Consider the following production possibilities table:
Option Y X
A 0 100
B 80 80
C 120 50
D 140 10
a)Provide a measure of the approximate marginal opportunity cost of an additional unit of X for each interval. Is the law of increasing cost satisfied? Explain
b) Is the production of 100 units of X and 85 units of Y feasible? Why or why not? If so, is it efficient?
C)Is the production of 80 units of X and 75 units of Y feasible? Why or why not? If so, is it efficient?
a) To calculate the marginal opportunity cost of an additional unit of X, we need to determine the change in Y for each interval divided by the change in X.
For the intervals A to B, B to C, and C to D, the change in Y is 80, 40, and 20, respectively. The change in X is 20, 30, and 40, respectively.
Therefore, we can calculate the marginal opportunity cost of X as follows:
Interval A to B: 80/20 = 4
Interval B to C: 40/30 = 4/3
Interval C to D: 20/40 = 1/2
The law of increasing cost states that as we produce more of a good, the opportunity cost of producing an additional unit of that good increases. In this case, the marginal opportunity cost of X is decreasing as we move from interval A to D (4 -> 4/3 -> 1/2).
Therefore, the law of increasing cost is not satisfied in this production possibilities table.
b) To determine if the production of 100 units of X and 85 units of Y is feasible, we need to check if it falls within the production possibilities curve.
Looking at the table, the maximum production of X is 140 units and the maximum production of Y is 100 units. Since the desired production is within these limits, it is feasible.
To determine if it is efficient, we compare it to the other options on the table. Option C, which produces 120 units of X and 50 units of Y, is more efficient because it produces more X and less Y. Therefore, producing 100 units of X and 85 units of Y is not the most efficient option.
c) To determine if the production of 80 units of X and 75 units of Y is feasible, we again need to check if it falls within the production possibilities curve.
The desired production falls within the limits of the table, so it is feasible.
To determine if it is efficient, we compare it to the other options on the table. Option B, which produces 80 units of X and 80 units of Y, is less efficient because it produces less Y for the same amount of X. Therefore, producing 80 units of X and 75 units of Y is more efficient than option B.