. Atlantis is a small, isolated island in the South Atlantic. The inhabitants grow potatoes and catch fresh fish. The accompanying table shows the maximum annual output combinations of potatoes and fish that can be produced. Obviously, given their limited resources and available technology, as they use more of their resources for potato production, there are fewer resources available for catching fish.
Maximum annual output options
Quantity of potatoes Quantity of fish
(pounds) (pounds)
A 1,000 0
B 800 300
C 600 500
D 400 600
E 200 650
F 0 675
a. Examine the Maximum annual output options table above and the resulting Production Possibility Frontier Graph below and answer parts b - f.
Production Possibility Frontier Graph
b. Can Atlantis produce 500 pounds of fish and 800 pounds of potatoes? Explain.
c. What is the opportunity cost of increasing the annual output of potatoes from 600 to 800 pounds?
d. What is the opportunity cost of increasing the annual output of potatoes from 200 to 400 pounds?
e. Can you explain why the answers to parts c and d are not the same?
f. What does this imply about the slope of the production possibility frontier?
what the answer ?
b. To determine if Atlantis can produce 500 pounds of fish and 800 pounds of potatoes, we need to locate these quantities on the production possibility frontier (PPF) graph. If the point (800, 500) lies on or within the PPF curve, then Atlantis can produce this combination.
c. The opportunity cost of increasing the annual output of potatoes from 600 to 800 pounds can be calculated by observing the change in fish quantity. Since the PPF shows a tradeoff between potatoes and fish, the opportunity cost of increasing potato production is the decrease in fish production. In this case, the opportunity cost would be the decrease in fish production from 500 to 300 pounds.
d. Similarly, the opportunity cost of increasing the annual output of potatoes from 200 to 400 pounds can be calculated by observing the change in fish quantity. The opportunity cost would be the decrease in fish production from 650 to 600 pounds.
e. The answers to parts c and d are not the same because the PPF is concave (curved inward). This concavity indicates that the opportunity cost of producing more potatoes increases as more potatoes are produced. In other words, the more resources are shifted from fish to potatoes, the larger the tradeoff in terms of fish production. So, as Atlantis produces more potatoes, the opportunity cost of each additional pound of potatoes increases.
f. The concavity of the PPF implies that the slope of the production possibility frontier is not constant. Initially, when Atlantis is producing fewer potatoes, the slope is not as steep, indicating a lower opportunity cost of potatoes (in terms of fish). As Atlantis produces more potatoes, the slope becomes steeper, indicating a higher opportunity cost for each additional pound of potatoes (in terms of fish). This reflects the diminishing marginal returns of resources as they are allocated to different activities.