I was catching up on some old Planet Money episodes and caught Allen Sanderson of the University of Chicago talking about how to allocate scarce resources. The first day of introductory economics, he says, there are always more students than seats. Say there are forty extra people, and he can only accept ten more into the class. He asks the class: how should the ten slots be allocated? You can easily guess the typical suggestions: by seniority, because seniors won’t be able to take the class later; by merit (e.g., GPA), because better students will contribute more to the class and get more out of it; to the first ten people outside his office at 8 am the next day, since that is a proxy for desire to get in; randomly, since that’s fair; and so on. Someone also invariably suggests auctioning off the slots.
This, Sanderson says, illustrates the core tradeoff of economics: fairness and efficiency. If you auction off the slots, they will go to the people to whom they are worth the most, which is best for the economy as a whole.* If we assume that taking the class will increase your lifetime productivity and therefore your lifetime earnings by some amount, then you should be willing to pay up to the present value of that increase in order to get into the class. An auction therefore ensures that the slots will go to the people whose productivity will go up the most. But of course, this isn’t necessarily fair, especially when you consider that the people who will get the most out of a marginal chunk of education are often the people who have the most already.
But I think the picture is still a bit more complicated. Even if we assume for a moment that allocative efficiency is the only thing we care about, it’s far from clear than an auction will give it to us. If people could (a) predict their increased productivity from taking the class, (b) predict their increased lifetime earnings, (c) discount those earnings to the present (which implies knowing the proper discount rate), and (d) borrow up to that amount of money at the risk-free rate, then, yes, everything would work out OK. But this is clearly not the case, since then people would be bidding thousands if not tens of thousands of dollars to get into the class.
Still, you might say that people’s willingness to pay for the class — even if it’s just that one person is willing to pay $60 and another is only willing to pay $5 — is a valid proxy for the value of the class to them. So instead of thinking in terms of lifetime productivity, we’re thinking of the class as a short-term consumption good, and it would provide $60 of utility to one person and $5 of utility to the other. (Note that we’ve given up the idea of maximizing the ultimately economic impact of the class.) But then we have to ask whether money is a valid proxy for utility, and at this point the chain of reasoning breaks down. My willingness to pay for various goods might reflect their relative utility to me, but saying that different people’s willingness to pay for the same good reflects the relative utility of that good to those people is a much greater leap. Most obviously, a rich person will be willing to pay more for some goods than a poor person, even if those goods would provide more utility to the poor person. Assume for example that the rich person has a wool overcoat, the poor person has no overcoat, and the good in question is a cashmere overcoat.
Discreteland and Continuousland
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