Suppose that two different castaways, Mr. and Mrs. Howell, end up on a different island. Mr. Howell can pick 1 pineapple per hour, or 1 coconut. Mrs. Howell can pick 2 pineapples per hour, but it takes her two hours to pick a coconut. a. Construct a table like Table 2 showing \(\mathrm{Mr}\). and Mrs. Howell's labor requirements. b. Who-Mr. or Mrs. Howell-has a comparative advantage in picking pineapples? In picking coconuts? Which of the two should specialize in which tasks? c. [Harder] Assume that Mr. and Mrs. Howell had originally washed ashore on different parts of the island, and that they originally each spent 12 hours per day working, spending 6 hours picking pineapples and 6 hours picking coconuts. How will their total production change if they find each other and begin to specialize?

Understanding the concept of opportunity cost is essential in evaluating the choices individuals or entities make with respect to optimizing their resources. It refers to the value of the next best alternative that is forgone when making a decision. In simpler terms, it's essentially what you miss out on when you choose one option over another.

For example, if Mr. Howell spends an hour picking a coconut, the opportunity cost is the pineapple he could have picked in that hour, and vice versa. The same goes for Mrs. Howell, only that her opportunity cost for picking a coconut is higher, as she forgoes the chance to pick two pineapples in the same amount of time. Recognizing these costs helps in determining where their time is best invested, essentially guiding them towards specialization, which in this context is choosing the task where they each have a comparative advantage.

Specialization is the process by which individuals or entities focus on the tasks they perform best, often leading to greater overall efficiency and productivity. In the case of Mr. and Mrs. Howell, specializing allows them to maximize their output based on their unique abilities, thereby enhancing their overall productivity on the island.

Mr. Howell's comparative advantage in picking coconuts and Mrs. Howell's in picking pineapples should lead them to specialize accordingly. By specializing in tasks where they have a comparative advantage, the Howells can collectively produce more than if they tried to split their time equally between tasks, thus reducing their opportunity cost and enhancing their total production. This increased efficiency due to specialization is a fundamental concept in economics and can be applied to various scenarios, from individual decisions to large-scale production processes.

The Production Possibilities Frontier (PPF) is a graphical representation that shows the maximum possible output combinations of two goods that can be produced given a set of resources (such as time, labor, and materials). Points inside the frontier represent inefficient use of resources, while points on the frontier represent the most efficient use of resources.

In the Howells' scenario, before they found each other, they were not producing on their PPF because they were dividing their time equally between picking pineapples and coconuts regardless of their comparative advantages. However, after discovering one another and deciding to specialize, their combined efforts would likely place them on the PPF, illustrating the most efficient use of their labor and time. This would be because each person is dedicating all of their labor to where they have the lowest opportunity cost, thereby maximizing their total production potential.