Page 1 of 18 Massachusetts Institute of Technology Department of Economics 14.01 Principles of Microeconomics Exam #1 Wednesday, October 10th, 2007 Last Name (Please print): ______________ First Name: __________________ MIT ID Number: __________________ Instructions. Please read carefully. The exam has a total of 100 points. Answers should be as concise as possible. This is a closed book exam. You are not allowed to use notes, equation sheets, books or any other aids. You are not allowed to use calculators. You must write your answers in the space provided between questions. DO NOT attach additional sheets of paper. This exam consists of (18) sheets (13 pages + 5 blank pages for scratch work). 0. Circle Your Section/Recitation (1 point): Please circle the section or recitation which you are attending below. The marked exam will be returned to you in the section or recitation that you indicate. You will loose 1 point if you leave it unselected. S01: MWF9 (Peter Schnabl) R01: F10 (Rongzhu Ke) S02: MWF10 (Chia-Hui Chen) R02: F11 (Rongzhu Ke) S03: MWF11 (Chia-Hui Chen) R03: F2 (Rongzhu Ke) S04: MWF1 (Monica Martinez-Bravo) R04: F12 (Marco Migueis) R05: F1 (Marco Migueis) R06: F2 (Marco Migueis) DO NOT WRITE IN THE AREA BELOW: Question 1 __/20 Question 2 __/10 Question 3 __/15 Question 4 __/25 Question 5 __/29 Question 0 __/1 Total __/100 Cite as: William Wheaton, Chia-Hui Chen, Rongzhu Ke, Monica Martinez-Bravo, Marco Migueis, Peter Schnabl, and Hongliang Zhang, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Page 2 of 18 1. True/False Questions (TOTAL: 20 points): In this section, write whether each statement is True or False. Please fully explain your answer, using a diagram if appropriate. No credit will be given for an answer without an explanation. (a) (5 points) A risk averse individual that has to decide between two different lotteries will always prefer a lottery with less risk. (b) (5 points) Steven only consumes two goods: X and Y. If X is a Giffen good for Steven, then Y must be a normal good for Steven. Cite as: William Wheaton, Chia-Hui Chen, Rongzhu Ke, Monica Martinez-Bravo, Marco Migueis, Peter Schnabl, and Hongliang Zhang, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Page 3 of 18 (c) (5 points) Ann and Bob consume clothes (C) and food (F) only. Ann’s utility function is U (C, F ) = aA ln C + bA ln F , and Bob’s utility function is U (C, F) = aB ln C + bB ln F . aA ,bA , aB ,bB > 0 . The price of clothes is PC , and the price of food is PF . Ann and Bob must have the same marginal rates of substitution (MRS) of clothes for food at the optimal level of consumption. (d) (5 points) If S and F are perfect complements you must be indifferent between these two bundles: i. One unit of S and one unit of F ii. Two units of S and one unit of F Cite as: William Wheaton, Chia-Hui Chen, Rongzhu Ke, Monica Martinez-Bravo, Marco Migueis, Peter Schnabl, and Hongliang Zhang, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Page 4 of 18 2. Short Answer Questions (TOTAL: 10 points): (a) (4 points) Mary’s demand curve for food is Q = 10 − 2P . Her price elasticity of 2demand for food at price P* equals − . How much is P*? 3 Cite as: William Wheaton, Chia-Hui Chen, Rongzhu Ke, Monica Martinez-Bravo, Marco Migueis, Peter Schnabl, and Hongliang Zhang, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Page 5 of 18 (b) (6 points) Ann and Bob are a couple. They are the only people in the family. Bob’s 1inverse demand curve for shirts is P = 5 − QB . Ann’s inverse demand curve for shirts 2 is P = 10 − 2QA . What is their family demand function for shirts? What is their family consumption of shirts when the price is 4? What’s their family consumption of shirts when the price is 6? Cite as: William Wheaton, Chia-Hui Chen, Rongzhu Ke, Monica Martinez-Bravo, Marco Migueis, Peter Schnabl, and Hongliang Zhang, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Page 6 of 18 Long Questions: 3. (15 points) Jane has utility function over her net income U (I ) = I (a) (2 points) What are Jane’s preferences towards risk? Is she risk averse, risk neutral or risk loving? [Explain briefly your answer] (b) (6 points) Jane drives to work every day and she spends a lot of money in parking meters. Many days the thought of cheating and not paying for parking crosses her mind. However she knows that there is a ¼ probability of being caught in a given day if she cheats, and that the cost of the ticket is $36. Her daily income is $100. What is the maximum amount of she will be willing to pay for one day parking? [Hint: by paying that amount she avoids the risk of getting a ticket!]. Cite as: William Wheaton, Chia-Hui Chen, Rongzhu Ke, Monica Martinez-Bravo, Marco Migueis, Peter Schnabl, and Hongliang Zhang, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Page 7 of 18 (c) (2 points) Paul also faces the same dilemma every single day. But he has a utility function U(I)=I. His daily income is also $100. What are Paul’s preferences towards risk? Is he risk averse, risk neutral or risk loving? (d) (5 points) If the price of one day parking is 9.25, will Paul cheat or pay the parking meter? Will Jane cheat or pay the parking meter under this price? Cite as: William Wheaton, Chia-Hui Chen, Rongzhu Ke, Monica Martinez-Bravo, Marco Migueis, Peter Schnabl, and Hongliang Zhang, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Page 8 of 18 4. (25 points) In Country Faraway, cigarettes are forbidden, so people trade cigarettes in a black market. The