Migrating Football Players, Transfer Fees and Migration Controls

talents. The market equilibrium, where the big league produces talents as in the closed
league and the small league does not have talents, emerges as a result.

Table 6 gives for a limited number of parameter combinations the home-grown rule and
the players’ allocation. The table also presents the welfare comparison between the home-
grown rule, the transfer fee system and the social-welfare optimum.

What emerges from the table is that the required value of the home-grown rule λhas to
be very high before becoming effective. At least 65% of the players have to be home
grown in order to make it advantageous for league 2 to have its own training facilities,
while, as said before, if α= 0.1 all talents have to be home grown. What we can also
infer from the table is that even if the home-grown rule is effective, i.e. if the rule makes
it possible for league 2 to employ talents, the actual obtained total welfare in the leagues
is lower than the welfare obtained in the market equilibrium with a transfer fee system.

4.2.4 Welfare comparisons

Wrapping up this section we make a welfare comparison between the different analyzed
cases in Table 7 for a subset of the considered parameter values.

Table 7: Welfare in the command optimum, the market, transfer fees and a home-grown rule*)

^*) W_i^* represents welfare under the social-welfare maximizing solution W_i^nt (W_i^t ) is the market solution without (with)
a transfer fee system. W_i^hg is the welfare under the home-grown rule. The welfare without training facilities and
talents for league i .would be 460.5 and 195.6, respectively. Total welfare in this case equals 656.1. Finally
N₁ =100and N₂ =50.

For low α and low σ, i.e. α = 0.1 and σ = 7 , the social welfare optimum gives a
welfare that is only slightly above the welfare under the market equilibrium with or
without transfers and the home-grown rule. At the other extreme, consider the case where
α = 0.9 andσ = 15. The social welfare maximum in this case is equal to 746.2 which is

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