The value of money

[mtbc]

Money is well-known to have a non-linear utility function. For example, from my position I would gladly trade a ⅓ chance of winning $20m for a ⅔ chance of winning $5m. What I have not thought through clearly is the effect on lottery tickets: can it make sense to buy only one ticket or, if it is worth buying any at all, is it likely that buying a few would make even more sense?

On the one hand, if running a lottery is profitable and the utility of money decreases the more I win then that might argue for never buying lottery tickets: the ticket cost is worth too much to me. But, the procedure by which unwon jackpots commonly roll over might make ticket-buying make sense at least for linear utility if the number of tickets purchased does not increase proportionally to the larger jackpot. Can rollovers ever make it rational to buy a bunch of tickets? Perhaps the non-linearity is always enough to scotch even that idea.

Comments

[aldabra]

I did this sum once. If I saved a pound a week, I would be able to buy a house in Cambridge in, I think, 4,000 years. If I bought a lottery ticket a week I would have a non-zero chance of being able to buy a house while I'm still alive.

It's not obvious that the decreasing marginal utility of money is the only game in town, here.