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Unformatted text preview: Professor Faingold Solution prepared by Zhentao Shi Economics 121b: Intermediate Microeconomics Solution to Problem Set 2 1. (a) A consumer chooses a bundle ( x 1 ,x 2 ) when the price is ( p 1 + t,p 2 ) and income is m under the commodity tax. He chooses ( y 1 ,y 2 ) when the price is ( p 1 ,p 2 ) and the income is m- I under the income tax. Since the revenue of the commodity tax, tx 1 , and the revenue of income tax, I , are equal, ( x 1 ,x 2 ) is also a ordable under the income tax I . Therefore, ( y 1 ,y 2 ) is revealed preferred to ( x 1 ,x 2 ) . By the Weak Axiom of Revealed Preference, ( y 1 ,y 2 ) must be una ordable under the commodity tax. ( y 1 ,y 2 ) yields the consumer a higher utility level. (b) One the one hand, Part (a) showed that when the income tax and the commodity tax are revenue equivalent, ( y 1 ,y 2 ) , the chosen bundle under the income tax, is una ordable under the commodity tax. Therefore the premise to apply WARP conversely is violated. On the other hand, a key point that validates the reasoning in (a) is that no matter how much the commodity tax rate t is, there exists a corresponding income tax I that generates the same revenue. However, this correspondence breaks down in the converse part. The commodity tax cannotcorrespondence breaks down in the converse part....
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- Spring '09