On the other hand, consider the case where a corner solution occurs, or, league 1 will
demand all the talents in the market, T1 = 1 . We know that league 1 will demand all the
talents if α= 0.1 and α = 0.3 and if α = 0.5 for σ = 11 and σ = 15 . Given that T1 = 1 and
T2 = 0 , we can derive from the definitions of MB1 and MB2 , given in condition (2), that
MB1 > MB2 will hold if N1 /N2 > (logσ- 1) /(logσ- 1/(1 -α). In other words, if this
inequality holds, the number of talents playing in league 2 is always too high from a
social welfare point of view. If it were possible to increase team size and if additional
talents came available, it would be optimal to have them migrating to league 1. It is easy
to check that the inequality will hold if N1 / N 2 > 2. However, if N1 / N 2 = 2, the
inequality will not hold for α= 0.5 if σ = 11and σ = 15 .
Panels B through D of Table 1 illustrate the above derived conditions. These panels
produce the optimal allocation of players as a function of the key parameters. If the
market demand for talents is high (α= 0.1 or α = 0.3), so that the market locates all the
talents in the big league, the market result generates even ‘too few’ talents in the big
league, as we have just seen.. For median demand (α= 0.5) the market leads to all talents
ending up in the big league if the talents’ capability is high enough (σ = 11, 15). As we
have just seen, this will not lead to an oversupply of talents in the big league, if the big
league has more than two times the small league’s market size. This is intuitively clear. If
the big league is relatively large, it is more efficient to locate the talents in the big league
where, given the public-good nature of football, they produce more value than in the
small league.
In the cases where the market generates an oversupply of talents in league 1, the
oversupply is larger, for a given value of α, if the difference between the market sizes in
the leagues, measured by N1 / N2 , is smaller. Moreover, the oversupply of talents in
league 1 increases with players’ capability, measured by the parameter σ. Note,
however, that for larger relative size of the big league and larger players’ capability more
talents should be located in the big league.
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