Question

4. A decision at the margin

Yakov is a hard-working college freshman. One Thursday, he decides to work nonstop until he has answered 250 practice problems for his math course. He starts work at 8:00 AM and uses a table to keep track of his progress throughout the day. He notices that as he gets tired, it takes him longer to solve each problem.

Time	Total Problems Answered
8:00 AM	0
9:00 AM	100
10:00 AM	175
11:00 AM	225
Noon	250

Use the table to answer the following questions.

The marginal, or additional, gain from Yakov’s first hour of work, from 8:00 AM to 9:00 AM, is

problems.The marginal gain from Yakov’s third hour of work, from 10:00 AM to 11:00 AM, is

problems.

Later, the teaching assistant in Yakov’s math course gives him some advice. “Based on past experience,” the teaching assistant says, “working on 37.5 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 his 4 hours of study time to get the best exam score possible, how many hours should he have spent working on problems, and how many should he have spent reading?

0 hours working on problems, 4 hours reading

1 hour working on problems, 3 hours reading

3 hours working on problems, 1 hour reading

4 hours working on problems, 0 hours reading

Answer 1

1) Marginal gain = Problems solved till 9:00 - Problems solved till 8:00 = 100 - 0 = 100 problems

2) Marginal gain = Problems solved till 11:00 - Problems solved till 10:00 = 225 - 175 = 50 problems

3) 3 hours working on problems, 1 hour reading

First 3 hours solves more problems than reading textbooks so student should work on problems for first 3 hours and then spend 1 hour in reading because it gives 37.5 which is greater than number of problems solved between 11 and noon.