Appendix
Table A1. Exogenous talents, optimal transfer fees and the demand for foreign talents*)
|
N1 / N 2 = 10 |
N1 / N 2 = 5 |
N1 / N 2 = 2 | |||||
|
α = 0.1 |
α = 0.5 |
α = 0.9 |
α = 0.1 |
α= 0.5 |
α = 0.9 |
α = 0.1 α = 0.5 |
α= 0.9 |
|
t21 τ |
t21 τ |
t21 τ |
t21 τ |
t21 τ |
t21 τ |
T21 τ T τ |
t21 τ |
ʌ ʌ
T1 = 0.5, T2 = 0.5.
|
σ = 7 |
0.50 |
0.12 |
0.41 |
0.04 |
0.03 |
0.01 |
0.50 |
0.24 |
0.37 |
0.07 |
0.03 |
0.02 |
0.50 |
0.50 |
0 |
0.18 |
0.02 |
0.04 |
|
σ = 11 |
0.50 |
0.19 |
0.50 |
0.07 |
0.13 |
0.03 |
0.50 |
0.37 |
0.50 |
0.12 |
0.11 |
0.06 |
0.50 |
0.74 |
0 |
0.19 |
0.07 |
0.15 |
|
σ = 15 |
0.50 |
0.25 |
0.50 |
0.09 |
0.18 |
0.04 |
0.50 |
0.45 |
0.50 |
0.16 |
0.16 |
0.07 |
0.50 |
0.91 |
0 |
0.21 |
0.11 |
0.18 |
ʌ ʌ
T1 = 0, T2 = 1.0
|
σ = 7 |
1.00 |
0.06 |
0.93 |
0.02 |
0.54 |
0.00 |
1.00 |
0.12 |
0.90 |
0.04 |
0.53 |
0.01 |
1.00 |
0.25 |
0 |
0.11 |
0.52 |
0.02 |
|
σ = 11 |
1.00 |
0.10 |
1.00 |
0.04 |
0.64 |
0.01 |
1.00 |
0.19 |
1.00 |
0.07 |
0.63 |
0.02 |
1.00 |
0.37 |
0 |
0.12 |
0.59 |
0.05 |
|
σ = 15 |
1.00 |
0.13 |
1.00 |
0.04 |
0.68 |
0.02 |
1.00 |
0.23 |
1.00 |
0.08 |
0.67 |
0.03 |
1.00 |
0.46 |
1 |
0.15 |
0.64 |
0.06 |
*)N1 =100 is used as the base for the calculations
Table A1 gives the optimal transfer rates for the case of exogenously given talents (section
3). It can be read from the table that the transfer rate should be a negative function of α , a
negative function of the relative size of the market ( N1 / N2 ) and a positive function of
players’ capability (σ).
The effect of the availability of talents in both leagues can be seen by comparing the case
where the talents are equally distributed among the leagues (T∣ = 0.5, T2 = 0.5) with the
case where the small league has all the talents (T∖ = 0, T2 = 1). Again with low α the big
league hires all the talents, this time all natives from the small league’s country.
However, although the big league starts without any talents, the optimal transfer rate in
this case is always lower, i.e., approximately half the rate when the talents are equally
spread. The total transfer payments to be paid will, therefore be about the same in the two
cases. This result implies that from a social welfare perspective the availability of a
relatively large exogenous endowment of talent in a small league does not entitle that
league to large financial compensations for transferring their talents.
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