Question

4. A decision at the margin

Beth is a hard-working college freshman. One Thursday, she decides to work nonstop until she has answered 200 practice problems for her chemistry course. She starts work at 8:00 AM and uses a table to keep track of her progress throughout the day. She notices that as she gets tired, it takes her longer to solve each problem.

Time	Total Problems Answered
8:00 AM	0
9:00 AM	80
10:00 AM	140
11:00 AM	180
Noon	200

Use the table to answer the following questions.

The marginal, or additional, gain from Beth’s second hour of work, from 9:00 AM to 10:00 AM, isproblems.

The marginal gain from Beth’s fourth hour of work, from 11:00 AM to noon, isproblems.

Later, the teaching assistant in Beth’s chemistry course gives her some advice. “Based on past experience,” the teaching assistant says, “working on 50 problems raises a student’s exam score by about the same amount as reading the textbook for 1 hour.” For simplicity, assume students always cover the same number of pages during each hour they spend reading.

Given this information, in order to use her 4 hours of study time to get the best exam score possible, how many hours should she have spent working on problems, and how many should she have spent reading?

1 hour working on problems, 3 hours reading

2 hours working on problems, 2 hours reading

3 hours working on problems, 1 hour reading

4 hours working on problems, 0 hours reading

Answer 1

a) Marginal gain from 9 AM to 10 AM = 140 - 80 = 60 problems answered

b) Marginal gain from 11 AM to noon = 200 - 180 = 20 problems answered

c) 2 hours working on problems, 2 hours reading

This is because gain from 8 AM to 9 AM and from 9 AM to 10 AM, student is able to solve more than 50 problems which means it gives him more benefit than reading book for an hour. After 10 AM i.e. from 10 AM to 11 AM and 11 AM to noon, person is able to solve less number of question so it is better to read the textbook.