Opportunity Cost, Yet Again

While I am temporarily unable to reference my previous posts, there is really no need. The following is from Marginal Revolution -- O C Problem

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, (c) $40, or (d) $50.

It is now clear that none of these answers is correct, and this is true even if there is no variation in the value of money.

Step 1 - Use all of the information in the problem to rank the possible subjective choices.

1. Free Eric Clapton Concert
2. $40 Bob Dylan Concert
3. $49.99 Bob Dylan Concert
4. Greater Free Generic Concert
5. $50.01 Bob Dylan Concert
6. Lesser Free Generic Concert

Here items 4 and 6 are stand-ins for whatever you would choose to do if neither Clapton or Dylan were performing.

The statement 'On any given day, you would be willing to pay up to $50 to see Dylan' implies that, with no Clapton possible, a Dylan ticket price of greater than $50 would result in you choosing whatever else is available that you value most.

From the ranking above, the opportunity cost of attending the free Clapton concert is the precluding of attending the Dylan concert with a $40 ticket.

In general, the best definition of an opportunity cost of action or choice A is the perceived benefit of a second-best package B of advantages and disadvantages that is precluded by the choice of A.

To see that the willingness to pay a $50 ticket price has no relevance to the opportunity cost pretend that item 4 ( the Greater Free Generic Concert) has improved by practicing, and now includes showgirls and a fireworks display. Because of the improved substitute, it is entirely plausible that your willingness to pay $50 for a Dylan ticket has now been reduced to $45, or even as low as $40.01 to keep the problem specifics the same.

Under this condition, the opportunity cost of the Clapton concert is still the exact same $40 ticket Dylan concert.

As a simpler example, how much would you be willing to pay for a chocolate ice cream cone? $2?

Same question, but everyone who enters the shoppe gets a free vanilla ice cream cone? Assuming that you prefer chocolate, maybe $0.50?

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You don't think the line "On

You don't think the line "On any given day, you would be willing to pay up to $50 to see Dylan" deals with your objection? Seems to me that means that you would always be willing to pay $50 for Dylan (unless free Clapton is an option), regardless of what other bands are playing and how much they've practiced.

Glen, You don’t think the

Glen,

You don’t think the line “On any given day, you would be willing to pay up to $50 to see Dylan” deals with your objection? Seems to me that means that you would always be willing to pay $50 for Dylan (unless free Clapton is an option), regardless of what other bands are playing and how much they’ve practiced.

Not at all. Remember that the generic concerts are stand-ins. Maybe the real third choice is taking a nap, if neither Clapton or Dylan are performing, for example.

The nap can be something that is highly or lowly valued. If the nap is highly valued, then you might be willing to only pay $10 for the Dylan concert, as it not that much better than a nap. If the nap is lowly valued, you might be willing to pay $100 to go to the Dylan concert instead.

The amount you are willing to pay relates to the value relationship, not just the ranking, between the opportunity cost of the Clapton concert (the $40 Dylan concert) and ITS opportunity cost (the nap).

The $40 Dylan concert is the opportunity cost of the Clapton concert. There is no reason why that should be affected by the number and values of even lower ranked alternatives. But the willingness to pay is always related to how much subjective valuation you lose if you must pass on the Dylan concert.

Regards, Don

Tom, Given your assumptions,

Tom,

Given your assumptions, your conclusions probably aren't far off. The problems relate to both the definition of OC used and the purpose of money. I can't deal with these in a comment, so I'll try to restate the general problem.

Start with a condition where no concerts are being held. You have to be doing something, reading from your private book library, watching TV, or napping, etc. Presumably you will be pursuing the activity that ranks highest on your individual subjective value scale.

Assume that the highest ranked activity is reading from your private book library. Also assume that you have $200 in your wallet. If you had $300, you would rank that activity state combination higher, and if $100, lower.

Bring in the additional choice of attending a Bob Dylan concert. If you say that you would be willing to pay up to $50 for a ticket, what do you really mean?

a. You would still choose reading and a $200 wallet content over attending the Dylan concert and $149.99 or less wallet content.

and b. You would choose attending the Dylan concert and a wallet content of $150.01 or greater over reading and a $200 wallet content.

