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 oppurtunity cost of reading 100 pages of sociology?
a. Maria's production possibilities frontier for reading economics and sociology can be represented by a line with a slope of -1/3, with the origin at (0,0) and the point (100,200) on the line.
b. The opportunity cost of reading 100 pages of sociology is reading 200 pages of economics.
a. To draw Maria's production possibilities frontier (PPF) for reading economics and sociology, we can assign the number of hours she spends on each subject on the x-axis, and the number of pages she can read on the y-axis.
Let's assume she spends 'x' hours reading economics and 'y' hours reading sociology. Given the information, we have the following production possibilities:
For economics:
E = 20x
For sociology:
S = 50y
Since Maria spends 5 hours per day studying, we have the constraint equation:
x + y = 5
Now we can plot the PPF using the equations E = 20x and S = 50y, along with the constraint x + y = 5 on a graph.
b. To calculate Maria's opportunity cost of reading 100 pages of sociology, we need to determine how many pages of economics she would have to sacrifice.
Since Maria can read 20 pages of economics per hour, for every 1 hour she spends reading sociology (50 pages), she could have read 2.5 hours (50/20) worth of economics, which is 2.5 * 20 = 50 pages of economics.
Therefore, for Maria to read 100 pages of sociology, she would have to sacrifice 50 pages (2.5 hours) of economics.
Hence, Maria's opportunity cost of reading 100 pages of sociology is 50 pages of economics.
To draw Maria's production possibilities frontier (PPF) for reading economics and sociology, we need to chart the different combinations of pages she can read in an hour for both subjects. The PPF shows the maximum possible combination, given her limited time.
a. Drawing Maria's production possibilities frontier:
- Let's assume the x-axis represents the number of pages of economics she reads in an hour, and the y-axis represents the number of pages of sociology she reads in an hour.
- Since Maria can read 20 pages of economics in an hour and 50 pages of sociology in an hour, we can plot two points on the graph: (20, 0) and (0, 50).
- Connect these two points with a straight line to create the PPF.
b. To find Maria's opportunity cost of reading 100 pages of sociology:
- The opportunity cost refers to the value of the next best alternative given up when making a choice.
- From the PPF, we can see that Maria's maximum possible combination is 20 pages of economics and 50 pages of sociology, or vice versa.
- If she wants to read 100 pages of sociology, she will have to sacrifice reading some pages of economics.
- Calculate the difference between her initial and final points on the PPF. In this case, she will have to read 30 fewer pages of economics.
- So, Maria's opportunity cost of reading 100 pages of sociology is giving up 30 pages of economics.