26 PREFERENCEs (Ch. 3) 3.8(0) Professor Goodheart always gives two midterms in his commu- nications class. He only uses the higher of the two scores that a student gets on the midterms when he calculates the course grade (a) Nancy Lerner wants to maximize her grade in this course. Let ai be her score on the first midterm and 2 be her score on the second midterm Which combination of scores would Nancy prefer, 1 20 and 2=70 or ai= 60 and 2=60 0?(20,70) (b)On the graph below, use red ink to draw an indifference curve showing all of the combinations of scores that Nancy likes exactly as much as 70. Also use red ink to draw an indifference curve showing the combinations that Nancy likes exactly as much as 1 =60 (c) Does Nancy have convex preferences over these combinations? No Grade on second midterm Blue curves Preference direction Grade on first midterm () Nancy is also taking a course in economics from Professor Stern Professor Stern gives two midterms. Instead of discarding the lower grade Professor Stern discards the higher one. Let i be her score on the first midterm and 2 be her score on the second midterm. Which combination of scores would Nancy prefer, 1 20 and 12=70 or 3=60 and r2=50?(60,50). (e) on the graph above, use blue ink to draw an indifference curve showing all of the combinations of scores on her econ exams that Nancy likes exactly as well as 1=20 and 2= 70. Also use blue ink to draw al indifference curve showing the combinations that Nancy likes exactly well as 31= 60 and 2=50. Does Nancy have convex preferences over these combinations? Yes
26 PREFERENCES (Ch. 3) 3.8 (0) Professor Goodheart always gives two midterms in his communications class. He only uses the higher of the two scores that a student gets on the midterms when he calculates the course grade. (a) Nancy Lerner wants to maximize her grade in this course. Let x1 be her score on the first midterm and x2 be her score on the second midterm. Which combination of scores would Nancy prefer, x1 = 20 and x2 = 70 or x1 = 60 and x2 = 60? (20,70). (b) On the graph below, use red ink to draw an indifference curve showing all of the combinations of scores that Nancy likes exactly as much as x1 = 20 and x2 = 70. Also use red ink to draw an indifference curve showing the combinations that Nancy likes exactly as much as x1 = 60 and x2 = 60. (c) Does Nancy have convex preferences over these combinations? No. 0 20 40 60 80 20 40 60 Grade on first midterm Grade on second midterm 80 Preference direction Blue curves Red curves (d) Nancy is also taking a course in economics from Professor Stern. Professor Stern gives two midterms. Instead of discarding the lower grade, Professor Stern discards the higher one. Let x1 be her score on the first midterm and x2 be her score on the second midterm. Which combination of scores would Nancy prefer, x1 = 20 and x2 = 70 or x1 = 60 and x2 = 50? (60,50). (e) On the graph above, use blue ink to draw an indifference curve showing all of the combinations of scores on her econ exams that Nancy likes exactly as well as x1 = 20 and x2 = 70. Also use blue ink to draw an indifference curve showing the combinations that Nancy likes exactly as well as x1 = 60 and x2 = 50. Does Nancy have convex preferences over these combinations? Yes
NAME 3.9(0 Mary Granola loves to consume two goods, grapefruits and avocados (a) On the graph below, the slope of an indifference curve through any point where she has more grapefruits than avocados is-2. This means that when she has more grapefruits than avocados, she is willing to give 2 grapefruit(s )to get one avocado (b)On the same graph, the slope of an indifference curve at points where she has fewer grapefruits than avocados is-1/2. This means that when she has fewer grapefruits than avocados, she is just willing to give up 1/2 grapefruit(s)to get one avocado Grapefruits 0 Avocado (d) Does Mary have convex preferences? Yes 3.10(2) Ralph Rigid likes to eat lunch at 12 noon. However, he also likes to save money so he can buy other consumption goods by attending the"early bird specials"and"late lunchers"promoted by his local diner Ralph has 15 dollars a day to spend on lunch and other stuff. Lunch at noon costs $5. If he delays his lunch until t hours after noon. he is able to buy his lunch for a price of $5-t. Similarly if he eats his lunch t hours before noon, he can buy it for a price of $5-t.(This is true for fractions of hours as well as integer numbers of hours. (a)If Ralph eats lunch at noon, how much money does he have per day to spend on other stuff? $10
