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Chapter 2: Problem 16

Atlantis is a small, isolated island in the South Atlantic. The inhabitants grow potatoes and catch 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. $$ \begin{array}{c|c|c} \begin{array}{c} \text { Maximum annual } \\\ \text { output options } \end{array} & \begin{array}{c} \text { Quantity of } \\\ \text { potatoes (pounds) } \end{array} & \begin{array}{c} \text { Quantity of } \\\ \text { fish (pounds) } \end{array} \\\ \text { A } & 1,000 & 0 \\\ \text { B } & 800 & 300 \\\ \text { C } & 600 & 500 \\\ \text { D } & 400 & 600 \\\ \text { E } & 200 & 650 \\\ \text { F } & 0 & 675 \end{array} $$ a. Draw a production possibility frontier with potatoes on the horizontal axis and fish on the vertical axis illustrating these options, showing points \(A-F\) b. Can Atlantis produce 500 pounds of fish and 800 pounds of potatoes? Explain. Where would this point lie relative to the production possibility frontier? 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 \(\mathrm{c}\) and \(\mathrm{d}\) are not the same? What does this imply about the slope of the production possibility frontier?

Short Answer

Expert verified
Answer: The different opportunity costs and the concave shape of the PPF imply that Atlantis experiences increasing opportunity costs as more resources are allocated to the production of one good (potatoes) at the expense of the other good (fish). This suggests that the resources used for the production of these goods are not perfectly substitutable, and as a result, reallocating resources becomes less efficient as production increases.

Step by step solution

01

a. Drawing the production possibility frontier

To draw the PPF, we plot the maximum output options (points A to F) on a graph with the quantity of potatoes on the horizontal axis and the quantity of fish on the vertical axis. Connect the points to form the PPF.
02

b. Analyzing production possibility of 500 pounds of fish and 800 pounds of potatoes

Comparing the given output combinations, it's evident that Atlantis cannot produce 500 pounds of fish and 800 pounds of potatoes simultaneously, since that combination is not listed as one of the maximum output options. This point would lie outside the PPF, indicating that it is not currently attainable by the island with its existing resources and technology.
03

c. Calculating the opportunity cost (600 to 800 pounds of potatoes)

The opportunity cost of increasing the output of potatoes from 600 to 800 pounds can be determined by comparing the output options C and B. When the potato production increases from 600 to 800 pounds, fish production decreases from 500 to 300 pounds. Therefore, the opportunity cost of producing an additional 200 pounds of potatoes is a loss of 200 pounds of fish.
04

d. Calculating the opportunity cost (200 to 400 pounds of potatoes)

The opportunity cost of increasing the output of potatoes from 200 to 400 pounds can be determined by comparing the output options E and D. When the potato production increases from 200 to 400 pounds, fish production decreases from 650 to 600 pounds. Therefore, the opportunity cost of producing an additional 200 pounds of potatoes is a loss of 50 pounds of fish.
05

e. Explaining the different opportunity costs and the PPF slope

The answers to parts c and d are different because the opportunity cost of producing more potatoes is not constant along the PPF. This implies that the PPF is not a straight line, but rather a concave curve. The slope of the production possibility frontier represents the opportunity cost of production, and a concave PPF indicates that the opportunity cost increases as more resources are allocated to the production of one good (potatoes, in this case), and fewer resources are used for the other good (fish).

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