Question

4. A decision at the margin Hilary is a hard-working college senior. One Thursday, she decides to work nonstop until she has answered 100 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 8:00 AM 9:00 AM 10:00 AM 11:00 AM Total Problems Answered 40 70 90 100 Noon Use the table to answer the following questions The marginal, or additional, gain from Hilary's first hour of work, from 8:00 AM to 9:00 AM, 40 problems. The marginal gain from Hilary's third hour of work, from 10:00 AM to 11:00 AM, Is 20 problems Later, the teaching assistant in Hilary's chemistry course gives her some advice. "Based on past experience," the teaching assistant says, "working on 35 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?

Answer 1

Marginal gain is the additional gain by solving problems for one more hour.

1) Marginal gain from first hour = Problems solved from 9 to 10 - Problems solved from 8 to 9 = 40 - 0 = 40 problems

2) Marginal gain from third hour = 90 - 70 = 20 problems

3) 1 hour working on problems, 3 hours reading

Working on problems for 1 hours gives student score of 40 while another hour on problems does not increase student score by more than 30 so student should prefer reading which increases score by 35.