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Unformatted text preview: Economics 104A Solution for Problem Set #3 Winter 2010 1. Suppose that a household in a state consumes 600 gallons of gasoline per year. A 15% gasoline tax is introduced and the household is provided with a $90 annual tax rebate. Will the household be better off or worse off under the new program? Support your answer. Answer: Let ¯ p G , ¯ p C , and ¯ m denote the per unit price of gasoline, the per unit price of consumption of all other goods, and the household’s income before tax. Let ( ¯ G, ¯ C ) be the optimal bundle before tax. Then, the additional income Δ m the consumer would need to but bundle ( ¯ G, ¯ C ) after the introduction of the 15% gasoline tax is given by Δ m = Δ p G ¯ G. (1) Since ¯ G = 600 and Δ p G = . 15¯ p G , (1) implies Δ m = 90¯ p G . (2) by (2), the additional income can be covered by the tax rebate if Δ m ≤ 90 ⇔ ¯ p G ≤ 1 . Thus, when ¯ p G ≤ 1, the optimal bundle ( ¯ G, ¯ c ) before tax is still affordable with the tax and the tax rebate. Since the price ratio is higher than before, the new optimal bundle will typically involves more consumption of all other goods and less use of gasoline. Hence, with ¯ p G ≤ 1, the new optimal would be directly re- vealed preferred to the optimal bundle before tax. This means that the consumer would be better off when ¯ p G ≤ 1. It’s not clear if the consumer is better off or1....
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This note was uploaded on 08/27/2011 for the course ECON 104 taught by Professor Staff during the Winter '10 term at UCSB.
- Winter '10