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MIC Unit 1 Practice Exam 3 Solutions

MIC Unit 1 Practice Exam 3 Solutions - N A ME SOLUTIONS...

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NAME _____ SOLUTIONS ______________________________ Student ID Number_________________ Northwestern University First Midterm Economics 310-1 Summer Quarter, 2011 Professor Hornsten INSTRUCTIONS: (1) Write your name and student ID number in the spaces at the top of this page. (2) This a 60 minute, closed-book examination. Answer all questions in any order. (3) There are 8 pages in this examination. Please check to see that you have received all 8 pages. (4) The use of calculators or other electronic devices is not permitted during the exam. (5) The examination is worth 100 points. The potential score on each question is indicated in parentheses at the beginning of each question. (6) Show all work clearly and concisely in the space provided after each question . You must support your answer with clearly demonstrated reasoning to receive any credit. Question 1 (15 points possible ) _________ ELASTICITIES: LINEAR, CES, ENVELOPE Question 2 (15 points possible ) _________ COBB-DOUGLAS 3D AND CONSTRAINED Question 3 (20 points possible ) _________ CALLING PLANS & C-D PREFS Question 4 (15 points possible ) _________ CEREAL AND (SKIM OR WHOLE) Question 5 (20 points possible ) _________ LEONTIEF ICC,ENGEL,PCC,DEMAND Question 6 (15 points possible ) _________ QUASI-LINEAR E.V. FOR PRICE CUT ================================== Total Score (100 points possible) ________
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Economics 310-1. Professor Hornsten Page 2 First Midterm, Summer 2011 1) ELASTICITIES. a) (5 points) A linear demand curve is given by the formula Q = 40 – P. Find the price-elasticity of demand at Q = 10. Q=10 P = 30, and dQ/dP = -1, so elasticity epsilon = (dQ/dP) (P/Q) = (-1)(30/10) = -3. b) (5 points) A nonlinear demand curve is given by the formula Q = 100 / P. Compute the price-elasticity of demand. Elasticity epsilon = (dQ/dP) (P/Q), where dQ/dP = 100(-1)P -2 , P is just P, and Q = 100P -1 . Thus, epsilon = (-100P -2 )(P) / 100P -1 = -1. This is a constant elasticity function! NOTE: If asked to compute something, you shd show the math, even if you know the answer will be -1. c) (5 points) You know that the price-elasticity of demand for coconuts at current prices is -0.5, the current price is $1, and coconuts are being purchased at a rate of 4 million per year. Find a linear demand function in the form Q = A – BP that fits this information. Elasticity epsilon = (dQ/dP) (P/Q) -0.5 = (dQ/dP) (1/4m) (dQ/dP) = -2m, and Q = A – BP dQ/dP = -B, so –B = -2m and Q = A – BP 4m = A – 2m(1) A = 6m. THUS, Q = A – BP = 6m – 2mP. [+2 if 4m = A – B(1), where B incorrect]
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Economics 310-1. Professor Hornsten Page 3 First Midterm, Summer 2011 2) Suppose U[x, y, z] = x 3 y 2 z, with prices P x = P y = P z = 1, and income I=120. a) (8 points) Find the utility-maximizing bundle (x*, y*, z*). Show your work for full credit. max x , y , z U [ x , y , z ] s.t. I " xP x + yP y + zP z # max x , y , z x 3 y 2 z s.t. 120 " 1 x + 1 y + 1 z If any of {x,y,z} equals zero, then U = 0, so we cannot have a corner solution! MRS x , y = MU x MU y = P x P y # 3 x 2 y 2 z 2 x 3 yz = 3 y 2 x = 1 1 # 2 x = 3 y # x = 3 2 y MRS y , z = MU y MU z = P y P z # 2 x 3 yz x 3 y 2 = 2 z y = 1 1 # 2 z = y # z = 1 2 y Budget :120 = 3 2 y + y + 1 2 y = 3 y # y * = 40 # x * = 60, z * = 20 CHECK :1(60) + 1(40) + 1(20) = 120.
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