However, what happens if you allow the reading quality and satisfaction of your book library to vary?

Then your willingness to pay for a concert ticket must logically vary as well. The higher the reading quality and satisfaction of your book library, the less you would be willing to pay for a concert ticket.

The attending of the actual Dylan concert, with a ticket price of $40, will fall on your subjective value scale at the point where the combination of the satisfaction due to the performance and a $160 wallet content place it.

This does not change with your willingness to pay. Your willingness to pay reflects the lower quality and satisfaction due to your book library relative to the concert and the $160 wallet content, in other words the subjective drop-off of the 3rd choice relative to the 2nd.

Thus, the opportunity cost of the free Clapton concert and a $200 wallet content IS the Dylan concert and a $160 wallet content, independent of what the 3rd through nth choices might be.

I'll stop here, as the above will be hard enough to understand.

Regards, Don

I've been puzzling over this

I've been puzzling over this since the original post appeared at Marginal Revolution. You've challenged me to think it through, and so I have. But I don't come to the same conclusion as you do.

Let's start with a definition of opportunity cost. Here's one, with an example, by economist David Henderson:

When economists refer to the "opportunity cost" of a resource, they mean the value of the next-highest-valued alternative use of that resource. If, for example, you spend time and money going to a movie, you cannot spend that time at home reading a book, and you can't spend the money on something else. If your next-best alternative to seeing the movie is reading the book, then the opportunity cost of seeing the movie is the money spent plus the pleasure you forgo by not reading the book.

Okay, using that definition, and the example for guidance, here's how I read the original problem, as stated in Alex Tabarrok's post at MR:

1. If you choose to use the free Clapton ticket you reveal that it is your best use of that block of time, all monetary considerations included.

2. Going to the Dylan concert is your next-best use of that block of time. (Your other options aren't in the original problem, so I disregard them here.)

3. What you give up by not going to the Dylan concert is the opportunity cost of going to the Clapton concert, which is what the problem asks us to evaluate.

4. The thing you give up is seeing Dylan. But to see Dylan would cost you $40. However, you are willing to pay $50 to see Dylan, so you give up what Tabarrok calls a "net benefit" of $10. ("Net benefit" also is known as "consumer's surplus.") That's the opportunity cost of going to the Clapton concert.

What's relevant is the benefit (or value) you forgo by attending the Clapton concert. That isn't measured by the price of a Dylan ticket, but by the value you place on the Dylan ticket, minus its price, which is $10. This means that the Clapton ticket is worth at least $10 to you: the net benefit of seeing Clapton must be at least as great as the net benefit you forgo by not seeing Dylan.

Anyway, that's my take. Any thoughts?

Tom, The problem is to

Tom,

The problem is to measure the opportunity cost of going to the Clapton concert if the next-best alternative is going to the Dylan concert, as the problem stipulates....

Not trying to be argumentative, you have to understand that Austrian Subjective Value Theory places a strong emphasis on the fact that subjective values cannot be measured, and especially, that they cannot be measured with money.

Subjective values can only be ranked in order of preference, and the preferences can only be demonstrated in action by actual choices between alternatives.

In this light, when you say "The problem is to measure the opportunity cost...", you are also changing the original problem, which asked what the opportunity cost IS.

Be that as it may, part of the confusion likely comes from the fact that there are two different types of opportunity cost. There is an opportunity cost which is entirely financial in nature, and has no subjective components. As an example, a company that invests $1M in a new machine incurs an opportunity cost of no longer being able to make a next-best investment, possibly a certificate of deposit paying a 10% annual interest rate.

The current problem relates to subjective choice, and happens to include money, but is not primarily about money.

Regards, Don

Tom, You’ve changed the

Tom,

You’ve changed the problem by introducing new “facts” – both in your original post and in your reply to my comment. That’s fine if you want to pose a different opportunity cost problem, but the answer to the one replicated in Alex Tabarrok’s post is $10. That’s my point.

New "facts" have to be introduced since their lack is what makes the given problem/solution invalid.

