Demand stochastics, supply adaptation, and the distribution of film earnings

Abstract

A market is analysed in which demand is a stochastic process and supply is contingent on the expected level of demand – a model that provides a realistic depiction of the motion picture market where consumer demand is a process of discovery and information sharing, and the supply of theatre screens expands through contingent contracts to accommodate demand. This model predicts that motion picture earnings will deviate from a power law and instead be distributed according to an exponential of a power law due to finite-size effects in demand. Empirical analysis on a large sample of motion pictures finds significant deviation from the power law distribution and a remarkably good fit for the stretched exponential distribution.

Acknowledgements

I would like to thank Art De Vany for much guidance on the topic of this paper. I acknowledge with gratitude financial support from the Committee on Research and Conference Grants of the University of Hong Kong and the University Research Grants Committee of the University of Calgary.

Notes

 De Vany and Walls (1996) provide a thorough analysis of role of adaptive exhibition contracts in the movie business.

 Sornette (2002) looks at importance of blockbusters when tails follow a power law. Much of the economics literature relating to power laws and deviations from them has been developed in the context of the distribution of firm sizes (Steindl, 1965; Ijiri and Simon, 1971, 1974; Vining, 1976).

 Laherrere and Sornette (1998) show that the stretched exponential distribution accounts for many deviations from power law distributions in physical and social sciences.

 From the relation X _n+1 = X _n x _n+1 the equation for the density function of X _n+1 can be written in terms of the density functions of x _n+1 and X _n and the pdf derived by the formal application of Laplaces’ method. See Frisch and Sornette (1997) for a detailed derivation of the stretched exponential distribution.

 Appreciation is extended to David T. of EDI for his generous assistance in providing the data.

 The empirical result of concave deviation from the power law distribution has been independently verified using different data sets by Walls (1997), Ghosh (2000), and Hand (2001).

 In terms of the level of revenue, the R ² is the squared correlation between fitted revenue and actual revenue.

 These R ² values are all calculated in terms of the level of box-office revenue.