In scanner data we find smaller panel elasticities than cross-section and that soda price increases are regressive.