small league. As a result, for α= 0.1 the small league will not find it advantageous to
train talents, while the big league still invests in training talents.
Table 3. Investment in players in a closed league*)
|
α |
= 0.1 |
α |
= 0.3 |
α = 0. |
5 |
α = 0. |
7 |
α = 0. |
9 | ||||||
|
N = 100 |
e |
"T^ |
W |
e |
T |
W |
e |
T |
W |
e |
T |
W |
e |
T |
-W |
|
σ=7 |
1.42 |
0.10 |
460.7 |
4.03 |
0.42 |
465.9 |
5.52 |
0.51 |
473.1 |
5.39 |
0.51 |
478.6 |
4.53 |
0.45 |
481.9 |
|
σ=11 |
2.13 |
0.23 |
461.4 |
6.70 |
0.57 |
473.2 |
9.83 |
0.69 |
488.2 |
9.11 |
0.66 |
498.9 |
6.91 |
0.58 |
504.5 |
|
σ=15 |
2.64 |
0.29 |
462.3 |
9.01 |
0.66 |
479.6 |
13.95 0.79 |
501.4 |
12.30 0.75 |
516.2 |
8.63 |
0.65 |
523.0 | ||
|
N = 50 |
e |
T |
W |
e |
T |
W |
e |
T |
W |
e |
T |
W |
e |
^T^ |
^^W |
|
σ=7 |
1.00 |
0.00 |
195.6 |
2.09 |
0.22 |
196.5 |
3.19 |
0.35 |
199.0 |
3.69 |
0.39 |
201.7 |
3.60 |
0.38 |
203.8 |
|
σ=11 |
1.05 |
0.01 |
195.6 |
3.32 |
0.36 |
198.7 |
5.44 |
0.51 |
204.5 |
6.27 |
0.55 |
210.2 |
5.68 |
0.52 |
214.1 |
|
σ=15 |
1.29 |
0.08 |
195.7 |
4.35 |
0.44 |
200.7 |
7.56 |
0.61 |
209.6 |
8.63 |
0.65 |
217.8 |
7.32 |
0.60 |
223.0 |
*)The value of the parameters used for this calculation are: T = 0, δ = 0.3. W stands for Ni ∣0g ∏i.
Increasing capabilities of players gives leagues more incentives to train talented players.
Welfare in the leagues, measured by Ni log(Πi), increases with players’ capability if
investment in talents (e>1) takes place. Moreover, raising talents (e>1) always increase
the welfare above the level when only mediocre players are employed (e=1). In the latter
case, welfare would equal 460.5 and 195.6 for the big league and the small league,
respectively. For all cases considered, however, the number of talented players turns out
to be lower than the maximal number.
4.1.1 The optimum in open leagues
Table 4 shows for parameter values that we used before how many talents should be
**
trained (indicated by T1 + T2 in the table) and how the talents should be allocated across
*
the leagues (indicated by Ti in the table), according to first-order conditions (9)-(11).
Just as when talents are exogenously given, talents should play only in the big league
when α is small. The talents should be raised in both leagues, however, in this case. A
transfer from the big league to the small league is enacted, that is very small in absolute
terms, but as a percentage of the wage sum it is large: 86 percent of the wage sum of the
emigrated players is transferred to the small league, if α= 0.1and ο= 7. Nevertheless,
total welfare for the small league is only marginally above the welfare the league would
receive if it only employed mediocre talents. When for α= 0.1 capability increases the
16
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