finally, we will consider whether a transfer fee system can correct the uncompensated
market equilibrium and mimic the social-welfare optimum.
|
Table 1 Number of players i |
n league 1 |
and welfare in both leagues*)____________________ | |||||||||||||
|
α = 0.1 |
α = 0.3 |
α = 0.5 |
α = 0.7 |
α = 0.9 | |||||||||||
|
Ti |
W1 |
W2 |
Ti |
Wi |
W2 |
Ti |
Wi |
W2 |
Ti |
Wi |
W2 |
Ti |
Wi |
W2 | |
|
A: Market demand | |||||||||||||||
|
σ=7 |
1.00 |
469.4 |
195.6 |
1.00 |
483.2 |
195.6 |
0.97 |
488.5 |
209.2 |
0.69 |
488.5 |
204.4 |
0.54 |
488.5 |
209.2 |
|
σ=11 |
1.00 |
474.0 |
195.6 |
1.00 |
496.8 |
195.6 |
1.00 |
511.1 |
195.6 |
0.83 |
512.8 |
203.4 |
0.65 |
512.8 |
214.5 |
|
σ=15 |
1.00 |
477.1 |
195.6 |
1.00 |
506.1 |
195.6 |
1.00 |
526.6 |
195.6 |
0.90 |
531.7 |
201.4 |
0.70 |
531.7 |
216.4 |
|
σ=7 |
1.00 |
469.4 |
23.0 |
1.00 |
B: Optimal location with N1 /N 483.2 23.0 0.92 488.5 23.4 0.66 |
2 =10 488.5 24.9 |
0.53 |
488.5 |
25.8 | ||||||
|
σ=11 |
1.00 |
474.0 |
23.0 |
1.00 |
496.8 |
23.0 |
1.00 |
511.1 |
23.0 |
0.80 |
512.7 |
24.9 |
0.63 |
512.8 |
27.0 |
|
σ=15 |
1.00 |
477.1 |
23.0 |
1.00 |
506.1 |
23.0 |
1.00 |
526.6 |
23.0 |
0.87 |
531.6 |
24.6 |
0.68 |
531.6 |
27.4 |
|
σ=7 |
1.00 |
469.4 |
60.0 |
1.00 |
C: Optimal location with N1 /N2 = 5 483.2 60.0 0.87 488.1 61.1 0.64 488.3 |
63.9 |
0.53 |
488.5 |
65.4 | ||||||
|
σ=11 |
1.00 |
474.0 |
60.0 |
1.00 |
496.8 |
60.0 |
1.00 |
511.1 |
60.0 |
0.77 |
512.3 |
64.2 |
0.61 |
512.6 |
68.1 |
|
σ=15 |
1.00 |
477.1 |
60.0 |
1.00 |
506.1 |
60.0 |
1.00 |
526.6 |
59.9 |
0.83 |
530.9 |
63.8 |
0.66 |
531.2 |
69.2 |
|
σ=7 |
1.00 |
469.4 |
195.6 |
1.00 |
D: Optimal location with N1 /N2 = 2 483.2 195.6 0.71 485.8 201.8 0.58 487.5 |
206.8 |
0.51 |
488.4 |
209.4 | ||||||
|
σ=11 |
1.00 |
474.0 |
195.6 |
1.00 |
496.8 |
195.6 |
0.85 |
507.1 |
200.7 |
0.66 |
509.3 |
210.6 |
0.56 |
511.3 |
217.8 |
|
σ=15 |
1.00 |
477.1 |
195.6 |
1.00 |
506.1 |
195.6 |
0.93 |
524.0 |
198.5 |
0.71 |
526.3 |
211.8 |
0.59 |
528.7 |
222.4 |
|
T1 |
E: Optimal location and lump-sum redistribution with N1 /N2 |
2**) SWNT |
SWLT | ||||||||||||
|
σ=7 |
1.00 |
663.5 |
665.2 |
1.00 |
678.8 |
679.7 |
0.75 |
687.6 |
687.9 |
0.58 |
694.3 |
694.3 |
0.51 |
697.8 |
697.8 |
|
σ=11 |
1.00 |
669.6 |
669.9 |
1.00 |
692.4 |
694.5 |
0.88 |
707.8 |
710.7 |
0.70 |
719.9 |
720.6 |
0.54 |
728.1 |
729.2 |
|
σ=15 |
1.00 |
672.7 |
673.1 |
1.00 |
701.7 |
705.0 |
1.00 |
722.5 |
728.9 |
0.72 |
737.1 |
740.5 |
0.58 |
750.1 |
751.6 |
|
*)The total number of players T is |
assumed to be equal to one; the big league has market size N1 = |
100. | |||||||||||||
The entries indicate the number of players in league 1, T1, generated by the market (Panel A); or
representing the optimal number of players in league 1 calculated from eq. (2), (Panels B-D), and the
welfare for the leagues, W1 and W2, defined by Wi = Ni logΠi,i = 1,2. For the market case, N2 = 50 is
assumed. **)Panel E displays the number of players and the total welfare without (SWNT) and with (SWLT)
lump-sum redistributions, respectively
3.1 The market without transfer fees
The most interesting case to consider is where in the big league at least the number of
talents available in the own country is less than the maximum number of players that can
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