Ask yourself the following question :

You are standing in a long line at the airport ticket counter. How much would you be willing to pay to go to the head of the line?

How can you answer this question without considering where you currently are in the line? Wouldn't you likely be willing to pay much more if you are 100th in line than if you are 2nd?

Wouldn't you be willing to pay more for a concert ticket if the alternative is reading a boring book than if reading an exciting one?

Regards, Don

Don, "My" assumptions are

Don,

"My" assumptions are nothing more than the "facts" stated in the original problem. There's nothing in the problem about what "I" am doing instead of choosing between Dylan and Clapton. You've read too much into the quotation I provided. My actual analysis (steps 1 through 4 in my comment) has nothing to do with reading books or the amount of money in my wallet, just as the original problem has nothing to do with those things.

The problem -- as originally stated, and as I analyzed it -- revolves around the choice between Clapton and Dylan. And given the assumptions of the original problem, the opportunity cost of seeing Clapton is $10, as I showed.

You've changed the problem by introducing new "facts" -- both in your original post and in your reply to my comment. That's fine if you want to pose a different opportunity cost problem, but the answer to the one replicated in Alex Tabarrok's post is $10. That's my point.

Can you show us how -- when you stick to the "facts" of the original problem -- that the opportunity cost is something other than $10?

Cheers,
Tom

Don, This may not change

Don,

This may not change your mind, but here goes:

The problem is to measure the opportunity cost of going to the Clapton concert if the next-best alternative is going to the Dylan concert, as the problem stipulates. In other words, if you choose the Clapton concert it is, by definition, your best alternative; it is unnecessary to imagine what else you might be doing with your time and money. The rest is straightforward, as I showed in my original comment.

By introducing new "facts" you're changing the problem, not finding a different "right" answer to the stated problem. I think that's the nub of our disagreement.

Perhaps you should try your analysis on Alex Tabarrok and see what he thinks.

Happy trails,
Tom

Don: The problem is that

Don: The problem is that your new facts are inconsistent with facts stated in the problem, namely that "on any given day, you would be willing to spend $50 to see the Dylan concert." If the money in your pocket and your third alternate options made enough difference from day to day to matter to your opportunity cost in this problem, they would affect how much you were willing to pay for the Dylan concert. Obviously, in practice this sort of statement is completely unrealistic. On some days I might be willing to pay 60-70 for some concert, and on other days, I might not go even if it were free, all depending on my other options and situation.

But that's not the problem as stated. In the problem as stated, you are willing to spend up to $50 and o more on Dylan in the absence of the free Clapton concert.

Thus the opportunity cost really is $10, as Tom stated.

Michael

This really is a laugh. I

This really is a laugh.

I deal with questions of "opportunity cost" on a regular basis in my work.

The "value" in Tom Anger's definition (which is an acceptable version) is not just the purchase value.

In fact it is the value of the income stream that that alternative is expected to generate. The value of that income stream includes measure of the purchase price. Substantially, the old tried and true DCF calculation is identical, the difference between the two is the important bit.

"Opportunity cost" is the cost of "not doing".

If Alternative 'A' produces greater revenue than Alternative 'B' then Alternative 'B' should include an opportunity cost representing the revenue foregone from Alternative 'A'. The principle being that the initial cost of 'B' should be sufficiently less than 'A' to allow investment of the difference to produce additional revenue to compensate.

If Alternative 'B' costs less than Alternative 'A' then 'A' has an opportunity cost representing the income foregone that investment of the difference might produce.

Simplistic examples such as that discussed here are stupid and totally misrepresent the idea of "opportunity cost" -

* - The argument starts from an incorrect interpretation of the definition.

* - The examples used (like concert tickets) NEVER produce an income or cost stream over a period of time.

If you want a simple example, try the alternatives of private car, bus, and taxi to travel from office to a meeting 5km across town. Remember that "income streams" can be negative.

Michael, ... On some days I

Michael,

... On some days I might be willing to pay 60-70 for some concert, and on other days, I might not go even if it were free, all depending on my other options and situation.

