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Notes: Transfers are the total revenues divided by 2 (equal amounts for Jack and Jill).

Jack and Jill live alone on an island. Their labour supply schedules are identical and
given by L  (1  t)w, where t is the income tax rate and w denotes the wage. Jill’s wage
is 6 and Jack’s is 2. The tax paid by an individual is twL and each receives a transfer
equal to half the total revenues. Jack and Jill have identical utility functions given by U 
C  (1/2)L2, where C denotes consumption (the individual’s income after tax and
transfer). If the social welfare function is W  3Ujack  UJill, what is the optimal tax rate?
[Hint: Write W as a function of the tax rate t.] Why is the optimal tax rate not 0? Why is
it not 1?
Notes: Transfers are the total revenues divided by 2 (equal amounts for Jack and Jill). twL (jack) + twL (Jill) = Total ravenues
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