Fall Midterm Examination Monday 10 November Please remember to write your name and student number on your exam.

Transcription

1 NAME: STUDENT NO.: EC & Fall 2014 Deniz Selman Bo¼gaziçi University Midterm Examination Monday 10 November 2014 Instructions Please remember to write your name and student number on your exam. You are to answer all questions. Please write your answer in the space provided for each question. Show all work. Credit will not be given for any answers for which work has not been explicitly presented. Furthermore, you may receive partial credit even if your nal answer is incorrect. Please put a circle or box around your nal answer to each question. For all questions, please assume that quantities can be consumed in any fractional amounts. No questions will be answered during the exam to any individual student. Any clari cations that need to be made will be announced to the entire class. You have exactly 90 minutes to complete the exam. Once time has expired, you will have 1 minute to hand in your exam to one of the proctors. No exams will be accepted after this 1 minute.

2 1. (25 pts) Defne is now in her senior year of high school and is preparing for her university entrance exam. Each week, she spends 40 hours at her high school, 26 hours at her dershane (cram school), 7 hours doing homework, 9 hours taking some form of transportation to and from her schools, and 6 hours preparing to leave for school. This means she has exactly 80 hours remaining in the entire week to do anything else. Her feasible options for things to do during these 80 hours are: sleeping (S) ; eating (E) and talking to her friends/family (F ). Let x = (x S ; x E ; x F ) represent Defne s activity bundle during her 80 free hours, where one unit of an activity represents one hour spent doing it. Defne s weekly utility function from these activities is given by u (x) = 4x S + 10x E x 2 E + x F : (a) (5 pts) Write down Defne s consumer problem which she must solve in order to maximize her utility. (Hint: Defne has a time constraint rather than a budget constraint.) (b) (12 pts) Solve Defne s consumer problem which you wrote down in part (a). Denote the solution as x = (x S ; x E ; x F ) : 2

3 ( B L A N K PA G E ) 3

4 (c) (8 pts) People sometimes say time is money. For this question, rede ne the concepts of normal and inferior by replacing income (in the standard de nition) with time. That is, a normal activity is one which Defne would spend more time doing if she had more time, and an inferior activity is one that she would spend less time doing if she had more time. For Defne, in her current situation as described in this problem, for each activity (sleeping (S) ; eating (E) and talking to her friends/family (F )), state and show whether the activity is normal, inferior, or time neutral. 4

5 2. (21 pts) Every evening at the dershane, the same meal (chicken) is served to the students for free (meaning the price of the chicken dinner is p C = 0). Defne has the option to either eat the free dinner or buy a dürüm next door for some price p D > 0: (a) (4 pts) Suppose one day that Defne chooses to eat the chicken dinner. Can we tell by observing this behavior whether she on that day prefers the chicken dinner or dürüm more? (b) (4 pts) Suppose one day that Defne chooses to buy a dürüm next door. Can we tell by observing this behavior whether she on that day prefers the chicken dinner or dürüm more? 5

6 (c) (13 pts) Let x = (x C ; x D ) be the dinner bundle for Defne in one week, where x C is the number of free chicken dinners and x D is the number of dürüms she eats. Let u (x) be Defne s weekly utility function from these dinners. Suppose that Defne has a weekly budget of m > 0 for dinners and that she chooses to eat 4 free chicken dinners and purchase 1 dürüm. That is, she chooses x = (x C ; x D ) = (4; 1) in order to maximize her utility. Given this much information, for each of the following utility functions, say whether or not the function could possibly be Defne s utility function from dinners. Explain your answers brie y. i. u (x) = 2x C + x D : ii. u (x) = x C + 2x D : iii. u (x) = x 2 C + x D: iv. u (x) = ln (x C + 1) + x D : 6

7 3. (40 pts) When Defne nally gets home and has some time to eat a snack, she goes shopping and chooses from three goods: K z lay Soda (K), green plums (G) and Perrier (P ). Her utility function from a goods bundle x = (x K ; x G ; x P ) is given by u (x) = 3 (x K ) 1=3 (x G ) 1=3 + x P : Prices are given by p = (p K ; p G ; p P ) and Defne s income is given by m: To simplify notation, assume that p P = 1: Throughout this entire question, assume that none of the solutions are corner solutions. (a) (10 pts) Find Defne s ordinary demand functions x (p; m) = (x K (p; m) ; x G (p; m) ; x P (p; m)) : 7

8 (b) (10 pts) Find Defne s compensated Hicksian demand functions h (p; u ) = (h K (p; u ) ; h G (p; u ) ; h P (p; u )) : (Continue to assume that none of the solutions are corner solutions.) 8

9 (c) (5 pts) Are K z lay Soda and green plums net substitutes or net complements for Defne? Explain your answer. (d) (5 pts) What is the income e ect of a marginal increase in the price of K z lay Soda on Defne s demand for Perrier? 9

10 (e) (5 pts) Are K z lay Soda and Perrier net substitutes or net complements for Defne? Explain your answer. (f) (5 pts) Is Perrier a Gi en good for Defne? Please answer either yes, no, or that we cannot tell from the information given, and explain your answer. 10

11 4. (14 pts) At the dershane, Defne takes a practice university entrance exam. Each question is multiple choice with ve choices. Each correct answer is worth 1 point, each incorrect answer is worth 0:25 points, and each question left blank is worth zero points. There are 160 questions total on the exam. Defne s score x on the exam is therefore given by x = c 0:25i; where c is the number of correct answers and i is the number of incorrect answers out of 160. (a) (7 pts) If Defne were to answer every question by guessing completely randomly on each one, what would be the expected value of her exam score? (b) (7 pts) Whenever Defne has no idea how to answer a question (i.e. when she cannot eliminate any of the ve choices), she always chooses to leave that question blank. In terms of Defne s utility function for points on the exam, u (x) ; is Defne risk averse, risk loving, risk neutral, or are her risk preferences not revealed by this behavior? Explain your answer. 11