Decreasing block rate pricing is a nonlinear price system often used for public utility
services. Residential gas services in Japan and the United Kingdom are provided under
this price schedule. The discrete/continuous choice approach is used to analyze the demand under decreasing block rate pricing. However, the nonlinearity problem, which
has not been examined in previous studies, arises because a consumer’s budget set (a
set of affordable consumption amounts) is nonconvex and, hence, the resulting model
includes highly nonlinear functions. To address this problem, we propose a feasible,
efficient method of demand estimation on the nonconvex budget. The advantages of
our method are as follows: (i) the construction of an 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 on the nonconvex budget set. The proposed method is applied to estimate the Japanese residential gas demand function and evaluate the effect of price schedule changes as a policy experiment.
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