Migrating Football Players, Transfer Fees and Migration Controls

In other words, the market equilibrium will not be a social optimum. The reason for the
possibility of a non-optimal migration equilibrium has been known for quite some time in
the fiscal-federalism literature (see, e.g., Boadway and Flatters, 1982 and the recent
survey by Boadway, 2004). In particular, in accepting the wage offer from the large
league the talents disregard the loss in the profit per capita they inflict on the owners of
the small country.

To elaborate this point, we assume that the inhabitants of the two countries are the
owners of the competition, and that the profit generates an individual utility equal to
logΠ_i . Moreover, a federal football institution (FFI), like the UEFA in European
football, exists that takes the utility of both league owners into account. This institution
maximizes social welfare that is equal to

W = N₁ log Π₁ + N₂ logΠ₂.                                        (1)

The total number of players equals T∖ + 12 = T. The FFI can calculate the optimal
allocation of the T talented players among the two leagues, assuming an interior
solution, by equating the marginal benefit of immigration for league 1 with the marginal
loss of immigration for league 2, which for this case can be written as:

αα

MBi ≡ N 1(^αlog^σ   ---—) = N2(^αlog^σ   ---—) ≡MB2          (²)

1 - αT₁                1 - αT₂

To learn whether condition (2) holds, consider first the case when the market generates an
interior solution T₁ < 1, i.e. α= 0.5 and σ = 7, α = 0.7, α = 0.9 . Insert the market demand
for talents in league 1 into the definition of MB₁ . Then we get MB₁ = 0. In league 2
T2 = T - Ti talents will play. Inserting this into the definition of MB2 we find that
MB2 > 0 if and only if (2 - αT)log σ - 2 > 0. Given our choice of parameters this
condition will always be fulfilled. So, the market demand by the big league implies that
in market equilibrium it will hold that MB₁ < MB₂ . In other words, the free market for
talented players generates a situation where too many talents are playing in the big
league.

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