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)L^{2}, where C denotes consumption (the individual's income after tax and transfer). If the social welfare function is W = 3U_{jack }+ U_{Jill}, 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?