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A cap on footballer’s wages. Bankers next?

The Premier League has recently agreed to new financial controls. Part of the deal is a cap on player wage bills. Economists usually criticize attempts to control market prices. But, sometimes a cap has merit, and I think this is one example.
   First, let’s go through the standard argument against a cap on salaries. Suppose that a player called Hotshot would add £10 million in revenue to a club. Then, competitive logic says Hotshot will be paid £10 million. Any less than this and other clubs would have an incentive to buy him and pay him a higher wage. Hotshot’s marginal product is £10 million and so that’s what he will be paid. A cap on salaries would just force clubs to find some roundabout way to reward the player for his worth. For example, they could offer him a longer contract, or perks. All a cap does is to distort the market.
    The flaw in this logic is that football is a zero-sum game. One team’s loss is another’s gain. The situation is, therefore, more akin to an all pay auction. To explain why this matters consider the famous dollar auction due to Martin Shubik. The story goes something like this:
    Imaging I am going to auction a £1 coin. The twist to the tale is that everyone who bids has to pay me the amount of their highest bid.
  • Andy starts the bidding off at £0.50. 
  • Dave then bids £0.60.
  • As things stand Andy has to pay me £0.50 and gets nothing in return. He bids £1.00.
  • As things stand Dave has to pay me £1.00 and get nothing in return. So, better to bid £1.50, win the £1 coin and only lose £0.50. He bids £1.50.
  • But then, Andy stands to lose £1.00. Better to bid £1.60, win the £1 coin and only lose £0.60. He bids £1.60. 
   If you’re wondering where this all ends – it doesn’t. We have to wait until Andy or Dave go bankrupt. Auctioning a £1 coin can be, therefore, a very profitable venture.
   And auctioning the Premier League trophy is a similarly profitable venture. All the premier league teams are vying for the trophy – the £1 coin. The analogous story would go something like this, where the value of winning the league is put at £100 million:
  • Manchester United have a team with wage bill £90 million and Manchester City a team with wage bill £80. This means Manchester United will win the league under current circumstances.
  • Manchester City believe that buying Hotshot will win them the league. That’s worth £100 million and so paying him £20 million looks like loose change. They buy Hotshot and pay him a wage of £20 million pushing up their overall wage bill to £100 million.
  • Manchester United respond by buying Hotshot’s twin brother Hamish. Again, that’s worth £100 million and so paying him £20 million looks like loose change. They buy Hamish and pay him a wage of £20 million pushing up their overall wage bill to £110 million.
  • Manchester City respond by buying Hotshot’s friend Doug. Again, that’s worth £100 million and so paying him £20 million looks like loose change. They buy Doug and pay him a wage of £20 million pushing up their overall wage bill to £120 million.
    The story goes on until one of the teams goes bankrupt. The key thing about this story is that marginal productivity is relative. On the day that Manchester City buy Hotshot he is worth £100 million to them because he will win them the league. However, on the day that Manchester United buy his twin brother Hamish the marginal productivity of Hotshot drops to £0. Instead Manchester City need to buy another player in order to win the league and recoup the sunk costs already spent on Hotshot. This is a dangerous game.
    A cap on wage bills can help clubs find a way out of this mess. Instead of clubs spending until they go bankrupt, they will now only have to spend until they hit the cap. Clearly clubs will try to find ways around the cap. But, it does make economic sense to try and enforce the cap.
   And what about bankers? Bankers often justify high salaries and bonuses on the grounds of marginal productivity. Banks, however, are playing a very similar game to football clubs. So, maybe we should help the banks with a cap on salaries? I doubt it would have the catastrophic effects many in the finance industry predict. 

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