10. 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.
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a) To construct the table for the production possibilities and corresponding number of hours of study, we can start by allocating an equal number of hours for both subjects.
Let's assume x represents the number of hours for mathematics and y represents the number of hours for economics.
| Hours of Study for Mathematics (x) | Hours of Study for Economics (y) |
| ---------------------------------- | -------------------------------- |
| 6 (half of the total hours) | 6 (half of the total hours) |
| 9 (6 + 3) | 3 (6 - 3) |
| 12 (6 + 6) | 0 (6 - 6) |
| 3 (6 - 3) | 9 (6 + 3) |
| 0 (6 - 6) | 12 (6 + 6) |
b) To plot the production possibilities data in a graph, we can use the hours of study for mathematics (x) on the x-axis and the hours of study for economics (y) on the y-axis.
The graph would show points (6, 6), (9, 3), (12, 0), (3, 9), and (0, 12) representing the combinations of study hours for each subject.
c) Yes, this production possibilities curve reflects the law of increasing opportunity cost. The trade-off between the two subjects is represented by the fact that as more hours are allocated to one subject, the grade in that subject increases while the grade in the other subject decreases. This indicates that the opportunity cost of gaining higher grades in one subject is the loss of grades in the other subject.