Choice-based conjoint (CBC) studies started to increasingly rely on concepts from industrial organization such as equilibrium pricing. A driver of this development is the recently prominent role of inference from CBC in lawsuits. While large stake decisions depend on CBC based inference, the economic assumptions implied by standard models may not apply to high-ticket purchases. Despite the prevalence in economic theory, standard CBC models often ignore or insufficiently approximate consumers' budget constraints. We offer a theoretically motivated improvement to the CBC model, especially for high-ticket durable goods, and develop a Bayesian method for the inference of unobserved budget constraints. The proposed MCMC method leverages respondents' stated budget constraints that suffer from measurement error and respondents' financial demographic variables as additional information to reduce the dependency on arbitrary functional form assumptions in the estimation. We show that - by disentangling price-sensitivity within a budget from the budget constraint itself - accounting for unobserved budgets substantially increases model fit and the accuracy of competitive prices in an industry-grade discrete-choice experiment on consumer preferences for high-end laptops.