Individual participant data meta‐analysis is a frequently used method to combine and contrast data from multiple independent studies. Bayesian hierarchical models are increasingly used to appropriately take into account potential heterogeneity between studies. In this paper, we propose a Bayesian hierarchical model for individual participant data generated from the Cigarette Purchase Task (CPT). Data from the CPT details how demand for cigarettes varies as a function of price, which is usually described as an exponential demand curve. As opposed to the conventional random‐effects meta‐analysis methods, Bayesian hierarchical models are able to estimate both the study‐specific and population‐level parameters simultaneously without relying on the normality assumptions. We applied the proposed model to a meta‐analysis with baseline CPT data from six studies and compared the results from the proposed model and a two‐step conventional random‐effects meta‐analysis approach. We conducted extensive simulation studies to investigate the performance of the proposed approach and discussed the benefits of using the Bayesian hierarchical model for individual participant data meta‐analysis of demand curves.