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.$\begin{array}{ccc}\begin{array}{c}\text{ Maximum annual }\\ \text{ output options }\end{array}& \begin{array}{c}\text{ Quantity of }\\ \text{ potatoes (pounds) }\end{array}& \begin{array}{c}\text{ Quantity of }\\ \text{ fish (pounds) }\end{array}\\ \text{ A }& 1,000& 0\\ \text{ B }& 800& 300\\ \text{ C }& 600& 500\\ \text{ D }& 400& 600\\ \text{ E }& 200& 650\\ \text{ F }& 0& 675\end{array}$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 $c$ and $\mathrm{d}$ are not the same? What does this imply about the slope of the production possibility frontier?

Key Concepts: Production Possibility Frontier, Opportunity Cost Explanation: The question is about production possibility frontier and opportunity cost. Step by Step Solution: Step 1. Draw a graph with potatoes on the horizontal axis and fish on the vertical axis. Step 2. Mark the points A, B, C, D, E, and F with the quantities of potatoes and fish corresponding to each point in the production possibilities table. Step 3. Join these points to form the Production Possibility Frontier (PPF). Step 4. Atlantis can produce 500 pounds of fish and 800 pounds of potatoes only if the production point is on or within the PPF. Since the given production point (500,800) falls outside the PPF, Atlantis cannot produce this combination of outputs. Step 5. To increase potatoes annual output from 600 to 800 pounds Atlantis will have to move from point C to B along the PPF. Opportunity cost of this movement is the fish output given up, which is (500-300)=200 pounds. Step 6. To increase potatoes annual output from 200 to 400 pounds Atlantis will have to move from point E to D along the PPF. Opportunity cost of this movement is the fish output given up, which is (650-600)=50 pounds. Step 7. The opportunity cost of increasing potatoes output from 600 to 800 pounds (200 pounds of fish) is higher than the opportunity cost of increasing potatoes output from 200 to 400 pounds (50 pounds of fish). This implies that the slope of the PPF is increasing i.e. the more potatoes Atlantis produces, the greater the opportunity cost, hence the steeper the PPF. Additionally, it shows that resources are not equally efficient in producing both goods, as there is an opportunity cost to shifting resources from one good to another.