The Baseline Scenario has a graph today that illustrates it perfectly at:

http://baselinescenario.com/2010/01/20/one-more-thing/

Of course with the news of the last two days everything seems dwarfed, or dependent on, abolishing the filibuster, and then with that, establishing very strong public campaign finance. For more on this see:

http://richardhserlin.blogspot.com/2010/01/why-government-regualtion-of-finance.html

]]>The greater the ratio between the pay of the winners of the tournament and that of an ordinary worker – the more individuals will tend to enter the tournament on the chance of making it to the big-time. But “entering the tournament” implies an opportunity cost – one gives up, say, a year of potential work for the practice/education required to be given a chance to compete. A rational individual’s decision process would try to compare that opportunity cost with the expected value of success in the tournament – and holding the chance of success constant – more pay means a higher expected value.

Another way to say it is that as you increase the relative pay of the winners, increasing numbers of people with diminishing levels of talent will change their mind and decide to compete instead of work. The demand curve vertical at the quota – and the competitor-supply curve will adjust with the price.

So, if the numbers of winners is held constant, the more they are paid relative to an ordinary person could potentially diminish aggregate production if the amount of output forgone by diverting additional labor into competition is greater than the extra output produced by the winners of the tournament that is attributable to the greater intensity of competition.

Without huge differences in pay, few people would bother with these long shots and concentrate instead on working for a more normal amount of compensation instead of actually expending their scarce resources to do the equivalent of buying an employment lottery ticket.

I believe that the taking of these long-shots is *rampant* in our society and, indeed, encouraged by inequality of pay, but also by our culture which celebrates the chasing of dreams against all odds. It is clear that a lot of people waste a lot of time and money pursuing fantasies (though, if you try to say this when the subject is education, be prepared to be immediately convicted of capital crimethink). Nevertheless, the question remains as to whether what is wasted is greater or less than what is produced by the winners.

I started playing around with modeling this idea mathematically in some very simple scenarios, and I was surprised by my results.

Before I began, my instinct-guess was that there was probably some optimal amount of “inequality” – too little and you don’t have enough competition and you end up with lousy, incompetent people as the winners of tournaments (Bureaucracy, anyone?), but too much and the whole society beggars itself on a tiny chance at well-compensated fame (American Idol, anyone?)

As a corollary to that idea, if inequality was higher than optimal, then a system of redistributive taxation from high-to-low could increase total output by discouraging excess competition. On the other hand, if inequality were less than optimal, then you would redistribute low-to-high for more inequality and greater output (which might strike people as odd and counter-intuitive, but follows from the assumption of an optimum and the need to encourage more competition). On the other foot, you could argue that market processes tend to naturally eliminate the occurrence of “too-low” inequality, and the only real risk is “too-high” inequality.

But, for the few super-simple general equilibrium models I’ve tried so far, this isn’t what I’ve found, and I got “optimal” answers at the extremes of no-inequality or infinite-inequality. It’s just an impression, but I find that result a little suspect and puzzling, so I’m continuing to add additional assumptions that make the situation more “realistic” (but also more complex to work with). I’ll let you know if I stumble on anything interesting.

]]>I’ve been a lurker around here a while, but a big fan all round. Looking forward to your inequality blog. I’m finding the ongoing debate pretty uninformative so far.

I’ve posted a piece on economic growth and median wages over at Josh Marshall’s TPM Café. I thought you might find it interesting – though it’s directed at a layman audience.

http://tpmcafe.talkingpointsmemo.com/talk/blogs/o/b/obey/2010/01/how-to-make-an-economist-cry-i.php