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*)
|
__ * WW |
__ * W2 |
W* |
W1nn |
W2n |
Wnt |
W1t |
W2 |
Wt |
W1hg |
W2 |
Whg | |
|
α = 0.1; σ = 7 |
460.7 |
195.7 |
656.4 |
460.7 |
195.6 |
656.3 |
460.7 |
195.6 |
656.3 |
460.7 |
195.6 |
656.3 |
|
α = 0.1σ = 15 |
463.0 |
196.8 |
659.8 |
462.3 |
195.6 |
657.9 |
462.3 |
195.6 |
657.9 |
462.3 |
195.7 |
658.0 |
|
α = 0.5; σ = 7 |
472.9 |
201.8 |
674.7 |
473.1 |
195.6 |
668.7 |
474.1 |
199.9 |
674.0 |
462.4 |
196.2 |
658.5 |
|
α = 0.5σ = 15 |
502.0 |
216.3 |
718.3 |
501.4 |
195.6 |
697.0 |
506.5 |
210.4 |
716.9 |
511.1 |
201.7 |
712.8 |
|
α = 0.9; σ = 7 |
480.4 |
205.5 |
685.9 |
481.9 |
195.6 |
677.5 |
481.9 |
203.8 |
685.7 |
485.1 |
199.0 |
684.1 |
|
α = 0.9σ = 15 |
520.6 |
225.6 |
746.2 |
523.0 |
195.6 |
718.6 |
523.0 |
223.0 |
746.1 |
527.6 |
215.0 |
742.6 |
*) Wi* represents welfare under the social-welfare maximizing solution Wint (Wit ) is the market solution without (with)
a transfer fee system. Wihg 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
23
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