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# final_ak - Final Exam Answer Key Econ 11 Summer Session C...

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Final Exam Answer Key Econ 11 °Summer Session C University of California, Los Angeles September 10, 2008 Write your name and ID number on your exam booklet. Exams without identi±cation will not be graded. Hand-held calculators are permitted. You have two hours to complete the exam. Each question is worth 20 points, for a total of 100. Good luck! 1. Let q = k 1 3 l 1 3 . Assume that both factors are variable, and the price of capital is v , while the price of labor is w . (a) Derive the cost function. Find the marginal and average cost func- tions. ANSWER: MRTS kl = l ° k ° = v w q = k ° 1 3 ° v w k ° ± 1 3 = ° v w ± 1 3 k ° 2 3 k ( q ) = ° w v ± 1 2 q 3 2 l ( q ) = ° v w ± 1 2 q 3 2 The cost function is C ( q ) = vk ( q ) + wl ( q ) = v ° w v ± 1 2 q 3 2 + w ° v w ± 1 2 q 3 2 = 2 ( vw ) 1 2 q 3 2 so the marginal and average cost functions are MC ( q ) = 3 ( vw ) 1 2 q 1 2 AC ( q ) = 2 ( vw ) 1 2 q 1 2 (b) Show that the marginal cost function intersects the minimum of the average cost function. ANSWER: The minimum of the average cost curve occurs where dAC ( q ) dq = ( vw ) 1 2 q ± 1 2 = 0 q = 0 1

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(b) Now assume there is no Social Security tax or bene±t. However, you want to make some savings s 1 in period one. The interest rate made on those savings, r = 100% . Compute your consumption in each period and the savings you make in period one.

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