Lifeboat Economics

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You're the purser of the Titanic and it has just hit an iceberg.

 You've escaped into a lifeboat with an 80 pound bag of gold, an 80 pound bag of silver, and an 80 pound bag of copper. The lifeboat starts to flounder* from being overloaded. You push Al Gore over the side, quieting and improving the lifeboat environment, but the lifeboat is still overloaded.

It is now clear that you will only be able to salvage one of the 80 pound bags if the lifeboat is to stay afloat.

You choose to save the gold bag, and toss the silver and copper bags into the Atlantic.

If this were an opportunity cost problem, then the opportunity cost would the second best choice, i.e. the 80 pound bag of silver. However, it is clear that the actual cost or sacrifice of saving the gold bag is the combination of both the silver and copper bags (and Al Gore, but he doesn't count).

QUESTIONS :

If this is an opportunity cost problem, why is the opportunity cost not equal to the standard opportunity cost definition? (the silver bag alone)

If this is not an opportunity cost problem, why not, and what is it?

These are not known to be trick questions, but they are currently open questions with no known answers.

 

* = Usage Note: The verbs founder and flounder are often confused. Founder comes from a Latin word meaning "bottom" (as in foundation) and originally referred to knocking enemies down; it is now also used to mean "to fail utterly, collapse." Flounder means "to move clumsily, thrash about," and hence "to proceed in confusion." If John is foundering in Chemistry 1, he had better drop the course; if he is floundering, he may yet pull through.

 

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My guess is that this is not

My guess is that this is not a typical opportunity cost problem because it involves the uncertainty of life or death (which have undefinable monetary value) and the bags of various metals (which do have definable monetary value, but only if there is a market for them).

The problem with choosing any of the bags is that it assumes that you are going to be rescued. If you are not rescued in this scenario, none of the bags have any value. If you were in warmer waters and were not rescued but ended up on a deserted island, the copper bag would be propbably be worth the most because you could, after creating fire and some kind of smelt (big assumption), make tools. Of course, if you and your lifeboat mates got comfortable with cannabalism, Al Gore might make a better choice than the copper.

Patinator, My guess is that

Patinator,

My guess is that this is not a typical opportunity cost problem because it involves the uncertainty of life or death (which have undefinable monetary value) and the bags of various metals (which do have definable monetary value, but only if there is a market for them)....

This doesn't matter since all economic actions are purposeful without any requirement on future reality or rationality of purpose. All that matters here is that the choices are ranked in order of perceived future value, but it doesn't matter what the values might actually turn out to be or even if the ranking actually turns out to be correct.

Regards, Don

 

The answer is obviously that

The answer is obviously that the bag of silver and copper are a sunk cost.

Seriously I don't know though :)

I'm probably floundering

I'm probably floundering here myself, but generally when we discuss opportunity costs we're talking about the next best alternative to a choice someone's made to improve their welfare. In the lifeboat example every choice leaves you worse off than you were before the moment of decision. The difference between your new welfare and the original welfare is your sacrifice, and the next least-bad alternative doesn't make sense as an opportunity "cost," because what you're foregoing is a bad outcome in itself.

Opportunity Cost

However, it is clear that the actual cost or sacrifice of saving the gold bag is the combination of both the silver and copper bags (and Al Gore, but he doesn't count).

Not as I see it. The cost of saving the gold bag can't be the combination of both the silver and copper bags, because you don't have the opportunity to save both the silver and copper bags. If it's simply not possible to do something, you can't really be said to be giving up the opportunity to do it, so it can't be considered an opportunity cost.

Think of it this way: What do you have to give up to save the bag of gold? You give up the option to save either the bag of copper or the bag of silver (or Al Gore, but that's straying into Hobson territory). Assuming that you always prefer the silver to the copper, the value of that option is equal to the value of the bag of silver. So essentially you're giving up the bag of silver to save the bag of gold. That's why it's the opportunity cost.

Brandon,  Yes, I think

Brandon,

 Yes, I think that you're right.

My problem was that the word cost seemed to work in precisely the wrong direction. If I have to chose between two nearly identical one ounce gold coins, the rejected one is the opportunity cost. If the rejected coin was a copper penny, that would be the opportunity cost. It's counter-intuitive that the higher valued rejected coin is associated with a higher cost.

The solution is apparently to take every place that I see the phrase 'opportunity cost' and think 'alternate benefit precluded only by choice.'

Regards, Don