Scholastica is taking a class from Professor Chaos. Professor Chaos gives two tests in this course and determines a student's grade as follows. He determines the smaller of the following two numbers: half of the score on the first test (which is a relatively easy test) and the total score on the second test. He gives each student a numerical score equal to the smaller number and then ranks the students. Scholastica would like to be ranked as high as possible in Professor Chaos's rankings. If we represent her score on the first exam on the horizontal axis and her score on the second exam on the vertical axis, then her indifference curves
A) are L-shaped with kinks where the two exam scores are equal.
B) have sections with a slope 22 and sections with a slope.
C) are positively sloped.
D) are L-shaped with kinks where the exam 1 score is twice the exam 2 score.
E) are straight lines with a slope of.

Question

Quizplus · Accepted Answer

We need to find the indifference curves for Scholastica's grades on the two exams. The indifference curve represents the combinations of the two grades that give Scholastica the same ranking. 
Let G1 be Scholastica's score on the first exam and G2 be her score on the second exam. The score that Professor Chaos will consider for Scholastica's ranking is min(G1/2, G2). Therefore, Scholastica's ranking curve (indifference curve) will have kinks where G1/2 = G2, because the ranking score will be determined by G2 in this region on the curve. 
Since we are looking for the highest ranking, Scholastica wants to maximize her ranking score. This means she wants to be as far to the upper right on the indifference curve as possible. To do this, she should choose G1 as large as possible, while still being no more than twice G2, because if G1 is more than twice G2, then her ranking score will be determined by G1/2 instead of G2. Therefore, her indifference curves will be L-shaped with kinks where G1 = 2G2. Hence, the best choice is D.

Scholastica Is Taking a Class from Professor Chaos