If the rescue attempt does not materialize as expected, hunger will drive some people into irrational behavior that could compromise safety of the group, in particular if there is still some food. I-based my decision on the belief that we should plan for the six days until we are rescued. Essentially, if the rescue happens earlier, we have consumption below the efficient frontier since we would have food left over when the rescue ship arrives. If the rescue takes longer than six days, we will have run out of food. However, we will have optimal health at that point given the information at hand when the allocation decision was made. The frontier will have shifted, which means that we will have consumed beyond the actual frontier, although we consumed at the expected frontier.

For eight people and six days, efficient consumption is 2.083% of the food per day per person. This, then, is my allocation. This is not likely going to be enough food to satisfy each person on the island. However, if each person ate to their heart's content, we would likely starve. We could survive six days, but our health would be compromised. The benefit that underlies my decision then is survival. With a small amount of food each day, we can sustain ourselves (however poorly) until rescue occurs. A rationing device is needed. Typically, this is price, but can be other things such as government intervention. In this scenario, I represent the government as I have been given unique authority to make this decision. Thus, I am the rationing device, taking the place of government intervention in the marketplace (or replicating the Communistic role of government in the island's economy). The decision is based on the benefit that I have deemed most important. Survival trumps comfort and minor health risks. The...

(2010). Economics basics: Production possibility frontier, growth and opportunity cost and trade. Investopedia. Retrieved January 15, 2010 from http://www.investopedia.com/university/economics/economics2.asp
Arnold, R. (2008). Economics. Mason, OH: South-western Cengage Learning