Migrating Football Players, Transfer Fees and Migration Controls

We make the implicit assumption that if the number of talents is not sufficient to man the
competition, talents will be supplemented by players with a mediocre talent, having a
capability equal to one, who are not paid for their services. Talents are assumed to be
scarce, while non-talented players are in abundant supply. Talented players get their
marginal product αY paid. Time is not playing an explicit role in the model. The time
horizon of the contract (Fees and Muehlheuser, 2003a and 2003b) is thus not relevant. If
T talents play in a competition total wage paid equals αTY . The parameter α< 1
indicates that the football industry is a profit generating business, so that salaries to the
players do not exhaust the profit. The profits in a league are equal to the value of the
product, Y , minus the wages for talented and the training costs, if any, plus or minus the
revenues or outlays associated with the possible existence of a transfer fee system.

The number of talents a league wants to employ follows from profit maximization. If this
number is larger than the number of native talents in the league the league has the option
to hire talents from the other league. Population in country 1 is larger than in country 2:
N₁ > N ₂ . This implies that the wage league 1 can pay to a talented player is higher than
the wage league 2 can afford. We, therefore, assume that the big league always gets the
talents from the small league that it wants to hire, and no negotiation with the small
league is needed to hire the talent. The small league can at most employ its own native
talents.

Regarding the total number of talents in the two countries we start in section 3 with the
assumption that the total number of talents is exogenously given. In section 4. we allow
for the possibility that by investing in talents the number of talents present in an economy
can be affected. We assume a logarithmic talent production function where an investment
e_i ≥ 1producesδlog e_i talents.

3. Migration with exogenous talents

In this section we first consider the market equilibrium in a world where talented players
can freely migrate to other leagues, without any compensating transfers to be paid by the
new league. The welfare properties of this market equilibrium are then derived, and,

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