Professor 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 horizontal axis and the final 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).

c) a line with slope - 0:5.

Explanation:

The final exam weights twice as much as the midterm.

Denote that by assuming that the final exam is Y and the midterms is X.

This would mean that the Course grade is,

= 2y + x

Since the Course grade is all the student cares about then that means that her Utility is the same.

U = 2y + x

If we were to draw an indifference curve based on a utility level of hers say for instance c, we would denote it as,

c = 2y + x

The equation of a line takes the form,

y = mx + c with m being the slope.

Denoting the indifference curve in this manner would therefore be,

c = 2y + x

c/2 = y + x/2

c/2 - x/2 = y

y = -x/2 + c/2

y = -½x + c/2

The slope will therefore be -½.

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