Why Non-monetary Opportunity Costs Cannot be Converted

In a previous post, the following opportunity cost problem was re-published and answered with respect to a definition of OC not repeated here. Note that the emphasized sentence below is extraneous for the non-monetary answer presented.

You won a free ticket to see an Eric Clapton concert (which has no resale value). Bob Dylan is performing on the same night and is your next-best alternative activity. Tickets to see Dylan cost $40. On any given day, you would be willing to pay up to $50 to see Dylan. Assume there are no other costs of seeing either performer. Based on this information, what is the opportunity cost of seeing Eric Clapton? (a) $0, (b) $10, © $40, or (d) $50.

Claimed monetary answer = (b)$10.
Non-monetary answer is the combined subjective benefit package consisting of the desired effect of the subjective satisfaction of seeing the Dylan concert and the undesired effect of giving up $40.

The emphasized sentence is the fundamental step used in trying to convert a non-monetary OC to a monetary one.

What I will attempt to show below is not that this step is invalid in and of itself, but rather that the result is not an opportunity cost, but something else entirely with different characteristics. Furthermore, the problem is not limited to money, but exists for any exchange-valued good that is attempted to be used instead.

A three position shelf contains a choice of three free apples. On the left is a fresh apple. In the center is a one-day-old apple. On the right is a two-day-old apple.

It is presumed that you would rank order your subjective preferences in choosing and consuming the apples from left to right, from newer to older. You are allowed to choose only one of the three.

The non-monetary opportunity cost of choosing the left-hand apple is the precluded benefit of the second best choice. In this case, the subjective satisfaction of choosing and consuming the one-day-old apple in the center.

Assume the following assertion :

On any given day you would be willing to sacrifice up to 7 strawberries in order to acquire and consume the center, day-old, apple.

This might come into play if someone else were competing against you for the center apple, for example.

Following the sense of attempts to convert to monetary opportunity costs, the opportunity cost of the left-hand apple would be 7 strawberries, what you would be willing to give up for the center apple.

The assumption at this point is that you are willing to give up 7 strawberries in order to get the center apple, and not be left with the right-hand apple.

We now need to consider what happens if the right-hand apple is not 2 days old, but two months old, and rotten.

Would it not be reasonable to assume that you would now be willing to give up more strawberries, say 18, to get the center apple and not be left with what is now a rotten apple?

Or what if the right-hand apple were not 2 days old, but one day and one hour? Maybe just 1 strawberry would now be all that the center apple is worth relative to the right-hand apple.

So we now have three choices as to what the opportunity cost of the left-hand apple, expressed in strawberries, is, 7, 18 or 1, depending on the characteristics of the right-hand apple. It should be easy to see that substituting dollars for strawberries doesn't really change anything of significance here.

However, the non-monetary opportunity cost of the left-hand apple is the subjective satisfaction of consuming the center apple, and is completely independent of the characteristics of the right-hand apple.

Calling both of these distinctly different situations by the same name, 'opportunity cost', would seem to be unreasonable. In the case where either strawberries or money is involved, we need to invent some new descriptive name, something like 'upgrade cost.'

Share this

IANAE, but does the Austrian

IANAE, but does the Austrian insistence on 'ordinal' value ranking of preferences in any way preclude the concept of intersubjectively valid opportunity costs?

I would think methodological

I would think methodological individualism would preclude intersubjectivity of value, and therefore opportunity costs.

"However, the non-monetary

"However, the non-monetary opportunity cost of the left-hand apple is the subjective satisfaction of consuming the center apple, and is completely independent of the characteristics of the right-hand apple."

This seems like a total nonsequitur from the rest of your post, and false too. Of course you get more subjective satisfaction from consuming fresh fruit when your alternative is picking through people's garbage.

You know, this is oddly

You know, this is oddly puzzling. Indeed, the problem arises from an artificial effort to monetized subjective preferences - but not from the effort to quantify them!

Three scenarios:

A. The Dylan problem: Opportunity cost is defined as the NET benefit of the best choice you must forsake in order to get your first choice - that is, the benefit of your second choice (quantified at $50) minus the opportunities you forsake for your second choice (quantified at $40).

B. The apple problem: Analogously, the opportunity cost of choosing the fresh apple is the net benefit of the best choice you must forsake in order to get that apple - that is, the benefit of the day-old apple minus the opportunity to pick the third-choice apple. So by changing the value of that third-choice apple, you change the opportunity cost of choosing the fresh apple. But that makes no intuitive sense!

C. The money problem: You may freely pick one of three bills: a $10, a $5, or a third bill which is unknown, but has a value < $5. What is the opportunity cost of picking the $10?

First observation: If you conclude that B. and C. are analogous, then you must conclude that the problem with 2. does not arise from monetizing or quantifying subjective preferences.

Second observation: A. is not analogous to B. and C. In the Dylan problem, the opportunity cost of the second choice (the $40 you’d have to pay for a Dylan ticket) reflects a benefit that you can enjoy IN CONJUNCTION WITH enjoying your first choice (Clapton). That is, if you go to the Clapton concert, you get to keep your $40. In contrast, scenarios B. and C. do not let you retain the benefit of forsaking a third choice apple or bill IN CONJUNCTION WITH choosing a first-choice apple or bill.

