This paper estimates a price elasticity using a flexible demand specification on survey data where prices are observed with errors and are correlated with household characteristics. The demand function is modeled as a polynomial/trigonometric in the unobserved true prices, and the form of the dependency between the observed prices and household characteristics is modeled parametrically. I identify and estimate the model by adapting the approach of Hausmann et al. (1991) and Schennach (2004). The flexible specifications allow us to observe that price elasticities vary across the price distribution, something missed in previous work using linear demand specifications.