Maria can read 20 pages of economics in an hour. She can also read 50 pages of sociology in an hour. She spends 5 hours per day studying.
a. Draw Maria’s production possibilities frontier for reading economics and sociology.
b. What is Maria’s opportunity cost of reading 100 pages of sociology?
The correct answer and explanation is :
a. Maria’s Production Possibilities Frontier (PPF)
Maria can read 20 pages of economics per hour and 50 pages of sociology per hour. Given that she spends 5 hours per day studying, we can calculate how many pages of each subject she could read if she dedicated all her time to one subject.
- Maximum pages of economics: In 5 hours, Maria can read:
[
20 \text{ pages/hour} \times 5 \text{ hours} = 100 \text{ pages of economics}.
] - Maximum pages of sociology: In 5 hours, Maria can read:
[
50 \text{ pages/hour} \times 5 \text{ hours} = 250 \text{ pages of sociology}.
]
The production possibilities frontier (PPF) would show the trade-off between reading economics and sociology. The PPF will be a straight line, with the maximum possible pages of economics (100 pages) on the x-axis and the maximum possible pages of sociology (250 pages) on the y-axis. The points on the line show the various combinations of pages Maria could read in 5 hours if she allocates her time differently between the two subjects.
b. Opportunity Cost of Reading 100 Pages of Sociology
To calculate Maria’s opportunity cost of reading 100 pages of sociology, we need to determine how much economics she sacrifices in the process.
- If Maria reads 50 pages of sociology in one hour, the opportunity cost of reading 1 page of sociology is:
[
\frac{20 \text{ pages of economics}}{50 \text{ pages of sociology}} = 0.4 \text{ pages of economics}.
]
So, for each page of sociology Maria reads, she gives up 0.4 pages of economics.
Now, if Maria reads 100 pages of sociology, the total opportunity cost in terms of economics will be:
[
100 \text{ pages of sociology} \times 0.4 \text{ pages of economics} = 40 \text{ pages of economics}.
]
Thus, the opportunity cost of reading 100 pages of sociology is 40 pages of economics.
Explanation:
Opportunity cost is the value of what you give up in order to pursue something else. In this case, when Maria chooses to spend time reading sociology, she is forgoing the opportunity to read economics. Since she can read 20 pages of economics in one hour, and 50 pages of sociology in the same time, the opportunity cost per page of sociology is 0.4 pages of economics. By reading 100 pages of sociology, she sacrifices the opportunity to read 40 pages of economics. Therefore, Maria’s opportunity cost of reading 100 pages of sociology is 40 pages of economics. This concept helps to illustrate the trade-offs Maria faces when dividing her time between the two subjects.