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Unformatted text preview: Economics 104B Solution for Problem Set #1 Spring 2011 1. Given his endowment of gas (g) and sugar (s), Jims MRS = MU Jim g MU Jim s = 4; given Jills endowment, her MRS = MU Jil g MU Jil s = 1. a. If the government collects a tax equal to .8 gallon of gas for each unit of sugar given up in exchange for gas, can John and Maria engage in mutually beneficial exchange? Explain why. Answer: Notice that if a mutually beneficial trade still exists fter the tax has been imposed on sugar used in exchange for gas, then it must be Jim exchanges sugar for gas and Jill does the opposite. However, due to the tax, at least . 8 + . 25 = 1 . 05 gallons of gas are needed for Jim to give up 1 bag of sugar; and at least 1 bag of sugar is needed for Jill to give up 1 gallon of gas. Thus, the price Jill is willing to pay for sugar is now smaller than the price Jim asks. Therefore, mutually beneficial trade is not possible. b. Compared to the absence of the tax, who is harmed by the tax? Who benefits? Explain why. Answer: In the absence of the tax, at least 1 4 of a gallon of gas is needed for Jim to give up 1 bag of sugar; and at least 1 bag of sugar is needed for Jill to give up 1 gallon of gas. Clearly, Jim values gas more than Jill does and Jill values sugar more than Jim does. Therefore, both Jim and Jill would be better off if Jim exchanges sugar for gas with Jill. However, as shown in part (a), mutually beneficial trade is not possible with the tax. This means that compared to the absence of the tax, both Jim and Jill are harmed by tax. 1 2. Consider an exchange economy in which there are two consumers A and B. A has an endowment w A = (10 , 0) and B has an endowment w B = (0 , 10). As utility function is u A ( x A ) = ln x A 1 + x A 2 and Bs utility function is u B...
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This note was uploaded on 12/26/2011 for the course ECON 104B taught by Professor Qin during the Fall '09 term at UCSB.
- Fall '09