Modeling box office revenues of motion pictures^✰

Weekly box office revenues for motion pictures show a pattern where peak revenues often appear in the first week, and then new revenues slowly die out. This paper proposes a simple model to describe such box office revenues. The new model assumes that there are two types of adopters, with the first being the moviegoers who are aroused to go to a movie based on intrinsic motivation, possibly aroused by trailers, advertising and social media content, and a second type of moviegoers who enjoy shared consumption. A second key feature of the simple model, which involves basic logistic diffusion patterns, is that the first type starts adopting already before the launch of a movie, but can only go a movie when it is launched, while the second type starts to adopt right from the launch onwards. The sum of the two S-shaped diffusion processes only gets observed from the launch of a movie onwards. Parameter estimation turns out to be easy as is illustrated for forty top lifetime grosses (as per 2020) for the USA.