NAME 27 3.9 (0) Mary Granola loves to consume two goods, grapefruits and avocados. (a) On the graph below, the slope of an indifference curve through any point where she has more grapefruits than avocados is −2. This means that when she has more grapefruits than avocados, she is willing to give up 2 grapefruit(s) to get one avocado. (b) On the same graph, the slope of an indifference curve at points where she has fewer grapefruits than avocados is −1/2. This means that when she has fewer grapefruits than avocados, she is just willing to give up 1/2 grapefruit(s) to get one avocado. (c) On this graph, draw an indifference curve for Mary through bundle (10A, 10G). Draw another indifference curve through (20A, 20G). 0 10 20 30 40 10 20 30 Avocados Grapefruits 40 45 Slope -2 Slope -1/2 (d) Does Mary have convex preferences? Yes. 3.10 (2) Ralph Rigid likes to eat lunch at 12 noon. However, he also likes to save money so he can buy other consumption goods by attending the “early bird specials” and “late lunchers” promoted by his local diner. Ralph has 15 dollars a day to spend on lunch and other stuff. Lunch at noon costs $5. If he delays his lunch until t hours after noon, he is able to buy his lunch for a price of $5−t. Similarly if he eats his lunch t hours before noon, he can buy it for a price of $5 − t. (This is true for fractions of hours as well as integer numbers of hours.) (a) If Ralph eats lunch at noon, how much money does he have per day to spend on other stuff? $10
28 PREFERENCEs (Ch. 3) (b) How much money per day would he have left for other stuff if he ate 2PM?$12 (c)On the graph below, use blue ink to draw the broken line that shows combinations of meal time and money for other stuff that Ralph can just fford. On this same graph, draw some indifference curves that would b consistent with Ralph choosing to eat his lunch at 11 A M 10 3.11(0)Henry Hanover is currently consuming 20 cheeseburgers and 20 Cherry Cokes a week. A typical indifference curve for Henry is depicted below Cherry Cok 1020 40
28 PREFERENCES (Ch. 3) (b) How much money per day would he have left for other stuff if he ate at 2 P.M.? $12. (c) On the graph below, use blue ink to draw the broken line that shows combinations of meal time and money for other stuff that Ralph can just afford. On this same graph, draw some indifference curves that would be consistent with Ralph choosing to eat his lunch at 11 A.M. 0 11 12 1 2 5 10 15 Time Money 20 10 3.11 (0) Henry Hanover is currently consuming 20 cheeseburgers and 20 Cherry Cokes a week. A typical indifference curve for Henry is depicted below. Cheeseburgers Cherry Coke 0 10 20 30 40 40 30 20 10
(a)If someone offered to trade Henry one extra cheeseburger for every Coke he gave up, would Henry want to do this? N (b)What if it were the other way around: for every cheeseburger Henry gave up, he would get an extra Coke. Would he accept this offer? Yes (c) at what rate of exchange would Henry be willing to stay put at his current consumption level? 2 cheeseburgers for 1 Coke 3.12(1) Tommy Twit is happiest when he has 8 cookies and 4 glasses of milk per day. Whenever he has more than his favorite amount of either food, giving him still more makes him worse off. Whenever he has less than his favorite amount of either food, giving him more makes him better off. His mother makes him drink 7 glasses of milk and only allows him 2 cookies per day. One day when his mother was gone, Tommys sadist sister made him eat 13 cookies and only gave him 1 glass of milk, despite the fact that Tommy complained bitterly about the last 5 cookies that she made him eat and begged for more milk. Although Tommy complained forced on him better than what his mother demanded (a) Use black ink to draw some indifference curves for Tommy that are consistent with this stor Milk (84) 31 Cookies
NAME 29 (a) If someone offered to trade Henry one extra cheeseburger for every Coke he gave up, would Henry want to do this? No. (b) What if it were the other way around: for every cheeseburger Henry gave up, he would get an extra Coke. Would he accept this offer? Yes. (c) At what rate of exchange would Henry be willing to stay put at his current consumption level? 2 cheeseburgers for 1 Coke. 3.12 (1) Tommy Twit is happiest when he has 8 cookies and 4 glasses of milk per day. Whenever he has more than his favorite amount of either food, giving him still more makes him worse off. Whenever he has less than his favorite amount of either food, giving him more makes him better off. His mother makes him drink 7 glasses of milk and only allows him 2 cookies per day. One day when his mother was gone, Tommy’s sadistic sister made him eat 13 cookies and only gave him 1 glass of milk, despite the fact that Tommy complained bitterly about the last 5 cookies that she made him eat and begged for more milk. Although Tommy complained later to his mother, he had to admit that he liked the diet that his sister forced on him better than what his mother demanded. (a) Use black ink to draw some indifference curves for Tommy that are consistent with this story. 0 (8,4) (13,1) (2,7) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Cookies 1 2 3 4 5 6 7 8 9 10 11 12 Milk
