Do state lotteries exploit their lottery power? Optimal lotto pricing with heterogeneous players: evidence from the United Kingdom

We propose a new model of revenue-maximising lottery pricing under income-related heterogeneity and apply it to 13 years of UK National Lottery data. Our pricing rule shows how a state's lottery power is shaped by heterogeneities in lotto demand and the income distribution, and we study its efficiency and distributional implications. We find that UK lotto was regressive, underpriced by up to 20% for Saturday games and overpriced by up to 20% for Wednesday games. But annual revenue losses reached only 3% (£57m) and legislated pricing was less regressive than optimal on Saturdays and more regressive on Wednesdays. We contrast results from our model with those of two extensions: 1. a dynamic, rollover-induced, model of revenue-maximising pricing and 2. a model of social welfare maximisation with a lotto revenue target.