Dec

14

  It's paper-reading-Friday-afternoon, and an essay by Jonathan Weinstein (Northwestern B School) entitled, "Fairness and Tax Policy– A Response to Mankiw's proposed 'Just Deserts'" caught my eye.

The author makes an interesting reference to Shapley Values in the context of tax theory/policy. He writes that he's never seen Shapley discussed in this context, and I concur. Whether one is liberal or conservative, it's food for thought– and he gives an intuitive example of Shapley at-work (pun intended.)

For some spec-listers, reading this essay may be akin to swallowing a tablespoon of Cod Liver Oil. And when Weinstein makes a pejorative reference to Atlas Shrugged, Ayn Rand fans may find the essay akin to taking an enema. (Of course both palliatives can leave one feeling better in the morning.)

If you like to read papers that challenge your beliefs, spend 5 minutes on this…. I look forward to Vic's explanation why applying Shapley fails…

Stefan Jovanovich writes:

Professor Weinstein's bedrock premise (and Shapley's?) is that profits are produced by cooperation and are, therefore, collective property to be divided - i.e. taxed - "fairly", not uniformly.

The authors of our Constitution had enough commercial experience to know that the very definition of profit was tricky and that even the most dedicated collective would be tempted to become a non-profit in the face of an income tax. They knew that it was far, far easier to apply an excise - to tax transactions. The only debate could be over the price and it would be very hard for the seller and buyer to cooperate to evade the excise when only one of them would be saving on the taxes. The rich would pay more, even if the excise rate was uniformly applied; the only "unfairness" (sic) would be that everyone would be treated equally.

Rocky Humbert adds: 

Stefan makes a fair point that profit/income taxes will, ceteris paribus, cause participants to produce less profit/income. However, similar logic can be applied to almost all taxes…

The tax aspects of Shapley are controversial but not necessarily re-distributionist — and it's interesting that no SpecListers picked up on the nuance: Turning the entire argument upside down, instead of "individual contribution," the quantity could be "individual benefit." And if a player gets "less benefit" from government, a Shapley argument might show that the player should pay less in taxes. Weinstein was definitely not making this case, however, it's always fun to turn an argument upside down and find that the argument also works in reverse.

A way to think about Shapley here is in the context of a basketball team, where the team owner has a fixed salary budget $, and can allocate the money amongst his current and future players. The team owner and the players all want to maximize their personal outcomes, yet Shapley demonstrates that there is a allocation of $ amongst the players where COLLABORATION CAN ONLY HELP BUT NEVER HURT. Of course there are non-Shapley outcomes where things could be even better (and this is arguably the Adam Smith argument), but we also know that there are many sub-optimal outcomes that include show-boating/selfish players too. Basketball fans can think of several notable examples where a marquee player stayed with championship-contender team — even though he could have signed for more money with a non-championship-contender team.

Of course, a difficulty with Shapley is the calculation of "individual fairness" and "individual contribution" i.e. every player gets at least as much as he or she would have got had they not collobrated at all. A libertarian might argue that the marketplace is the best arbiter of individual contribution, while a liberal might argue that the market will fail at this calculation. A shareholder of a company that is paying its CEO gazillions of dollars while the stocks goes south might find himself a bedfellow with the liberal.


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