The discrete/continuous choice approach is often used to analyze the demand for public utility services under block rate pricing, which is a nonlinear price system. Although a consumer's budget set is convex under increasing block rate pricing, a consumer's budget set is nonconvex under decreasing block rate pricing as is the case with the gas supply in Japan and the United Kingdom. The nonlinearity problem, which has not been examined in previous studies, arises under nonconvex budget sets in which the indirect utility function corresponding to the demand function becomes highly nonlinear. To address this problem, this article proposes a feasible, efficient method of demand on the nonconvex budget set and implements a case study using household-level data on Japanese residential gas consumption. The advantages of our method are as follows: (i) the construction of an efficient Markov chain Monte Carlo algorithm with an efficient blanket based on the Hermite-Hadamard integral inequality and the power-mean inequality, (ii) the explicit consideration of the (highly nonlinear) separability condition, which often makes numerical likelihood maximization difficult, and (iii) the introduction of normal disturbance into the discrete/continuous choice model.