The figure shows the indifference curves of a student for the two ‘goods’, free time and final grade. Based on this information, read the following statements and select the correct one(s).

Question

BlackTom AI · Accepted Answer

Marginal rate of substitution (MRS) at A equals the rate the student will trade grade points for free hours; on an indifference curve this is the absolute slope, i.e. grade change divided by hours change.

1) Relevant concepts
- Indifference curves represent combinations of two goods (free time and final grade) that give the same utility.
- The MRS = −(Δgrade)/(Δfree time) at a point on the curve; it tells how many grade points the student will give up to gain one extra hour of free time while remaining equally well off.
- Utility is ordinal, so you cannot meaningfully say someone is “50% happier” just from indifference curves.

2) Step-by-step reasoning
- The statement claims: “At A, the student is willing to give up 34 grade points for five extra hours of free time.” That is exactly an assertion about the MRS at A for a Δfree time = +5 hours and Δgrade = −34 points.
- Compute the MRS per hour: MRS = 34 grade points / 5 hours = 6.8 grade points per hour. That means for each extra hour of free time at A, the student requires a compensation of 6.8 grade points forgone to stay on the same indifference curve.

3) Intermediate calculations
- Δgrade = 34 (points), Δtime = 5 (hours)
- MRS = 34 / 5 = 6.8 grade points per hour

4) Why this option is correct
- The definition of willingness to give up grade points for extra free time is precisely the MRS computation above. The numerical division shows the tradeoff is consistent with giving up 34 points for 5 hours, so the statement is true.

5) Why the other options are incorrect
- “A is the student's most preferred choice as she would be attaining the highest grade.” Incorrect: preference depends on both goods and the position of indifference curves; having the highest grade alone does not imply highest utility if free time differs.
- “The student strictly prefers a grade of 54 with 19 hours of free time to a grade of 67 with 18 hours of free time.” Use the MRS: increasing free time by 1 hour (18→19) costs about 6.8 grade points, so 67 at 18 hours is equivalent to about 60.2 at 19 hours (67 − 6.8 = 60.2). Since 60.2 > 54, the student prefers 67/18, so the statement is false.
- “If at B the number of free hours is 10, then the student is 50% happier at A than at B.” Incorrect: utility from indifference curves is ordinal; you cannot compute percentage increases in “happiness” from this graph.

6) Conclusion
The only correct statement is: “At A, the student is willing to give up 34 grade points for five extra hours of free time.” This matches the provided answer.

The figure shows the indifference curves of a student for the two ‘goods’, free time and final grade. Based on this information, read the following statements and select the correct one(s). 多项选择题

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