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a) The government is contemplating introducing one of two alternative taxes: a tax on commodity x...

a) The government is contemplating introducing one of two alternative taxes: a tax on commodity x (that would double the price of x, expressed in terms of the numeraire good, y) and a lump-sum tax. Assume that the government knows the preferences (i.e., the indifference map) of a representative taxpayer and his/her indifference curves have the usual convex shape. Suppose that government could predict how much tax revenue it could raise if it introduced the commodity tax. With the aid of a fully labeled graph, show that the government could raise the same tax revenue by means of lump-sum tax on y, where y is a numeraire good, while allowing the representative taxpayer to enjoy a greater utility than he/she would experience with the commodity tax on x.

b) Could the government instead impose a lump-sum tax that would leave the taxpayer exactly as well-off as he/she would be with the commodity tax, but would enable the government to raise more tax revenue than with the tax on commodity x? Explain with the aid of a separate fully labeled diagram.

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