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?
(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?
(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?
(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?