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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 1st midterm and x2 be her score on the 2nd midterm. Which combination of scores would Nancy prefer, x1 = 20 and x2 = 70 or x1 = 60 and x2 = 60?
(b) On a graph with the grade on the 1st midterm on the x-axis and the grade on the 2nd on the y-axis, draw an indierence curve showing all of the combinations of scores that Nancy likes exactly as much as x1 = 20 and x2 = 70. Also draw an indierence curve showing the combinations that Nancy likes exactly as much as x1 = 60 and x2 = 60.
(c) 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 rst 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?
(d) On a similar graph drawn before, draw an indierence curve showing all of the combinations of scores on her economics exams that Nancy likes exactly as well as x1 = 20 and x2 = 70. Also draw an indierence curve showing the combinations that Nancy likes exactly as well as x1 = 60 and x2 = 50. Does Nancy have convex preferences over these combinations?
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