∂Π
—— = αY1 ((1 - αTι - α(l + τ)T2i)log σ - (1 + τ ))≤ 0 (14)
∂T21
dπ1 = αY1 ((1 -αT1 -α(1 + τ)T21)logσ -1)5/e1 -c ≤ 0 (15)
∂e1
4.2.1 No transfer fee system
Consider first the case that no transfer fee system exists, so that τ = 0 in the first-order
conditions (14) and (15). It is then trivial to prove that if the big league wants to import
talents, T21 > 0, it will be optimal not to train talents. Hiring players from the small
league without the obligation to financially compensate that league thus obviates the need
to have an own training system for native talents, and the big league restricts itself to
attracting talents from abroad. Unless the demand for foreign players exerted by the big
league is relatively small, the small league, on the other hand, will have no incentive to
train talents either if it knows that it will lose its talents without being compensated for
the emigration of its talents.
In a system without transfers, therefore, the only equilibrium can be one where the small
league will have no talents, and the big league will employ home-grown talents only, so
that T21 = 0. For the big league this case is therefore identical to the case of a closed
league. The results for this case are described in table 3. The small league can only
employ mediocre talents and welfare equals N2 logN2.
4.2.2 A transfer fee system
Let us now turn to the case with positive transfer rates, τ > 0. The small league will have
an incentive to train talents if it can derive a positive profit from exporting talents to the
big league. Crucially this depends on how the small league perceives the relation between
their training efforts and the emigration of talents. We assume here that the small league
knows the demand for their talents by the big league, T21. If the small league trains a
number of talents, then, given the dominant position of the big league on the players’
market, the small league knows that the first T21 of these home-grown talents will
emigrate to the big league, while the remainder can be employed in the small league.
Obviously, if the small league chooses not to train talents to satisfy the big league’s
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