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101-2010-PS3ans

101-2010-PS3ans - Economics 101 Intermediate Macroeconomic...

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Economics 101 Marek Kapiˇ cka Intermediate Macroeconomic Theory Spring 2010 Problem Set 3 Solution Please write your name and your section on the top of your problem set. 1 Distorting Taxation 1. Solve Question 4.8 in Williamson. Suppose that we start with a proportional tax. Under the proportional tax the consumer’s budget line is EFH in figure 1. The consumer chooses consumption, C * , and leisure, l * at point A on indifference curve I 1 . A shift to a lump-sum tax steepens the budget line. The absolute value of the slope of the budget line is (1 - t ) w and t has fallen to zero. The imposition of the lump-sum tax shifts the budget line downward in a parallel fashion. By construction, the lump-sum tax must raise the same amount of revenue as the proportional tax. The consumer must therefore be able to continue to consume C * of the consumption good and l * of leisure after the change in tax collection. Therefore, the new budget line must also pass through point A. The new budget line is labeled LGH in the figure below. With the lump-sum tax, the consumer can do better by choosing
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