CHAPTER 3 Preferences Topic: Preferences Difficulty: 0 y Correct Responses: 0 Discriminat ion Index: 0 Correct Answer: D 3.25 In Professor meanscore's c ass the first midterm exam and the second mi dterm exam are weighted equally toward the final grade. With the first midterms score on the horizont al axis, and the second mi dterm's score on the vertical axis, indi fference curves between the two exam scores are (a) L-shaped with lir (b)L-shaped with (d) straight lines wit h slope -1 e )straight lines wit h slope 2 Topic: PI %o Correct Responses: 0 Discrimination Index: 0 3.26Professor Stern's colleague, Dr. Schmertz, gives one midterm exam and a final exam.He weights the final twice as heavily as the midterm to determine the course grade. No grades can be dropped. If the midterm score is represented on the horizont al axis and the final score on the vertical axis, and if a st udent in Dr. Schmertz s cl ass cares only a bout her course grade, her indif- erence curve Is (a)a line wit h slope-2 (b)a line with slope -1 (d)L-shaped with the kink at(J, 2.2) (e)L-shaped with the kink at(2.1, a Difficulty: 0 %o ce Discriminat ion Index: 0 Correct Answer: E 3.27 I prefer 6 apples and 1 orange to 5 apples and 2 oranges. From this we can concl ude that (a)my preferences are transitive (d) my preferences o bey the Law of Dem and (e) none of the a bove
CHAPTER 3 Preferences 36 Topic: Preferences Diculty: 0 % Correct Responses: 0 Discrimination Index: 0 Correct Answer: D 3.25 In Professor Meanscore's class, the rst midterm exam and the second midterm exam are weighted equally toward the nal grade. With the rst midterm's score on the horizontal axis, and the second midterm's score on the vertical axis, indi erence curves between the two exam scores are (a) L-shaped with lines extending upward and to the right. (b) L-shaped with lines extending downward and to the left. (c) parabola shaped. (d) straight lines with slope 1. (e) straight lines with slope 2. Topic: Preferences Diculty: 0 % Correct Responses: 0 Discrimination Index: 0 Correct Answer: C 3.26 Professor Stern's colleague, Dr. Schmertz, gives one midterm exam and a nal exam. He weights the nal twice as heavily as the midterm to determine the course grade. No grades can be dropped. If the midterm score is represented on the horizontal axis and the nal score on the vertical axis, and if a student in Dr. Schmertz's class cares only about her course grade, her indifference curve is (a) a line with slope 2. (b) a line with slope 1. (c) a line with slope 0:5. (d) L-shaped with the kink at (x; 2x). (e) L-shaped with the kink at (2x; x). Topic: Preferences Diculty: 0 % Correct Responses: 0 Discrimination Index: 0 Correct Answer: E 3.27 I prefer 6 apples and 1 orange to 5 apples and 2 oranges. From this we can conclude that (a) my preferences are transitive. (b) my preferences are complete. (c) my preferences are convex. (d) my preferences obey the Law of Demand. (e) none of the above
Essay P references Topic: Preferences Difficulty %o Correct Responses: 0 Discrimination Index: 0 3.1 Draw graphs with quantities of pepperoni pizza on the horizont al axis and ancho y pizz a on the vertical axis to illustrate the following sit uations. In each case draw two different indifference curves and make a little arrow pointing in the direction of greater preference a) Marvin loves pepperoni pizz a and hates anchovy pizza b) Mav is hates anchovy pizz a and is completely indifferent about pepperoni pizz a Answer: a) Indifference curves slopes up and to the right. Arrow points down and to the left. b) Indifference curves are horizont al lines. Arrow points down
Essay Preferences Topic: Preferences Diculty: 3 % Correct Responses: 0 Discrimination Index: 0 3.1 Draw graphs with quantities of pepperoni pizza on the horizontal axis and anchovy pizza on the vertical axis to illustrate the following situations. In each case draw two di erent indi erence curves and make a little arrow pointing in the direction of greater preference. a) Marvin loves pepperoni pizza and hates anchovy pizza. b) Mavis hates anchovy pizza and is completely indi erent about pepperoni pizza. Answer: a) Indi erence curves slopes up and to the right. Arrow points down and to the left. b) Indi erence curves are horizontal lines. Arrow points down
