Question

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 6.00 hours per week? Round your answer to two decimal places.

Answer 1

Utility is given by :

u = 500*PAY - 5*HW - 3*EXAMS

Now it is given that he wants to reduce homework hours by 6 hours, thus Change in HW = -6 . Also EXAMS remain same implies Change in Exam = 0

Change in u = 500* change in Pay - 5*Change in HW - 3*Change in exams --------------------------(1)

Thus We have to calculate Amount that he will be willing to give up to reduce homework by 5 hours and that amount will be that amount at which change in utility = 0

We have to calculate Change in PAY such that Change in u = 0

We can see from above that Decrease in 1 homework hour will leads to increase in utility by (-5)(-1) = 5 utils.

From (1)

we have 0 = 500*Change in PAY - 5*(-6) - 3*0

=> -Change in PAY = 30/500

=> Change in PAY = -0.06 (negative sign means that PAY should decrease)

as pay is in thousands implies that PAY has to decrease by 0.06*1000 = 60

Thus, he is willing to give up $60 of weekly pay.