depend on the size of the compensating transfer fee rate. From the table it can be seen
that the transfer fee rate can be set in such a way that both the optimal allocation of
talents and the optimal welfare can be reached.
We conclude that the transfer fee rate should be a positive function of the demand for
talents, or, in other words a negative function of α . For the other key parameters of the
model, i.e., the relative size of the market ( N1 /N2 ) and players’ capability (σ) the result
of analogous calculations as in Table 2 are summarized in Table A1 in the Appendix.
With a given talent size σ, the smaller the receiving country is, the lower the Pareto-
efficient number of talents is in that country, and so, the lower the optimal transfer fee
rate should be. Moreover, a higher capability implies that a migrating player imposes a
relatively large loss on his home country, and, therefore, a relatively large transfer is
needed to compensate the small league.
Note from the Appendix that buying all the talents from the small league does not have to
imply large transfer rates for the big league. In particular, for this case of complete
migration the rates τrange from 6% of the wage sum (N1 /N2 = 10, α = 0.5, σ = 9) to
80% of the wage sum (N1 /N2 = 2, α= 0.1, σ = 12) . If the market sizes of the two
leagues are about equal, and when, furthermore, highly capable talents (large σ) are in
high demand (low α), migration of players to the big league should go along with
substantial transfer payments in return. But, if the leagues are substantially different in
size, demand and players’ capability are low, transfer fee rates should be low.
4. Migration with endogenous talents
In this section we assume that both leagues have the opportunity to train individuals to
become talented players. To model this the product is assumed to be generated as
follows:
Y1 = N1σα(T1+T21) Y2 =N2σα(T2-T21) (6)
and:
л
Ti= T'i+ £log ei ( i = 1,2) (7)
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