substantially above the market equilibrium (718.6). A transfer fee system is doing
reasonably well in approaching the social-welfare optimum, though. Compared to a
system without transfers, transfer fees are, of course, especially beneficial to the small
league. However, compared to the social-welfare optimum transfer fee system benefits
the big league. In other words, the redistribution, which is necessary to correct the market
inefficiency in an unrestricted market, turns out to be too low in a transfer fee system.
The home-grown rule is a rather blunt device for approaching the social-welfare
optimum. The effective value of the home-grown rule appears to lead to too low
emigration of talents, when emigration should be high (low α and σ), and it leads even
to too much emigration when emigration should be low (high αand σ). Take the latter
case, i.e., α= 0.9 and σ = 15. Under the home-grown rule the small league will train
their own talents, but those who are allowed to emigrate according to the rule move for
free to the big league. League 1 is by rule forced to have its own training facilities.
However, compared to both a transfer fee system and the command optimum, they will
train less own talents and import more talents from the small league. As a result, in this
case the big league will benefit from the home-grown rule, compared to the command
optimum and a transfer fee system
So, compared to the social optimum, the market generates large losses when especially
αis large and talent capability is high. A home-grown rule is not a suitable correction
device, but a transfer fee system is, although, compared to the social optimum, the
compensation for the small league is too small.
5. Conclusion
In a common football market with mobile players, like the European football market
actually is, a free-market equilibrium will only under very special circumstances be
efficient. How large the efficiency loss in equilibrium actually will be depends, among
other things, on the relative market sizes of the leagues. Market size is modeled here as a
positive function of population size. In European football this seems a reasonable
approximation. The ‘big’ football leagues in Europe, like the Premier League in England
and the Primera Division in Spain, serve a much larger potential crowd than smaller
24
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