Question

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 $\mathrm{c}$ and $\mathrm{d}$ are not the same? What does this imply about the slope of the production possibility frontier?

Short answer

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

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.

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.

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.

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.

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).

Key concepts

Opportunity Cost

Opportunity cost is a crucial concept in economics, helping to understand the cost associated with choosing one option over another. In the context of Atlantis, when the inhabitants decide to grow more potatoes, they have to give up some potential fish catch due to limited resources. This trade-off reflects the opportunity cost. For instance, when increasing potato production from 600 to 800 pounds, they lose 200 pounds of fish, making that amount the opportunity cost for those additional potatoes. On the flip side, when raising potato production from 200 to 400 pounds, only 50 pounds of fish are sacrificed, indicating a lower opportunity cost. The difference in these two scenarios showcases how opportunity cost is not always the same, depending on resource allocation and efficiency.

Concave Curve

A concave curve on the Production Possibility Frontier (PPF) signifies varying opportunity costs. Unlike a straight line, which would indicate a constant trade-off rate, a concave PPF shows that as more of one good is produced, the opportunity cost of producing each additional unit increases. This is evident from the increasing cost in terms of fish forgone as more potatoes are produced in Atlantis. The concave nature represents diminishing returns, highlighting that resources are not equally efficient in producing every good. Hence, as the production shifts more towards potatoes, inhabitants start losing out more on fish due to rising inefficiencies, making resource allocation crucial.

Resource Allocation

Effective resource allocation is the key to maximizing the use of available resources on Atlantis. With limited resources like land, labor, and tools, deciding where to allocate them can significantly influence production efficiency. The inhabitants need to weigh their options based on their needs and the PPF. Reviewing points like A through F helps in deciding the best allocation. For example, at point B (800 pounds of potatoes and 300 pounds of fish), resources are divided to suit a balanced production. Allocation should consider the opportunity costs and the demand for each product, ensuring the best possible economic outcome without dipping into unattainable production levels.

Economic Trade-offs

Economic trade-offs involve making decisions that inevitably forgo one thing in favor of another. On Atlantis, choosing between potatoes and fish production embodies this concept. Each point along the PPF represents different trade-offs. Moving along the curve, the islanders must decide what combination of goods satisfies their needs the best. If they choose a higher potato output, more fish need to be given up. These trade-offs not only apply to goods but also to how they invest in technology or improve methods to shift the curve outward, potentially increasing attainable production options. Understanding these trade-offs helps in making informed decisions to achieve economic growth and sustainability.