30 PREFERENCES ( Ch. 3) (b) Tommy's mother believes that the optimal amount for him to consume is 7 glasses of milk and 2 cookies. She measures deviations by absolute values. If Tommy consumes some other bundle, say, (c, m), she measures his departure from the optimal bundle by D=7-mI+12-c. The larger D is, the worse off she thinks Tommy is. Use blue ink in the graph above to sketch a few of Mrs. Twits indifference curves for Tommys consumption. (Hint: Before you try to draw Mrs. Twit's indifference curves, we suggest that you take a piece of scrap paper and draw a graph of the locus of points( 1, 2)such that z1+ 2= 1.) 3.13(0)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, then Coach Steroid prefers A to B, but if B is better than A in two of these three characteristics, then Steroid prefers b to A. Otherwise, Steroid is indifferent between them. Wilbur Westinghouse weighs 340 pounds, runs very slowly, and is fairly obedient. Harold Hotpoint weighs 240 pounds runs very fast, and is very disobedient. Jerry Jacuzzi weighs 150 pounds rage speed, and is extremely obedient (a)Does Steroid prefer Westinghouse to Hotpoint or vice versa? He prefers Westinghouse to Hotpoint (b) Does Steroid prefer Hotpoint to Jacuzzi or vice versa? prefers Hotpoint to Jacuzzi (c) Does Steroid prefer Westinghouse to Jacuzzi or vice versa? He prefers Jacuzzi to Westinghouse (d) Does Coach Steroid have transitive preferences? No (e) After several losing seasons, Coach Steroid decides to change his way of judging players. According to his new preferences, Steroid prefers player a to player B if player A is better in all three of the characteristics that Steroid values, and he prefers b to A if player B is better at all three lings. He is indifferent between A and B if they weigh the same,are equally fast, and are equally obedient. In all other cases, Coach Steroid simply says"A and B are not comparable () Are Coach Steroids new preferences complete? No (9) Are Coach Steroids new preferences transitive? Yes
30 PREFERENCES (Ch. 3) (b) Tommy’s mother believes that the optimal amount for him to consume is 7 glasses of milk and 2 cookies. She measures deviations by absolute values. If Tommy consumes some other bundle, say, (c,m), she measures his departure from the optimal bundle by D = |7 − m| + |2 − c|. The larger D is, the worse off she thinks Tommy is. Use blue ink in the graph above to sketch a few of Mrs. Twit’s indifference curves for Tommy’s consumption. (Hint: Before you try to draw Mrs. Twit’s indifference curves, we suggest that you take a piece of scrap paper and draw a graph of the locus of points (x1,x2) such that |x1| + |x2| = 1.) 3.13 (0) 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, then Coach Steroid prefers A to B, but if B is better than A in two of these three characteristics, then Steroid prefers B to A. Otherwise, Steroid is indifferent between them. Wilbur Westinghouse weighs 340 pounds, runs very slowly, and is fairly obedient. Harold Hotpoint weighs 240 pounds, runs very fast, and is very disobedient. Jerry Jacuzzi weighs 150 pounds, runs at average speed, and is extremely obedient. (a) Does Steroid prefer Westinghouse to Hotpoint or vice versa? He prefers Westinghouse to Hotpoint. (b) Does Steroid prefer Hotpoint to Jacuzzi or vice versa? He prefers Hotpoint to Jacuzzi. (c) Does Steroid prefer Westinghouse to Jacuzzi or vice versa? He prefers Jacuzzi to Westinghouse. (d) Does Coach Steroid have transitive preferences? No. (e) After several losing seasons, Coach Steroid decides to change his way of judging players. According to his new preferences, Steroid prefers player A to player B if player A is better in all three of the characteristics that Steroid values, and he prefers B to A if player B is better at all three things. He is indifferent between A and B if they weigh the same, are equally fast, and are equally obedient. In all other cases, Coach Steroid simply says “A and B are not comparable.” (f) Are Coach Steroid’s new preferences complete? No. (g) Are Coach Steroid’s new preferences transitive? Yes