demand, it is not able to train talents for the own league as well. Therefore, a small league
will choose to export talents, even at a loss, if the gain from employing talents in the own
league is enough to compensate the possible loss from exporting talents.
If the loss associated with training talents for the export is too high to make raising
additional talents for the own league worthwhile, then the only option for the small
league is not to train talents and employ mediocre talents. For the big league the
equilibrium is in that case given by the closed-economy solution, illustrated in Table 3.
Table 5. Market equilibrium for training and transferring talents with transfer fee rates *)
|
τ = 0.1 τ = 0.3 τ = 0.5 |
α = 0.5; σ = 7 T1 t21 t2 W1 W2 W W * |
α = 0.9; σ = 7 T1 t21 t2 W1 W2 W W * |
|
0.51 0.00 0.00 473.1 195.6 668.7 675.7 0.42 0.19 0.18 474.1 199.9 674.0 675.7 0.51 0.00 0.35 473.1 199.0 672.2 675.7 |
0.34 0.13 0.32 482.5 203.0 685.5 685.9 0.45 0.00 0.38 481.9 203.8 685.7 685.9 0.45 0.00 0.38 481.9 203.8 685.7 685.9 | |
|
τ = 0.1 τ = 0.3 τ = 0.5 |
α = 0.5; σ = 11 T1 t21 t2 W1 W2 W W * |
α = 0.9; σ = 11 T1 t21 t2 W1 W 2 W W * |
|
0.69 0.00 0.00 488.2 195.6 683.8 698.3 0.54 0.29 0.23 491.5 205.3 696.9 698.3 0.65 0.06 0.45 488.4 205.6 694.0 698.3 |
0.47 0.12 0.47 505.1 213.2 718.3 718.8 0.58 0.00 0.52 504.5 214.1 718.6 718.8 0.58 0.00 0.52 504.5 214.1 718.6 718.8 | |
|
τ = 0.1 τ = 0.3 τ = 0.5 |
α = 0.5; σ = 15 t1 t21 t2 W1 W2 W W * |
α = 0.9; σ = 15 t1 t21 t2 W1 W 2 W W * |
|
0.79 0.00 0.00 501.4 195.6 697.0 718.3 0.63 0.32 0.28 506.5 210.4 716.9 718.3 0.74 0.10 0.51 502.1 211.6 713.7 718.3 |
0.57 0.09 0.57 523.4 222.5 745.9 746.2 0.65 0.00 0.60 523.0 223.0 746.1 746.2 0.65 0.00 0.60 523.0 223.0 746.1 746.2 |
*)The value of the parameters used for this calculation are: N1 = 100, N2 = 50, T = 0, δ = 0.3. T1is the
number of talents trained and playing in league 1. T21 (T2 ) is the number of players trained in league 2
and playing in league 1 (2). Wi stands for Ni logΠi. and W = W1 +W2. W* = W1* +W2*can be found in
table 4. For α= 0.1the equilibrium is the closed-league solution for league 1 and e2 = 0for the small
league in all cases.
The procedure for calculating the equilibrium is as follows. In the first stage the big
leagues determines their optimal training efforts and their demand for talents from abroad
by means of eqs. (14) and (15). The small league takes the demand for their talents T21
as given and maximizes its profit function which reads:
Π2 =Y2(1-α(T2-T21))+ταY1T21 (16)
19