Question

Juanita is a hard-working college sophomore. One Saturday, she decides to work nonstop until she has answered 100 practice problems for her economics 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 40 10:00 AM 70 11:00 AM 90 Noon 100 Use the table to answer the following questions. The marginal, or additional, gain from Juanita’s second hour of work, from 9:00 AM to 10:00 AM, is problems. The marginal gain from Juanita’s fourth hour of work, from 11:00 AM to noon, is problems. Later, the teaching assistant in Juanita’s economics course gives her some advice. “Based on past experience,” the teaching assistant says, “working on 15 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? 0 hours working on problems, 4 hours 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

Answer 1

The marginal, or additional, gain from Juanita’s second hour of work, from 9:00 AM to 10:00 AM is 70-40=30 problems ie the change from the question done at 9AM to questions done at 10AM.

The marginal gain from Juanita’s fourth hour of work, from 11:00 AM to noon, is 100-90=10 problems . This is the additional gain in the number of problems solved in the last hour of work.

Junita has 4 hours to study. Also we are given that her 1 hour of textbook reading is equal to 15 problems being solved. So as long as she is solving more than 15 questions, her gain is more in solving questions than in the textbook reading.

So finding the marginal gains of each hour , we see that in the first hour, she is getting 40 questions done, the second hour 30 questions done, the third hour 20 questions and the fourth hour 10 questions. SO her utility would be maximum when she is able to study maximum which is the first three hours being dedicated to problem-solving because the gain is more than 15 problems. The next hour the gain is 10 problems so she could gain by reading textbook which would give her the gain equal to 15 problems.

Hence 3 hours working on problems, 1 hour reading

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