Assume that a study was done on students who were completing their last semester of college and had already secured offers of employment. That study showed that the students’ utility could be modeled as u(HW, PAY, EXAMS) = 500PAY – 5HW – 3EXAMS, where PAY is weekly starting pay after graduation, in thousands of dollars; HW is hours of homework per week from all classes for the semester; and EXAMS is the number of exams per semester. Based on the observed utility function, how much weekly pay would students be willing to give up to reduce homework by 3.00 hours per week? Round your answer to two decimal places.
The Correct Answer and Explanation is:
Correct Answer: 0.03 (thousand dollars) or 30 dollars per week
Explanation:
We are given a utility function:
u(HW, PAY, EXAMS) = 500PAY – 5HW – 3EXAMS
This function shows how students value their starting pay, homework hours, and exams in terms of overall utility.
Step 1: Understand the coefficients in the utility function
- 500PAY: For every increase of 1 (i.e., $1000) in weekly pay, utility increases by 500.
- -5HW: For every increase of 1 hour of homework per week, utility decreases by 5.
- -3EXAMS: For every additional exam per semester, utility decreases by 3.
Step 2: Determine marginal utilities
- Marginal utility of PAY = 500
- Marginal utility of HW = -5
We want to know how much weekly pay (PAY) a student would be willing to give up to reduce homework by 3 hours per week. This means we are comparing a negative change in homework with a negative change in pay while holding total utility constant.
Step 3: Use marginal rate of substitution (MRS)
To maintain the same utility:
Change in utility from pay = Change in utility from homework
Let ΔPAY be the amount of weekly pay students are willing to give up.
Then:
500 × ΔPAY = 5 × 3
500ΔPAY = 15
ΔPAY = 15 ÷ 500 = 0.03
Since PAY is measured in thousands of dollars, this means:
Students would be willing to give up $30 (or 0.03 thousand dollars) in weekly pay to reduce their homework by 3 hours per week.
This result shows that although students care about their pay, they also value reduced homework time. Giving up a small portion of income for better work-life balance is consistent with the tradeoffs in the utility function.