CHAPTER 3 Preferences Topic: Preferences Difficulty: 3 y Correct Responses: 0 Discrimination Index: 0 2 Coach Steroid li kes his players to be big, fast, and o bedient. If player A is better t han playe B in two of t hese t hree characterist ics, St eroid will prefer A to B. T hree players try out for quar- ter back. Wilbur Westingho use weighs 320 pounds, runs Very slow ly, and is quite o bed ient. Harold Hot point weighs 240 pounds, runs extremely fast, and is extremely diso be d ie nt. Jerry Jacuzzi weighs 150 pounds, runs at aVerage speed, and is ext re mely o bedient. Does Coac h Steroid have transitive pre ferences? Explain your answer Answer: No. Stero id prefers w to h because W is hea vier and m ore o bed ie nt. He preferes H to J because H is he avier and faster. But he prefers j to w because j is m ore o be die nt and faster t han W. Since his pre ferences have a cycle, t hey cannot be transitive Difficulty: 3 y Correct Responses Discrimination Index: 0 3.3 Belind a loves chocolate and always t hin ks t hat more is better t ha be worse t han none at all but if she had enough piano lessons to get good at playing t he pia ns ti on the horizo nt al ax is and cho colate on the Vertical ax is. On your grap h ske tc h two indifference curVes for Belinda t hat would be consistent wit h t his story. La bel t he better of t he two indifference Aa and the ly conVex. )The b gher
CHAPTER 3 Preferences 38 Topic: Preferences Diculty: 3 % Correct Responses: 0 Discrimination Index: 0 3.2 Coach Steroid likes his players to be big, fast, and obedient. If player A is better than player B in two of these three characteristics, Steroid will prefer A to B. Three players try out for quarterback. Wilbur Westinghouse weighs 320 pounds, runs very slowly, and is quite obedient. Harold Hotpoint weighs 240 pounds, runs extremely fast, and is extremely disobedient. Jerry Jacuzzi weighs 150 pounds, runs at average speed, and is extremely obedient. Does Coach Steroid have transitive preferences? Explain your answer. Answer: No. Steroid prefers W to H because W is heavier and more obedient. He preferes H to J because H is heavier and faster. But he prefers J to W because J is more obedient and faster than W. Since his preferences have a cycle, they cannot be transitive. Topic: Preferences Diculty: 3 % Correct Responses: 0 Discrimination Index: 0 3.3 Belinda loves chocolate and always thinks that more is better than less. Belinda thinks that a few piano lessons would be worse than none at all but if she had enough piano lessons to get good at playing the piano, she would prefer more lessons to less. Draw a graph with piano lessons on the horizontal axis and chocolate on the vertical axis. On your graph sketch two indi erence curves for Belinda that would be consistent with this story. Label the better of the two indi erence curves AA and the worse one BB. Answer: The indi erence curves would look something like inverted U 0s. (The area under these curves needn't be necessarily convex.) The better of the two curves drawn is the higher one
ESSAY Topic: Preferences Difficulty: 3 Correct Responses: 0 Discrimination Index: o 4 Mac Rowe doesnt sweat the petty st uff. In fact, he just cannot detect small differences. He consumes two goods, x and y. He prefers the bundle (x,y) to the bundle(x0yg if and only if xy xQO> 1. Ot herwise he is indifferent between the two bundles. Shor (a)that the relation of indi fference is not transitive for Mac(Hint: Give an example. (b) that the preferred rel ation is transitive for Mac Answer: Consider the bundles A/(1, 1),B/(1, 1: 75),C/(1, 2: 5). Then A is indi fferent to B and B to c but c is preferred to A. To see that strict preference is transitive, suppose we have any three bundles, (x, x),(x0,y and ((0, y g If the fi rst is preferred to the second and the second to the third, then xy=x o>I and xQ0xQ Simple algebra shows that xy =x y>I.Therefore the first must be prefer red to the third Topic: Preferences %o Correct Responses: 0 Discrimnation Index: 3.5 Blanche Carter has devised a system for rating the males in her economics cl ass. She cares about their intelligence and t heir looks. She has ranked each male on a scale of l to 5 for intelligence and 1 to 3 for looks. She defines a preference re lation, R, as follows: x Ry if boy x scores at leas as high as boy y in eit her looks or in intelligence. Give an example to show t hat Bl anche's method of determining preferences might not lead to transitive preferences Answer: Suppose boy x has rankings l and 2, boy y has rankings 3 and 1 and boy z has rankings 2 and 3. Then x ry because x is better looking than y and y h Rz because y is smarter than :. But it is not true that xrz. in fact e is bot h smarter and better looking than x Topic: Preferen Difficulty: 2 %o Correct Responses: 0 Discrimnation index: o 3.6 Ex plain how it would be possible to cheat someone who had int ransitive preferences. Be explicit about what you would offer him if you were trying to exploit his intransitivity and what he would do in response e t hat he has bundle C right now and prefers A to B, B to C, and C to A. If you offer him him at B instead of C, he will accept the deal. If you now offer him a rade that him at A instead of B, he will accept that. But he will prefer to be back where he origi nally was to where he is. So uld offer to give him back I nal bundle, minus reward to you for your efforts and he would accept the deal
