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PIERPAOLO GIANNOCCOLO
Where, from (A2)
a2TA
x=Am^m>0	<17)
and, for the region (2)
f2[\ + Y]-a-bs2 + f2=0	(18)
A2r>l
Where X = Y > 0
The (11), by the symmetry, becomes:
f -_£l__ni')
1 kU'(uf-tf)	K '
and the (16) can be rewritten
;i=4d ±f±A-l	(i6')
Since (13), (IT), (16') and the positive value of X, we have in the case with two steps a greater redistribution of income and a greater provision of education respect the one step case. These results due the fact that in the two steps case we reduce either the uncertainty either the opportunity of each jurisdiction to attract the educated workers by using the FC. Then, we obtain in the two steps case a solution that it's more closed to the op-timal redistribution and optimal provision of education (Autarky case) respect to the one step case.
3.2. One generation model - Subjective utility function
Let us analyse the case in which the government has a subjective utility function. Then the regional authority maximizes the utility of the workers, using a different objective function by the use of lump sum taxes (/p to educated workers and lump sum subsidies it") to the non-educated workers.
Autarky solutions
In this case there is not migration so hi = s, is the total amount of educated workers and /,=1 — s, is the total amount of non-educated workers. Assume that each government maximizes the utility of the workers using a new objective function. Therefore each government chooses s, and ft so as