Suppose, unfortunately , your mathematics and economics professors have decide to give tests 2 day from now and you can spend only a total of 12 hours studying for exams .After some thought, you conclude that dividend your study time equally between each subject will give you an expected grade of C in each course . For each addition 3 hours study time for one of the subjects, your grade will increase one letter for that subject, and your grade will fall one letter for the other subject.
a. Construct a table for the production possibilities and corresponding number of hours of study in this case.
b. Plot these production possibilities data in a graph.
c. Does this production possibilities curve reflect the law of increasing opportunity cost? Explain.
To construct the table for the production possibilities and corresponding number of hours of study, we need to consider the different combinations of study time for mathematics and economics. Since we have a total of 12 hours, let's assign the variables x and y to represent the hours of study for mathematics and economics, respectively.
a. The table can be created as follows:
| Mathematics Study Hours (x) | Economics Study Hours (y) |
|-----------------------------|---------------------------|
| 0 | 12 |
| 3 | 9 |
| 6 | 6 |
| 9 | 3 |
| 12 | 0 |
b. To plot these production possibilities data in a graph, we will use the x-axis for mathematics study hours (x) and the y-axis for economics study hours (y). Each point on the graph corresponds to a combination of study time for the two subjects.
The graph would look like a straight line connecting the points (0, 12), (3, 9), (6, 6), (9, 3), and (12, 0).
c. Yes, this production possibilities curve reflects the law of increasing opportunity cost. As we allocate more study time to one subject, the opportunity cost in terms of the other subject increases. In this case, when we increase the study time for mathematics, the grade in economics decreases. This demonstrates the trade-off between the two subjects, where the more we specialize in one, the less time we have available to study the other.