Question

The test will be held 15 hours later. Ben has yet to study for it. Suppose an hour of study can increase the score by 5 in the test.

(a) Draw the budget constraint of Ben. (Hint: good x is sleeping in hours, and good y is test score

) (b) The test is unexpectedly delayed for 5 hours. Do you think that ben's test score must be higher? Explain your answer intuitively and graphically.

(c) Although the test is delayed for 5 hours, ben finds that some of the course materials are much more difficult than expected. For the first 10 hours, an hour of study can increase the score by 5. For the rest, an hour of study can increase the score by 3 only. Draw the new budget constraint of ben.

(d) Suppose ben choose to sleep for 10 hours in part c. Will ben be worse off in part d? Explain your answer intuitively and graphically.

Answer 1

a) Each hour of study increases Ben's score by 5 in the test. the test is due in 15 hours which implies that if he uses all his time studying he can increase his score by 75 marks, but then rest is of importance as well and therefore those 15 hours has to be used for both studying and sleeping. Ben's constraint is to spend those 15 hours judiciously between work and sleep.

b) When the test is delayed by another five hours, it is expected that Ben's performance will improve because he gets sufficient time to divide between sleep and study and the increased hours of study will improve his test results.

c) Ben finds that even with increased time, the course material gets tougher and each hour of preparation for the first 10 hours increases 5 marks but any hour of study beyond 10 hours, increases test score by 3 marks, the budget constraint for Ben now shrinks and he is clearly worse off.

d) With the new schedule, if Ben decides to sleep for the first 10 hours which instead if used for studying would have increased his score by 5 marks each hour of preparation, Ben is clearly worse off in this case.