be employed in the competition, T1 < 1. where a hat ^ indicates the exogenously given
number of talents in a country. As the big league can afford to pay higher wages to
talents, the league has the option to ‘import’ talents from the small league 2. Whether it is
profitable for the big league to supplement their own talents by talents from the other
league follows from profit maximization. The profit obtained by league 1 equals
Π1 = Y1 (1 - αT1). Profit maximization will lead to a demand for talented players equal to
T1 = (1 - 1/log σ )/ α.
Notice that the demand for players is a decreasing function of α and an increasing
function of σ, but is independent of market size. Moreover, if an interior solution holds,
i.e. T1 < 1, profit only depends on σ, while the assumed scarcity of talents will hold as
long as(1 - 1/logσ)/α > (T + 7^2)/2. Finally, the demand by league 1 will imply a
complete manning of the league with talented players, i.e., T = 1, ifα < 1 - 1/logσ.
The effects of changes in the parameters on the allocation of talents can be read off from
panel A of Table 1 that illustrates the relationship between the market allocation and the
key parameters of our model of the football market, i.e., the profitability of the football
industry, the size of the market and players’ capability. In Table 1 the total number of
available talents for both leagues together is equal to one. If the demand for talents is high
(α = 0.1 or α= 0.3 ) the market locates all the talents to the big league. For a median
value of α, i.e., α= 0.5 league 1 demands all the talents only if their capability is high
(σ = 11 or σ = 15). For low demand (α = 0.7 orα= 0.9) league 2 will receive some of
the talents, but this amount will decrease with rising players’ capability.
3.2 The social optimum: the efficient allocation of players
Given symmetry in the parameters α and σ for both leagues, the demand for talents will
be the same in the two leagues. The market, however, allocates most of the players to
league 1, implying that league 1 can, but league 2 cannot maximize its profits. From a
social welfare perspective this migration equilibrium can be motivated if the welfare gain
for country 1 from the immigration of the marginal talented player is larger than the
welfare loss for country 2 from the emigration of this player from country 2. In the
context of our model and given our parameter choice this will actually never be the case.