Migrating Football Players, Transfer Fees and Migration Controls

Profits are maximized with respect to the number of additional home-grown talents,
represented by the parameter μ , and the number of talents hired from abroad, T21. The
first-order conditions for the decision problem read;

⅛ = αY1 ((1 -α(1 + ε)T_π)logσ -1)≤ 0                           (18)

∂T₂₁

^dπ1 = αY₁ ((1 -α(1 + ε)T₂₁)logσ -1>5/e₁ -c ≤ 0                      (19)

∂μ

It is easy to see from these first-order conditions that if an interior solution for the number
of imported talents hold, T₂₁ > 0, no additional talents will be raised at home, i.e.
μ = 0. The optimal import of talents can then easily be derived from (18) as:

T21 = (1 - ɪ)-ɪ-                             (20)

logσ α(1 +ε)

What remains to be considered is how high the required home-grown rate λ has to be in
order to make it advantageous for league 2 to have training facilities of their own. For a
too low value of λ league 2 will lose ‘too many’ of its talents and not start training
facilities and play with mediocre talented players only. Actually, it turns out with our
sample of parameters that if α= 0.1 league 1’s demand for foreign talents for any
λ< 1will be such that the small league will have no incentive to start training their

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