So if the expected return is lower than the actually than the actually stake why do people play? ‘The standard economic framework for analyzing decisions in the face of risk and uncertainty is the expected utility model’2. So this says that the utility gained from undertaking a risky activity can be measured by the expected utility associated with the activity. The fact that outcomes of this random choice or gamble are consumption goods that will be consumed in different circumstances means that only one of those outcomes is going to occur. Which is what the national lottery is, if you’re playing for the jackpot. For simplicity from now on we will look at the 14million to 1 chance of the jackpot. So either you win it big or your £1 down.
Looking at the player’s wealth, using the above assumptions of wealth above, the consumer is only going to be concerned of his wealth in three situations. Your wealth now w, your wealth if you play and lose, w-£1, and your wealth if you win (Which would said would be £7million).
Then the rational consumer looks at the odds calling as the probability of winning, so the utility function looks like u (, 1-, w, w-1, 7million). This would be the assumption of a rational consumer and his or hers preferences. ‘When people are considering a choice between two things the amount of a third thing typically matters’1. The amount of the third thing in this is to any person a great deal of money. But according to a paper on the National lottery ‘2/3rds of the population surveyed said they felt the jackpot was too large and 4/5th's said they thought there should be more smaller prizes. 2’ This contradicts the suggestion made earlier that players play because of the size of the prize or the amount of what the wealth of the player could be, suggesting that the motivation for playing is simply the fun of participating.
Looking at two different consumers a risk-averse consumer and a risk-loving consumer we maybe shed more light on this fact and introduce a different economic explanation.
In fig. 1 you can see that the utility of expected wealth, U E(w), is greater than the expected utility of wealth, E U(w). This means the person would rather not risk his money, using this as well as the odds above suggest a rational consumer would not play the lottery.
In fig. 2 U E(w)<E U(w). So a consumer would rather have a flutter, which sounds like our consumer. This shows that the expected utility model of consumer choice can explain why the consumer plays the lottery if he or she is risk loving. Even if the odds were the same as the possible winnings only a risk-loving consumer would play, or so the theory suggests.
This is unlikely, looking at the utility function, u (, 1-, w, w-1, 7million) and taking note of the very close values of w and w-1, this was the consumers wealth without playing and losing, respectively. These values are very close, so compared to what could be won it is a small initial lose of money can bring a big price, or when you open it up, it can bring in smaller prizes which can increase your wealth.
So why is there this contradiction? Obviously there is an additional benefit of buying the lottery ticket. ‘Players enjoy the opportunity to join in this aspect of popular culture and to discuss with friends and family their choice of numbers. Also one could postulate that players receive a "warm glow" from the knowledge that they have made an donation to charity. 2’ These reasons would defiantly contribute towards why a rational consumer would buy a ticket but would probably not be the most contributing factors to that extra hidden benefit. It may be the change of winning the large jackpot that attracts players to the game even given the very long odds associated with such a win. ‘Some authors describe this motivation as buying a dream2’ i.e. the possibility of winning a "life style changing" amount of money.
An interesting fact is that the wealthier a person is less likely to play as wealthier people have a higher reservation price, so they demand a higher expected return before they will play, this is to do with opportunity cost of there time. Looking at statistics of people who played the lottery, typical lottery participant is male middle-aged married/cohabiting with a low school leaving age. There is an even greater suggestion that people play for fun for a life changing amount of money, going against the statistic that people would like a greater amount of smaller winning tickets i.e. £10 winning tickets.
Bibliography
Odds obtained from,
1 Varian, ch12, Intermediate Microeconomics, version 6.
2 Prof. Stephen Creigh-Tyte, the Economics of the National Lottery.
