The Effect of New Jersey Lottery Promotions on Consumer Demand and State Profits

We estimate elasticities of demand for New Jersey’s Pick 3 and Pick 4 midday/evening numbers games by exploiting random price variation generated by episodic promotions for each game. These Pick 3 Green Ball and Pick 4 Red Ball promotions lower the price of a lottery ticket for an evening numbers game by increasing prize payments during the 28-day promotion periods. The own-price elasticities of demand for the evening Pick 3 and Pick 4 games are both approximately –0.5. During the promotions, the loss in profit margins outweighs the gain in sales because of this inelastic demand. However, the combined effects of lower evening Pick 3 profits and increased sales of complementary products boost lottery profits by $30,000 per day, or $840,000 during the 28 days of the Green Ball promotion, while the combined effects of lower evening Pick 4 profits and reduced sales of substitute products decrease lottery profits by $129,000 per day, or $3.61 million during the 28 days of the Red Ball promotion. If higher sales after the promotion are included, the total increase in profits potentially reaches $14.48 million under the Green Ball game, while the Red Ball promotion loses money for the lottery even considering its positive lagged effect.