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)Tπ)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)
|
Table 6. Home-grown rule, players’ allocation and welfare*) | |||||||
|
λ |
T1 |
t21 |
T2 |
Whg |
Wtr |
„ * W____ | |
|
α = 0.5; σ = 7 |
0.86 |
0.84 |
0.14 |
0.23 |
658.8 |
674.0 |
674.7 |
|
α = 0.5; σ = 11 |
0.83 |
0.83 |
0.17 |
0.35 |
690.2 |
696.9 |
698.3 |
|
α = 0.5; σ = 15 |
0.81 |
0.81 |
0.19 |
0.42 |
712.8 |
716.9 |
718.3 |
|
α = 0.9; σ = 7 |
0.65 |
0.35 |
0.19 |
0.29 |
684.1 |
685.7 |
685.7 |
|
α = 0.9; σ = 11 |
0.68 |
0.44 |
0.21 |
0.42 |
715.8 |
718.6 |
718.8 |
|
α = 0.9; σ = 15 |
0.70 |
0.49 |
0.21 |
0.51 |
742.6 |
746.1 |
746.2 |
|
*)The value of the parameters used for this calculation |
are: N |
=100, N2 =50. λis the minimum home- | |||||
|
grown rule for which the small league 2 finds it advantageous to train talents, T1 |
is the number of players | ||||||
|
trained in country 1, T21 ( T2 ) |
is the number of players trained |
in league 2 and playing |
in league 1 (2). | ||||
|
Whg, Wtr , W* |
are welfare under the |
home-grown rule, |
the transfer-rate |
system |
and the social | ||
|
optimum, respectively | |||||||
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
22