To put it another way, we take consideration of the cost of a second-choice option only if it has some potential to influence behavior. If I were to reduce the cost of a Dylan ticket low enough (perhaps below $0 even), you’d eventually choose to go to the Dylan concert rather than the Clapton one. In contrast, I cannot see how reducing the value of the third-choice apple or third-choice bill would ever influence your first-choice of apples or bills. The lost opportunity to make a third choice does not qualify as an “opportunity cost.”

I think you're playing a

I think you're playing a switcheroo with cost and value.
The opportunity cost of the best apple is the second best apple,
since we can choose one or the other. But the difference between
values of the apples is what we would hypothtically give to have one
apple rather than the other.

If we want to try to measure the opportunity cost of the best apple (in dollars or strwberries), we should use the value of the second apple, not the opportunity cost.

Nobody and George, Some

Nobody and George,

Some excellent points.

You are standing at a bus stop at a fork in the road. You can get home by waiting for the bus, or by walking, taking the left fork or taking the right fork.

If you wait for the bus, you will find a $10 bill on the back seat of the bus.

If you take the right fork, you will find a $5 bill on the sidewalk, and have no economist's qualms about picking it up.

If you take the left fork, the bill on the sidewalk is unknown, but is less than $5.

The order of preference will be bus, right fork, left fork.

At this point, the opportunity cost of taking the bus is $5, the value of the right hand fork.

The right hand fork is actually a public toll sidewalk, with a toll of $1.

Now the opportunity cost of taking the bus is $4, the net value of the right hand fork. For simplicity, the bill to be found on the left hand fork will from now on be less than $4 so as to maintain the preference order.

The right hand fork has been taken private and you now need to buy a subscription to be allowed to pay the $1 toll.

What is the most you would pay for a subscription, ignoring the left fork?

If you were to pay $1, the opportunity cost would be the new $3 net value.

If you were to pay $2, the opportunity cost would be the new $2 net value.

If you were to pay $3, the opportunity cost would be the new $1 net value.

If you were to pay $4, the new opportunity cost would be the new $0 net value. This is the most you would pay and agrees with the $4 net value if no subscription was needed.

If we now bring the left fork into play, the opportunity cost isn't affected. It is still the net value of the right fork. That is, $5 minus the $1 toll minus the actual subscription price paid.

However, it does affect the maximum you would pay for a subscription. You would pay no more than would reduce the net value of the right hand fork to that of the left hand fork, whatever it might be, still less than $4.

Attempting to summarize, a question of the form "How much would you be willing to pay?" is not a necessarily a valid method of determining value, and thus opportunity cost. Instead, it indicates how much profit can be sacrificed before killing a potential exchange.

Regards, Don

hmm... george is right.

hmm...

george is right. perhaps some additional thinking:

wikip defines opportunity cost as 'the cost of something in terms of an opportunity forgone', and proceeds to use the guns and butter example.

opportunity cost exists only in the context of scarcity, i.e. fundamentally in the context of an *economy*. economies are defined as fluid markets or exchanges of value where the unit of value, the currency, is scarce. (if the unit of value is not scarce, then it cannot act as a store of value.)

if you have $10 then you can use it to buy all guns, all butter, or a mix of the two, and your opportunity cost of buying 10 guns is 10 butters (assuming they both cost $1).

the way they use the example does not seem to imply *net* benefit, but simply the entire sum of what you weren't able to do/get. you like both guns and butter, so you'd like to be able to take your $10 and buy 10 guns and 10 butters, but you can't--money is scarce. so the opp. cost is what you potentially lost.

in your apple example, what is scarce is the space in your stomach. in an ideal world, you would eat all three apples--but you can't. the opportunity cost of eating the freshest apple is either the 1-day old or 2-day old apple. please note the added complexity of a 3-way choice. and the fact that the opportunities are all apples makes it confusing.

imagine that the opportunities are an
apple
orange
banana

you only have room in your tummy for one. so, the opportunity cost of the apple is either an orange or a banana. --> but not *both*. because you never could have eaten both. this would be like adding tricycles to the world of guns and butter. it's a third dimension.

the bus-ride example of yours is interesting too. i think george's point applies here too-- you have quietly taken money and removed it as the store of value, and put it back in as the benefit.

what is scarce in your bus example? it's the trip, isn't it? you can only take one trip home. you have to decide which to take. it's like having three glasses in front of you. one has a quarter in it, one has a nickel and one has a dime. what is scarce? it's the artificial constraint of only being able to choose one. which do you choose? the one with most money i guess, right? so the benefit is the money you receive. but you are basing your choice of cups on optimizing what you perceive in the outside world as a store of value. adding subscriptions or other calculations in just makes it a math problem-- ultimately what does it work out to?

imagine if you said you had 10 guns and you could either use them to buy a $10 bill or a $20 bill, what is the opportunity cost of buying the $10 bill? you could come up with an answer, but it really has a kind of nonsense quality to it. in an economics problem, the "money" is what is traded for end benefit. making money the end benefit for which other things are traded is a little odd.

my .02.

dan

In the apple example, the

In the apple example, the opportunity cost of the left apple remains the same- the center apple, what changes is your subjective valuations of the two apples. In other words, the opportunity cost doesn't change (the center apple), what does change is what each individual apple is worth to you.

