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Say that the local lottery system has decided to innovate. Lottery tickets can now be used as money. A ticket with a face value of $x can be used to buy $x worth of stuff at any checkout counter in the country. Or they can be held in digital form and transferred instantaneously across the lottery's new payments system to friends, the utility company, or the government tax department.

With the payments infrastructure in place, will people actually use lottery tickets to pay their bills, transact with friends, or settle their taxes? Can lottery tickets become money-like?

I'm skeptical. Here's my thinking. Say that Jane has just bought $10 worth of digital lottery tickets. At the same time she's chosen to leave $10 in her bank account (she likes the fact that they aren't risky). She spies a coffee stand and suddenly has an urge to buy a $2 coffee. When she arrives at the till, how will she decide to pay? With lottery tickets or deposits?

By paying for the $2 coffee with a bit of both—$1 in lottery tickets and $1 worth of bank deposits—she could end up with $9 of each, re-attaining her pre-coffee 50/50 allocation. But let's assume that every transaction is a bit costly to make, both in terms of time to completion and the small fixed fee associated with each payments network. So paying with both will be too expensive. She'll have to choose one or the other.

A lottery ticket is more than just a bet. Jane is investing in a fantasy in which she is fabulously rich. So from Jane's perspective, swapping her lottery ticket for a mere cup of coffee would be silly. Once she owns it, her ticket is worth more than hundreds of cups of coffee. A form of Gresham's law kicks in. Given that the coffee seller accepts both lottery tickets and deposits at their face value, Jane will only spend her deposits, which she perceives as being overvalued, while hoarding the lottery ticket, which she thinks are being undervalued by the coffee seller. If every lottery player is like Jane, than 'undervalued' lottery tickets will never circulate as money.

Jane could of course consider buying the coffee with lottery tickets only to purchase replacement tickets in time for the draw. But there's always a risk that she'll forget, or not have enough time because something unforeseen suddenly intervenes. By paying with a boring deposit, she doesn't have to fear missing out on a jackpot.

If it seems unlikely that Jane will want to purchase the coffee with a lottery ticket, what about Jim, who owns the coffee stand? Would he prefer to receive lottery tickets or bank deposits?

Again, a mix of the two instruments would be costly for him to accept given a doubling up of payments processing fees. In the unlikely event that Jim is also a lottery player and hasn't yet bought his tickets yet, then he may prefer that Jane buys a coffee with lottery tickets.

Consider that Jim has a constant stream of business expenses ahead of him, but rarely knows precisely when he'll have to make a purchase. Because the lottery tickets will most likely expire worthless in the future, they don't provide him with a suitable means of solving for his future uncertainty. Deposits, on the other hand, will always retain their value. As long as he keeps them on hand, he knows that he can meet his bills. So I think that Jim will probably prefer that Jane pays with deposits. (See more here).

In the unlikely event that Jane insists on paying with lottery tickets, Jim will probably acquiesce—the customer is always right. Since he doesn't want to be exposed to the uncertainty of lottery tickets, he will probably try to exchange them as quickly as possible for deposits, but this will be subject to a conversion fee. Anticipating this expense, Jim could very well decide at the outset to incentivize Jane to pay with deposits. He might place a small surcharge on lottery ticket payments, or offer a small discount if customers pay with deposits. Jim might even pretend that his lottery payments terminal is broken.

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The combination of Jane's reticence to pay with lottery tickets, a form of Gresham's law, and Jim's preference to avoid them will doom lottery tickets as money. Even though the infrastructure is in place for lottery tickets to be transported instantaneously from one person to the other, the incentives just aren't present. Investing in the infrastructure turned out to be a waste of money.

I think this setup also explains why bitcoin has never been adopted as a form of money. Like Jane's lottery ticket, a bitcoin owner's bitcoins aren't just bitcoins, they are a dream, a lambo, a ticket out of drudgery. Spending them at a retailer at mere market value would be a waste given their 'destiny' is to hit the moon. Sure, a bitcoiner can always spend a few precious bitcoins on a coffee, only to replenish his stock later in the day. But this would be dangerous, since bitcoin's price could spike at any moment. Far safer to spend one's deposits and hoard one's bitcoins.

Even when they claim to be accepting bitcoins, retailers like Jim actually rely on intermediaries like BitPay to step in and purchase the bitcoins while relaying dollars to the retailer. For instance, see last month's post on Ohio tax payments.

I also wonder how well my story fits with other examples of volatile media being used as money. For instance, John Cochrane has blogged about a world where one might trade an "S&P500 index share for a candy bar." If lottery ticket buyers and bitcoin owners are consuming a dream, then perhaps an  owner of an equity ETF is doing the same. In which case, no one would bother buying candy bars with stocks, and so building out the payments infrastructure necessary to facilitate this would be pointless.

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