What is the optimal tax rate, Public Economics

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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?


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