This is all true if strawberries are only used as a unit of account, but by introducing strawberries as a tradeable commodity that you can use to "upgrade" to the next best apple (read: purchase) the situation is a bit more complicated. If you are willing to spend 7 strawberries to upgrade to the center apple, then you are most assurredly willing to spend 7 plus x strawberries to upgrade to the left apple. The opportunity cost of the left apple is now the center apple plus x strawberries. This increases the value of the opportunity cost of the left apple even more than just simply noticing that the right apple is rotting. Now the value of the opportunity cost of the left apple is whatever you value the center apple at PLUS whatever you value those three strawberries at.

The problem is equating value with cost. A candy bar may cost you $1, but you value that $1 differently depending on how much money you have, how much money you like to keep handy, any emotional attachment you had to that one dollar bill that you grandma gave you right before she died, etc.

dano- I don't think it has a nonsense quality to it, it is just nonsensical to deliberate between 20$ and 10$ because they are already in the same units.

Spooly, You make a number of

Spooly,

You make a number of valid points.

This is all true if strawberries are only used as a unit of account, but by introducing strawberries as a tradeable commodity that you can use to “upgrade” to the next best apple (read: purchase) the situation is a bit more complicated. If you are willing to spend 7 strawberries to upgrade to the center apple, then you are most assurredly willing to spend 7 plus x strawberries to upgrade to the left apple. The opportunity cost of the left apple is now the center apple plus x strawberries. This increases the value of the opportunity cost of the left apple even more than just simply noticing that the right apple is rotting. Now the value of the opportunity cost of the left apple is whatever you value the center apple at PLUS whatever you value those three strawberries at.

I'm having trouble making this all click.

Have you accounted for the following facts? --

1. The value of the left hand apple, the one for which we are attempting to find the opportunity cost, cannot have any effect other than remaining the preferred choice.

2. The strawberries themselves cannot be part of any opportunity cost unless they are precluded by the choice of the left hand apple.

3. No opportunity cost can ever actually be realized. It is a projected hypothetical imagined by the chooser.

None of the above necessarily have anything to do with your presentation. I'm just trying to see there is any modification that might bring it into focus for me.

Thanks, Don

1. Agreed, the left apple is

1. Agreed, the left apple is still valued higher than the combined value of the center apple plus x strawberries.

2. You are certainly giving up x strawberries to make the upgrade, regardless of what the strawberries are used for. This may be confusing because we think of the problem looking like this initially:

Left apple - x strawberries > center apple

This represents the both choice packages, on the one hand you can have the left apple but give up some strawberries, on the other you can have the center apple. But we don't care about the opportunity cost of the left apple minus x strawberries, we care about the opportunity cost of just the left apple, so by adding x strawberries to both sides, we end up with:

Left apple > center apple + x strawberries

This still may be confusing if we think of x strawberries as money and not something we can consume. In this case, think of the formula like this:

Left apple > center apple + the best thing you could do with x strawberries

The best thing you could do with x strawberries could be anthing from eating them to giving them up get a glass of water. So you are actually choosing between either the left apple or the center apple and whatever you would buy with x strawberries, including flat out eating the strawberries. Assuming you would have gotten the glass of water to go along with the center apple, our formula is now:

Left apple > center apple + glass of water

3. Agreed. I think i cleared this one up in 2.

Hopefully this clarifies things a bit.

Spooly, Since we are talking

Spooly,

Since we are talking about opportunity cost, the left hand apple could be solid gold and not have any effect.

When we determine the value of the second best choice, the opportunity cost of the first choice, the first choice can be assumed to not exist at all.

Any assumption about the degree of preference for the left hand apple over the center apple is unwarranted, even if it were not rendered moot by this being an opportunity cost problem. Not being an eater of apples myself, I'm not even sure that a fresh apple is better than a day old one, and certainly not that the degree of preference for a fresh apple over a day old one is greater than for a one day old apple over a two day old one.

Thanks, Don

Hmm, now Im unsure. Either

Hmm, now Im unsure. Either there is no opportunity cost of the left apple, but an opportunity cost of the "left choice" (the left apple minus x strawberries) which is the center apple, or the opportunity cost of the left apple is the center apple plus either x strawberries or whatever those strawberries are spent on.

The strawberries still have to be part of the pictue if you can give some up to go from the center apple to the left apple. If you can give up some strawberries to go from right to center, the you presumably you can give some up to go from center to left. But if the strawberries are simply a unit of account and not a tradeable commodity that you can use to upgrade your apple position, then the strawberries don't matter in terms of opportunity cost.

Spooly, One way we can

Spooly,

One way we can eliminate the confusion is to say that no willing counter-party necessarily exists. All we have said is that we would have been willing to make a particular exchange of up to so many strawberries. This is true whether we can find someone to trade with or not.

Regards, Don