November 24, 2011

"They've traded more for cigarettes / than I've managed to express"; or, Dives, Lazarus, and Alice

Attention conservation notice: 1000+ words on the limits of welfare economics, in the form of a thought experiment or parable superficially tuned to the holiday (and brooding on my hard-disk for months). Gloomy, snarky, heavy-handed, academic, and obvious to anyone who knows enough about the subject to care. Have you no friends and family to whom you should be showing your love (perhaps in the form of food)?

Let us consider a simple economy with three individuals. Alice is a restaurateur; she has fed herself, and has just prepared a delicious turkey dinner, at some cost in materials, fuel, and her time.

Dives is a wealthy conceptual artist1, who has eaten and is not hungry, but would like to buy the turkey dinner so he can "feed" it to the transparent machine he has built, and film it being "digested" and eventually excreted2. To achieve this, he is willing and able to spend up to $5000. Dives does not care, at all, about what happens to anyone else; indeed, as an exponent of art for art's sake, he does not even care whether his film will have an audience.

Huddled miserably in a corner of the gate of Dives's condo is Lazarus, who is starving, on the brink of death, but could be kept alive for another day by eating the turkey. The sum total of Lazarus's worldly possession consist of filthy rags, of no value to any one else, and one thin dime. Since, however, he is starving, there is no amount of money which could persuade Lazarus to part with the turkey, should he gain possession of it.

Assume that everyone is a rational agent, with these resources and preferences. What does economics tell us about this situation?

First, whatever Alice has spent preparing the turkey is a sunk cost, and irrelevant to deciding what to do next.

Second, Alice would be better of selling the turkey to either Dives or Lazarus than keeping it for herself, and either trade would also benefit the buyer, so that's a win-win. Either trade would be Pareto-improving. However, neither trade is strictly better for everyone than the other: if she sells to Lazarus, Dives is disappointed, and if she sells to Dives, Lazarus starves. Of course, if we are being exact, Lazarus starves to death whether Alice keeps the turkey or sells it to Dives, so that trade makes Lazarus no worse off.

Third, Lazarus can only offer ten cents. Since Dives would be willing to spend up to $5000, Alice will prefer to sell to Dives. Since Dives, being a rational agent, knows how much Lazarus can pay, he will offer 11 cents, which Alice will accept as the superior offer. (Alternately, we add in a Walrasian auctioneer, and reach this price by tatonnement.) [Update: See below.] The market clears, Alice is 11 cents better off, Dives enjoys a consumer surplus of $4999.89, and Lazarus starves to death in the street, clutching his dime.Nothing can be changed without making someone worse off, so this is Pareto optimal.

And so, in yet another triumph, the market mechanism has allocated a scarce resource, viz., the turkey, to its most efficient use, viz., being turned into artificial shit. What makes this the most efficient use of the scarce resource? Why, simply that it goes to the user who will pay the highest price for it. This is all that economic efficiency amounts to. It is not about meeting demand, but meeting effective demand, demand backed by purchasing power.

(Incidentally, nothing in this hinges on some failure of perfect competition arising from having only three agents in the market. If we had another copy of Alice, another copy of Dives, and another copy of Lazarus, both Alices will sell their turkeys to the Diveses, and both Lazaruses will starve. By induction, then, the same allocation will be replicated for any finite number of Alices, Diveses, and Lazaruses, so long as there are at least as many Diveses as there Alices.)

You may be refusing to take this seriously, objecting that I have loaded the rhetorical deck pretty blatantly --- and I have! (Though not more than is customary in teaching economics.) But this is the core of Amartya Sen's model of famines, which grows from the observation that food is often exported, at a profit, from famine-stricken regions in which people are dying of hunger. This occurs not just in cases like the USSR in the 1930s, but in impeccably capitalist situations, like British India. This happens, as Sen shows, because the hungry, while they have a very great need for food, do not have the money to buy it, or, more precisely, people elsewhere will pay more. It is thus not economically efficient to feed the hungry, so the market starves them to death.

I do not, however, want to end this on a completely gloomy note. As Sen said, the same market would feed the hungry if they could afford it, so the way to combat famines is to make sure they have money or paying work or both. (If in this country we don't have to worry about famine, it's because we've arranged things so that most of us do have those resources; we still have a hunger problem because our arrangements are imperfect.) The larger point is that while what is technologically efficient depends on facts of nature, what is economically efficient is a function of our social arrangements, of who owns how much of what. Economic efficiency may be a good tool, but it is perverse to serve your own tools, and monstrous to be ruled by them. Let us be thankful for the extent to which we escape perversion and monstrosity.

Update, 27 November: Yes, I was presuming an ascending-price auction to get a price of 11 cents. If the auctioneer uses a descending-price auction, Alice could extract up to $5000 from Dives, driving his consumer surplus to zero; Lazarus, of course, starves at any price which clears the market. No, I did not say (and do not think) that we should abolish the market and replace it with a National Turkey Allocation Board. No, Dives having orders of magnitude more money than Lazarus is not essential; Dives just needs to be willing and able to spend 11 cents.

Also, further to the theme of delicious food and the invisible hand.

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1: It's a thought experiment.

2: I actually saw such a machine at the modern art museum in Lyon in 2003, fed in turn by the city's leading restaurants, but I cannot now remember the artist's name. Perhaps this is just as well. Update: Cris Moore, with whom I saw it, reminds me that the work in question was "Cloaca", by Wim Delvoye.

The Dismal Science; Modest Proposals

Posted by crshalizi at November 24, 2011 10:48 | permanent link

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