For all combinations of parameters that are used in Table 1 it holds that ∂W / ∂τ > 0 in
τ = 0 . So, in all cases total welfare increases if transfer fees are used to compensate the
small league for the emigration of their talents. This is even the case if it is optimal to
have all the talents playing in the big league.
Table 2. Transfer fees, the demand for foreign talents and social welfare*)
|
α = 0.1 |
α = 0.3 |
α = 0.5 |
α = 0.7 |
α t21 |
= 0.9 SW | |||||
|
t21 |
SW |
t21 |
SW |
t21 |
SW |
t21 |
SW | |||
|
τ = 0.00 |
0.50 |
665.0 |
0.50 |
678.8 |
0.47 |
684.8 |
0.19 |
692.9 |
0.04 |
697.7 |
|
τ = 0.05 |
0.50 |
665.1 |
0.50 |
679.1 |
0.40 |
686.6 |
0.15 |
693.8 |
0.01 |
697.8 |
|
τ = 0.10 |
0.50 |
665.1 |
0.50 |
679.3 |
0.34 |
687.5 |
0.11 |
694.2 |
0.00 |
697.8 |
|
τ = 0.15 |
0.50 |
665.1 |
0.50 |
679.4 |
0.28 |
687.9 |
0.07 |
694.3 |
0.00 |
697.8 |
|
τ = 0.20 |
0.50 |
665.1 |
0.50 |
679.6 |
0.22 |
687.9 |
0.04 |
694.1 |
0.00 |
697.8 |
|
τ = 0.25 |
0.50 |
665.1 |
0.47 |
679.6 |
0.17 |
687.7 |
0.01 |
693.8 |
0.00 |
697.8 |
|
τ = 0.30 |
0.50 |
665.2 |
0.39 |
679.5 |
0.13 |
687.4 |
0.00 |
693.7 |
0.00 |
697.8 |
|
τ = 0.35 |
0.50 |
665.2 |
0.31 |
679.0 |
0.08 |
687.0 |
0.00 |
693.7 |
0.00 |
697.8 |
|
τ = 0.40 |
0.50 |
665.2 |
0.24 |
678.5 |
0.04 |
686.6 |
0.00 |
693.7 |
0.00 |
697.8 |
|
τ = 0.45 |
0.50 |
665.2 |
0.18 |
677.9 |
0.01 |
685.9 |
0.00 |
693.7 |
0.00 |
697.8 |
|
τ = 0.50 |
0.50 |
665.2 |
0.12 |
677.4 |
0.00 |
685.9 |
0.00 |
693.7 |
0.00 |
697.8 |
|
τ = 0.55 |
0.50 |
665.2 |
0.06 |
676.8 |
0.00 |
685.9 |
0.00 |
693.7 |
0.00 |
697.8 |
|
τ = 0.60 |
0.50 |
665.2 |
0.00 |
676.2 |
0.00 |
685.9 |
0.00 |
693.7 |
0.00 |
697.8 |
|
*)The value of the parameters used for this calculation |
are: σ |
= 7, N1 |
= 100, N 2 |
= 50, T |
= 0.5, T2 |
= 0.5. | ||||
In Table 2, the effect of one of the key parameters of the model, i.e., α the parameter
decisive for the demand for exogenous talents by the football industry, on the optimal
transfer rate is displayed. In this example talents are scarce (i.e. T1↑ = 0.5 and T2 = 0.5),
and their capability is relatively low (σ = 7 ). The big league’s market size is twice the
small league’s size, i.e., N1 = 100 and N2 = 50. If, for this case, the demand for talents
is high (α = 0.1 and α = 0.3 ) the big league is eager to import all the talents from the
small league as long as no transfer fee system exists. As it appears, whatever the transfer
fee rate actually is, the small league is left with no talents for α= 0.1 . The same holds for
α = 0.3 if the transfer fee rate is not set too high. In these cases the transfer fee system
merely functions as a lump-sum mechanism to equalize the profit per capita, and the
optimal welfare according to Panel E of Table 1 is reached. When the demand for talents
diminishes (α = 0.5 and higher), the incentive for the big league to import talents does
12