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2011HW1

# 2011HW1 - diagram and label your diagram completely b Find...

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Economics 104B Problem Set #1 (Due April 14) Spring 2011 1. Given his endowment of gas (g) and sugar (s), Jim’s MRS = MU Jim g MU Jim s = 4; given Jill’s 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. b. Compared to the absence of the tax, who is harmed by the tax? Who beneﬁts? Explain why. 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). A’s utility function is u A ( x A ) = ln x A 1 + x A 2 and B’s utility function is u B ( x B ) = x B 1 + ln x B 2 . a. Is the allocation x A = (7 , 3), x B = (3 , 7) Pareto optimal? Why or why not? If the above allocation is not Pareto optimal, how to make A better oﬀ without making B worse oﬀ? Illustrate your answer in an Edgeworth box
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Unformatted text preview: diagram and label your diagram completely. b. Find conditions that determine Pareto optimal allocations for this economy. c. Find a competitive equilibrium for this economy. 3. Let f ( x 1 ,x 2 ) = √ x 1 + √ x 2 be the production function of a ﬁrm. Let input prices be w 1 = \$2, w 2 = \$8, and output price p = \$16. Assume input 2 is ﬁxed in the short run at ¯ x 2 = 100. a. Are the inputs perfect substitutes or perfect complements? b. Find the LR and SR proﬁt-maximizing quantities of the inputs at the given prices. Calculate maximum proﬁts. c. What are the LR and SR cost-minimizing quantities of the inputs that the ﬁrm should use to produce y = 90? d. Find the ﬁrm’s LR and SR cost functions. 1...
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