ESSAY 39 Topic: Preferences Diculty: 3 % Correct Responses: 0 Discrimination Index: 0 3.4 Mac Rowe doesn't sweat the petty stu . In fact, he just cannot detect small di erences. He consumes two goods, x and y. He prefers the bundle (x; y) to the bundle (x0; y0) if and only if xy x0y0 > 1. Otherwise he is indi erent between the two bundles. Show: (a) that the relation of indi erence is not transitive for Mac (Hint: Give an example.) (b) that the preferred relation is transitive for Mac. Answer: Consider the bundles A = (1; 1); B = (1; 1:75); C = (1; 2:5). Then A is indi erent to B and B to C but C is preferred to A. To see that strict preference is transitive, suppose we have any three bundles, (x; y); (x0; y0) and (x00; y00). If the rst is preferred to the second and the second to the third, then xy x0y0 > 1 and x0y0 x00y00 > 1. Simple algebra shows that xy x00y00 > 1. Therefore the rst must be preferred to the third. Topic: Preferences Diculty: 3 % Correct Responses: 0 Discrimination Index: 0 3.5 Blanche Carter has devised a system for rating the males in her economics class. She cares about their intelligence and their looks. She has ranked each male on a scale of 1 to 5 for intelligence and 1 to 3 for looks. She de nes a preference re lation, R; as follows: xRy if boy x scores at least as high as boy y in either looks or in intelligence. Give an example to show that Blanche's method of determining preferences might not lead to transitive preferences. Answer: Suppose boy x has rankings 1 and 2, boy y has rankings 3 and 1 and boy z has rankings 2 and 3. Then xRy because x is better looking than y and yRz because y is smarter than z. But it is not true that xRz. In fact z is both smarter and better looking than x. Topic: Preferences Diculty: 2 % Correct Responses: 0 Discrimination Index: 0 3.6 Explain how it would be possible to cheat someone who had intransitive preferences. Be explicit about what you would o er him if you were trying to exploit his intransitivity and what he would do in response. Answer: Suppose that he has bundle C right now and prefers A to B; B to C; and C to A. If you o er him a trade that leaves him at B instead of C; he will accept the deal. If you now o er him a trade that leaves him at A instead of B ; he will accept that. But he will prefer to be back where he originally was to where he is. So you could o er to give him back his original bundle, minus a reward to you for your e orts and he would accept the deal
chaPter 3 Preferences Topic: Preferences Difficulty: 1 Correct Responses: 0 Discrimination Index: 0 If good X is measured on the horizont al axis and good y on the vertical, what can you say about the preferences of someone whose indi fference curves are a) Parallel to the y axis? b) Positively sloped with more desirable indiffernce curves as one moves to the right? c) Negatively sloped wit h more desirable indifference curves as one moves to the left? A ns wer. a) This person doesnt care how much X he has. b) This person likes X but hates y. c) This person hates bot h goods Topic: Preferences Difficulty y Correct Responses: 0 Discrimination Index: 0 3.8 Suppose that there are two commodities and a consumer prefers more to less of each good If the consumer has transitive preferences, can her indifference curves cross? Sketch a brief proof of your answer, and illustrate with a diagram a ns uer See the text book
CHAPTER 3 Preferences 40 Topic: Preferences Diculty: 1 % Correct Responses: 0 Discrimination Index: 0 3.7 If good X is measured on the horizontal axis and good Y on the vertical, what can you say about the preferences of someone whose indi erence curves are a) Parallel to the Y axis? b) Positively sloped with more desirable indi ernce curves as one moves to the right? c) Negatively sloped with more desirable indi erence curves as one moves to the left? Answer: a) This person doesn't care how much X he has. b) This person likes X but hates Y . c) This person hates both goods. Topic: Preferences Diculty: 2 % Correct Responses: 0 Discrimination Index: 0 3.8 Suppose that there are two commodities and a consumer prefers more to less of each good. If the consumer has transitive preferences, can her indi erence curves cross? Sketch a brief proof of your answer, and illustrate with a diagram. Answer: See the textbook