optimal transfer rate increases, even to values above the wage sum that is paid to the
emigrated talents who are playing in league 1. Naturally, when the transferred talents are
more capable, the loss for the small league of exporting the talents gets larger and a
higher transfer fee rate is required to compensate the small league for the loss of their
talents. Moreover, an increase in players’ capability also requires a higher training effort.
For all values of α and/or σ, both leagues stand to gain from the optimal allocation of
training facilities and players, compared to the outcome without training and without
employing any talents.
Table 4: Optimal investment in talents and allocation of talents*)
|
_* T1 |
_* T2 |
_* _* T1 + T2 |
τ |
W1* |
_ * W2 |
W10 |
W20 | |
|
α = 0.1; σ = 7 |
0.21 |
0.00 |
0.21 |
086 |
460.7 |
195.7 |
460.5 |
195.6 |
|
α = 0.1; σ = 11 |
0.46 |
0.00 |
0.46 |
1.14 |
461.8 |
196.2 |
460.5 |
195.6 |
|
α = 0.1; σ = 15 |
0.60 |
0.00 |
0.60 |
1.32 |
463.0 |
196.8 |
460.5 |
195.6 |
|
α= 0.5; σ = 7 |
0.73 |
0.03 |
0.76 |
0.31 |
472.9 |
201.8 |
460.5 |
195.6 |
|
α= 0.5; σ = 11 |
0.99 |
0.01 |
1.00 |
0.31 |
488.6 |
209.7 |
460.5 |
195.6 |
|
α = 0.5; σ = 15 |
1.00 |
0.16 |
1.16 |
0.37 |
502.0 |
216.3 |
460.5 |
195.6 |
|
α = 0.9; σ = 7 |
0.47 |
0.36 |
0.83 |
0.32 |
480.4 |
205.5 |
460.5 |
195.6 |
|
α = 0.9; σ = 11 |
0.59 |
0.51 |
1.10 |
0.39 |
502.3 |
216.5 |
460.5 |
195.6 |
|
α= 0.9; σ = 15 |
0.65 |
0.59 |
1.24 |
0.44 |
520.6 |
225.6 |
460.5 |
195.6 |
*)The value of the parameters used for this calculation are: T = 0, δ = 0.3. Moreover, T*indicates the
optimal number of talents in i. Wi* represents welfare under the social-welfare maximizing solution and
Wi0 is welfare without training facilities and talents for league i. The transfer rateτis defined by
2Γ /((T1* - T2)αY1 ). Finally # 1 = 100 and #2 = 50.
4.2 Market equilibrium
Let us now consider how the market equilibrium looks like. The big league has the option
to train native talents and/or to import talents from the small league. The small league,
however, only has the option to train talents.
If transfer fees have to be paid, the big league maximizes the following profit function:
Π1 = Y1(1 -α(T1 +(1+τ)T21))-c(e1 -1)
(13)
The first-order conditions for the decision problems read,
17
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