The small league only decides on its training efforts, e2 , generating, say, T2 (e2) talents.
If T2(e2) > T21 part of the trained talents can be employed in the own league. On the
other hand, if T2 (e2) < T21 not enough talents are raised to satisfy the big league’s
demand. League 1 then has to recalculate its optimal own training efforts, while given the
lower number of talents the small league will have to supply, the small league should re-
optimize as well. The outcome of the latter calculation can result in higher investment in
talents by the small league than in the first-round calculation. However, the big league
will be motivated to reconsider its demand for foreign talents once again, as the supply of
talents in the small league turns out to be larger. This iterative process does not
necessarily lead to equilibrium. In that case, the only feasible equilibrium is where the big
league is like a closed league and the small league only employs mediocre talents.
For some of the specific parameter values that we employed the market equilibrium is
shown in Table 5. In the cases where α = 0.5 and the transfer rate equals τ= 0.1 , the
above described procedure did not result in a consistent equilibrium. By assumption the
closed-economy annex mediocre talents case arises. The no-talent case for league 2
implies a welfare equal to 195.6.
In all other cases shown in the table some export of talents takes place, or no foreign
talents are demanded at all. In those cases the welfare for league 2 is considerably above
the welfare that would be obtained when league 1 is not able to satisfy its demand for
foreign talents.
Not surprisingly, the market always produces a lower welfare than the corresponding
social optimum in Table 5. More interestingly, in the market equilibrium with positive
transfer fees the small league will employ more talents in their own competition than in
the social optimum. The reason is that the transfer rate in the market has a substitution
effect that makes the demand for foreign talents by league 1 move away from the optimal
amount and makes it instead more advantageous to train their own talents. In the social
optimum the transfer fee system is of a lump-sum nature. As a result, by introducing a
transfer fee system for emigrating players the transfer fee rate that maximizes welfare W
will generally be lower than the optimal transfer fee rate that maximizes social welfare
W*. This is most clear for α= 0.9 . According to Table 4 the optimal transfer fee rate in
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