We develop an approach for estimating individual level preferences for a large set of quality differentiated goods and for constructing Hicksian welfare measures for price and quality changes within a demand system framework. Our approach uses a simulated maximum likelihood estimation procedure for recovering estimates of the structural parameters and an adaptive Metropolis-Hastings algorithm for constructing Hicksian consumer surplus estimates. We illustrate our approach with a recreation data set consisting of day trips to 62 Mid-Atlantic beaches.