You have at least gotten part of the situation. Even if every day was the same as every other day, you still could have either high or low valued alternatives to the Dylan concert. The number of dollars you are willing to pay for a ticket is NOT a value measurement of the Dylan concert, but an indication of your relative subjective valuations of the concert and whatever your every day situation is. If the dollar amount you are willing to pay is low then the concert is minimally preferable to your normal every day situation. If the dollar amount is high, then the concert is greatly preferable to the everyday. It works in reverse as well. Higher or lower preference for the concert leads to more or less dollars willing to be paid for a concert ticket.

What is the answer to this simple question?

If both the Clapton and Dylan concerts were free, and you choose to go to the Clapton concert, what would be the opportunity cost of this choice?

The opportunity cost would be the Dylan concert, specifically not being able to attend it.

This answer should generate no controversy among economists. (but I've been shocked before)

Why would the unprovoked statement that I would be willing to pay $50 for a ticket to the free Dylan concert change the opportunity cost? I would be $50 better off attending the free Dylan concert than buying a $50 ticket to it, but I'm not attending the Dylan concert at all. What has this to do with the opportunity cost for the Clapton concert?

Regards, Don

In the second scenario (free

In the second scenario (free Dylan, free Clapton), you are correct. Your opportunity cost is "the dylan concert", or more precisely "the value to you of seeing the dylan concert". What would you say if you were asked to put a dollar amount on your opportunity cost to go to the Clapton concert?

I'd say the closest we could get to putting a dollar amount on the value to you of going to the dylan concert would be your answer to the question "What would you be willing to pay to go to the Dylan concert if it were not free?"

If the answer is $10, then your opportunity cost of going to Clapton would be $10.

In the actual question, you have revealed this preference by stating in the assumptions that you'd pay $50 to go to Dylan. But the Dylan concert is also not free. If Dylan cost $60 and was worth $50, then your opportunity cost wouldn't be the Dylan concert, but some other activity, right?

We can think of the Dylan concert as a security worth $50, and the fact that tickets are available for $40 as if you are holding a non-transferable $40 call option on the concert.

So the opportunity cost of forgoing the dylan concert would be the value to you of exercising the $40 call option to see the $50 Dylan concert, in otherwords, $50-$40 == $10.

Michael

PS, I find it very amusing that I'm using an options analogy to explain a simple purchasing decision, and that I actually believe it will make my position clearer.

Why a Willingness-to-Pay

Why a Willingness-to-Pay Premium Cannot be an Opportunity Cost
While responding to comments on my recent post on Opportunity Cost, it eventually became clear that being willing to pay more than an actual ticket price for a second-best choice cannot possibly called an opportunity cost.
I repeat the Marginal Revolut...

[...] be an Opportunity

[...] be an Opportunity Cost
0 Comments

While responding to comments on my recent post on Opportunity Cost, it eventually became clear that bein [...]

Michael, I’d say the

Michael,

I’d say the closest we could get to putting a dollar amount on the value to you of going to the dylan concert would be your answer to the question “What would you be willing to pay to go to the Dylan concert if it were not free?”

Why would we want to put a dollar amount on the value ... etc.?

Dollar amounts are a} money prices that emerge from the market interactions of of supply and demand for both goods and money, and b) quantities of money that are voluntarily held in order to provide for future needs.

For b), you can equally well ask how many cookies would you be willing to give up for ... etc. The cookies are held to provide for the satisfaction of future hunger. Money is more flexible, but the motive is qualitatively the same.

... What would you say if you were asked to put a dollar amount on your opportunity cost to go to the Clapton concert?

If I had chosen the free Clapton concert over the free Dylan concert, then it would seem to follow logically that I would have been willing to give up at least as much or more for a Clapton ticket as for a Dylan ticket.

I think that may help explain why $50 is not the opportunity cost. To the extent that a free Dylan concert is considered a $50 pseudo-profit given up if I attend the Clapton concert, I instead receive a greater than $50 pseudo-profit from the Clapton concert itself.

Regards, Don

All, See my new post

All,

See my new post entitled "Why a Willingness-to-Pay Premium Cannot be an Opportunity Cost."

Regards, Don