Date published: 2008/02/11
The BBC often runs stories which are basically just advertising for its own programs. Along this line, Garth Sundem says, apparently in relation to an upcoming Horizon program on BBC2:
Should you invest £2 a day or use it to buy lottery tickets?
Maths makes the decision obvious. Suppose you invest two quid every day at the reasonable rate of 10%. It will take you almost exactly 50 years to accumulate £1m. To earn this same £1m in the National Lottery, you would (on average) have to match five numbers and a bonus ball, at odds of 2,330,635-to-1.
If you spent two quid a day for 50 years you would total just over 36,500 tickets and would thus have only a 1-in-63 chance of making that million pounds. However, the available image of immediate wealth subverts this rationality.
Sundem might know his simple maths (and this is very simple maths). But he fails miserably as an economist. First of all, he must be a pretty rich person if he thinks that an average punter investing 2 pounds a day will earn a rate of 10%. And anyone rich enough to earn a rate of 10% on their investments is probably a higher rate taxpayer, so the interest would be charged tax at 40%, and the net rate would thus be 6%.
And Sundem completely ignores inflation. A million pounds in 50 years does not have the same value as a million pounds today. If the inflation rate was 2.8% then a million pounds in 50 years is worth around 250 thousand pounds today. Of course there is also an inflation rate associated with the lottery, but if you were one of the 1-in-63 theoretical people who won the lottery then you would on average have done so after 25 years, which means the million pounds would be worth around 500 thousand pounds today.
And Sundem completely ignores the discount factor. Everybody would rather have a million pounds today than a million pounds tomorrow (even adjusting for inflation).
Of course, no matter how you look at it, the "return" on the National Lottery is poor (since less than half the ticket revenue ends up being handed out in prizes). It's just that Sundem makes a very poor argument out of a trivial fact.
The fact that the "return" is poor does not mean that it is crazy for people to play the lottery. For ordinary people, it is the only chance they will ever have of being rich. For many people, that near negligible chance is worth a small weekly loss.
Horizon is not a very good "science" program these days.
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