Chocolate and Gold Coins

Sunday, February 20, 2005

Lottery Technology

I was reading a post by Prof. Richard Posner on the Becker-Posner blog when I came to the following paragraph:

Young people find it strange that such a large fraction of overall medical expenses is incurred in the last few months of life—that is, by people who are dying. (Last-year-of-life medical care accounts for 26 percent of Medicare expenditures and 22 percent of all medical expenditures. PubMed. ) Having nothing to look forward to, why are they willing to spend so much on a meager extension of life?

The link in the above quote shows that medical expenses in 1996 for the last year of life averaged $37,500. When I saw this, I was shocked for a moment. Was this a non-convexity? ... Lottery technology? I gasped at the implications.

Minnesota economics

If the reference to lottery technology means nothing to you, then you are an ordinary human being. Even most economists have never heard of the term. However, the people associated with the University of Minnesota Department of Economics in the 1990’s would instantly know what my reference was.

During the 1990’s in Minnesota, the Deparment of Economics was dominated by the theories of Prof. Edward Prescott, who won the Nobel Prize in economics just last year. Prof. Prescott was famous for real business cycles, and for furthering the theory on rational expectations and dynamic general equilibrium. But he had other pet ideas as well. One of them was the lottery technology. Like many ideas of brilliant academics, it was an idea that was both brilliant and daft at the same time. It was brilliant because it nicely transformed a nasty economic model into a nice one in which a bunch of theorems would apply. It was daft because a lottery in the way that Prof. Prescott envisioned it would be nothing you would ever see in a real marketplace (a small detail in the world of economic theory). I'm not saying that Prof. Prescott is daft; I'm saying that the idea of a lottery technology is academic. But I always wondered if someone could find a practical application for this idea.

What is a lottery technology? It is a coin-flip. It is a device that can produce a random number. The lottery technology enables us to take chances. However, we would not use it for entertainment, we would use it to solve a fundamental economic problem. An example will illustrate the idea.

Mrs. Kenny’s trip to Europe

Suppose in the near future, end of life medical expenses grows to $100,000 in today’s dollars. Medicine finds many new futile ways of extending life a few agonizing weeks. Then much of the elderly’s wealth will be tied up in the last few weeks of life. Some people might think that they would rather have the $100,000 in cash and then die a quick painless death. However, if you die, what good would the money do you?

Mrs. Kenny is in her 80’s and does not expect to live more than 5 extra years. She can still walk around, but her strength is beginning to fade. She would dearly love to take a trip to Europe with a senior tour group, but she fears that if she does not go soon, it will be too late. The trip to Europe will cost $10,000 and she does not have that money.

Luckily for Mrs. Kenny, the Libertarians have swept into government and have completely deregulated the FDA. Now all drugs are legal including the new little black pill: the lottery pill. In fact, Medicare and Social Security will pay her to take the little black pill. Medicare and Social Security owe Mrs. Kenny approximately $200,000 in future benefits, including $100,000 in last-year-of-life benefits. They are willing to give her some of that now, if she would just take the little black pill.

Mrs. Kenny orders the pill. She has to take it at the Medicare office, in view of witnesses. They give her the pill. She looks a the small round black pill with the number “0.05” on it. Ninety-five times out of a hundred, this pill just has sugar in it. In that case, she will receive $10,000, enough to pay for the trip to Europe she dreams of. But that other five times out of a hundred greatly troubles Mrs. Kenny. She trembles as she places the pill in her mouth. “Is it worth it?” she wonders. She takes the pill and drinks some water. Her heart pounds. She begins to feel faint. “It’s happening. Oh, no, now I will never know who will be the next American Idol.” She closes her eyes for what will surely be the last time.

Then, miraculously, her eyes open. She takes a deep breath of relief. “I won! I won the lottery! I’m going to Europe!”


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