<p>The joke is conflating the value of the item you get and the value of the option to determine which item you get.</p>
<hr />
<ol>
<li>Suppose I value the Snickers at <span class="math-container">$\\\$.4$</span> and the M&amp;Ms at <span class="math-container">$\\\$.75$</span>.
If I am offered a Snickers for free my economic profit is <span class="math-container">$\\\$.4$</span>. If I could get the <em>additional</em> option to choose between the Snickers and a bag of M&amp;Ms, rather than just get a Snickers for free, that would be worth an <em>extra</em> <span class="math-container">$\\\$.35$</span> to me. The entire event of getting the Snickers or a bag of M&amp;Ms for free is still worth <span class="math-container">$\\\$.75$</span>.
<br><br>
If, instead of the Snickers, I was offered a free bag of M&amp;Ms, then the <em>additional</em> option to choose from two identical bags of M&amp;Ms would not yield any benefit. The economic profit resulting from the <em>additional option to choose</em> is indeed 0. <br>
Note that compared to getting nothing you are better off if you can choose from two identical bag of M&amp;Ms, but you are not better off compared to getting one bag without the option to choose. This is how we could deduce the value of the option to choose.</li>
</ol>
<br>
<ol start="2">
<li>Similarly, if your options broaden in a decision situation, it is possible that the <em>additional</em> benefit each new option yields diminishes. This is captured by the increasing opportunity cost. It does not mean that the entire value of getting to choose from a wide variety is approaching zero.</li>
</ol>
<hr />
<p>I usually find that opportunity cost examples are overly complicated, perhaps to make the notion seem more intellectually demanding than it really is - therefore I can relate to the joke.</p>
<p>I used to teach microeconomics. With sunk costs it is important to get people to accept that the sunk costs are lost, hence doing something could be worthwhile even if the final outcome yields a loss, as long as the loss is smaller than the sunk cost.</p>
<p>In my experience most students understand the above two sentences perfectly, but they can be greatly confused when trying to pin down opportunity costs. Because of this I was never sure if this was a useful concept to teach.</p>

CC BY-SA 4.0
2021-06-30T12:52:04.447Z
In the meanwhile I'm almost convinced that the concept is rather vague and impossible to formalize. I never teach it.
VARulle
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2021-06-30T13:46:53.873Z
@VARulle I agree, I always found the concept of opportunity costs very "ambiguous", and I've never seen it formalized in a good way. In addition, if you know the value of the second best option, then by definition, you should also know what the best option is. If so, what's the point?
tdm
CC BY-SA 4.0
2021-06-30T12:39:00.113Z
2021-06-30T14:10:16.267Z
2021-06-30T14:10:16.267Z
Giskard
<ol>
<li>First of all its all just joke so you should not read too much into it. Most jokes are based on some false/overly simplified premise.</li>
<li>You are right:</li>
</ol>
<blockquote>
<p>There are two problematic claims here:</p>
</blockquote>
<blockquote>
<p>Being offered a choice between two identical packages of M&amp;Ms is equivalent to being offered nothing.</p>
</blockquote>
<p>This is erroneous argument if for no other reason than that in such case there is no opportunity cost. In fact if you read papers on opportunity cost such as <a href="https://link.springer.com/chapter/10.1007/978-1-349-21315-3_69" rel="nofollow noreferrer">Buchanan (1991)</a>, opportunity cost requires some choice between mutually exclusive options.  Thus having option M&amp;M vs M&amp;M is not an option at all. So in that case there is no opportunity cost.</p>
<p>Next you are also correct that your absolute utility depends on absolute consumption of goods and services.</p>
<p>In addition, the most valued option might not be in your original choice set. For example, you might value chocolate at whooping \$5. Thus if you expand your choice set you might discover that suddenly M&amp;M is not the best option. It is also sometimes argued consumers have preferences for diversity where they derive utility just from having more options (e.g. monopolistic competition models with consumer preferences for product differentiation).</p>
<p>This being said you can construct games* or there are behavioral experiments that show that <em>sometimes</em> having more choices can be worse, and sometimes people might purposefully constrain their choices to deal with behavioral biases. For example, in response to hyperbolic discounting one might purposefully install some program that restricts your access to the internet when you want to study, but you know that you suffer from hyperbolic discounting. In addition, there is some experimental evidence from psychology that having more choice can be sometimes demotivating <a href="https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.79.6.995&amp;source=post_page---------------------------" rel="nofollow noreferrer">(see Iyengar &amp; Lepper 2000)</a>, although I think results there can be interpreted with caution, it is possible that having more choice is not <em>always</em> strictly better in behavioral setting.</p>
<hr />
<p><sub>* I recall seeing some examples of that in Tadelis Game Theory: An Introduction </sub></p>

CC BY-SA 4.0
2021-06-30T12:22:13.923Z
1/2 > "Being offered a choice between two identical packages of M&Ms is equivalent to being offered nothing."

This is erroneous argument if for no other reason than that in such case there is no opportunity cost. [...] opportunity cost requires some choice between mutually exclusive options.< The two M&M bags are mutually exclusive options even though they are identical. You could make arbitrary alterations, where one bag is red and the other blue, but they are valued equally, or you could have two different types of candies that are valued equally.
Giskard
CC BY-SA 4.0
2021-06-30T12:23:32.163Z
2/2 Perhaps you would not dispute mutual exclusivity if one of the (otherwise identical) bags contained 10 fewer M&M pieces. Or 5. Or 1. Or $\epsilon$. Why would this change with at 0?
Giskard
CC BY-SA 4.0
2021-06-30T12:29:07.260Z
@Giskard I think of mutual exclusivity in terms of sets of characteristics. If there are red M&Ms then the color is different and there you do have a choice but its not really between M&Ms as a whole as you still get the same chocolate, but between coloring. In any case, if you look at the literature like the paper I cited, textbooks etc you see that all definitions of opportunity cost either explicitly or implicitly require some mutually exclusive choice. In the joke itself though its even simpler since the comedian does not say M&M packs are different
1muflon1
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2021-06-30T12:30:14.160Z
I do not dispute the requirement, I dispute your claim that this (the one between two identical bags) is not a mutually exclusive choice.
Giskard
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2021-06-30T12:34:29.783Z
@Giskard  Well but lets think about it in terms of set theory. You have choice set A = { M&M}, You have choice set B={M&M}, these two sets are identical A=B, so you are in essence just choosing between A and A, you just rename A B, that does not make it mutually exclusive. Or think of it in terms of Venn diagrams, the set A and B completely overlap each others
1muflon1
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2021-06-30T12:40:53.343Z
Come on man. You seem to be saying that each set contains 1 element as  does their union. So if there are two identical bags of M&Ms in the supermarket, are there even two bags or just one and the world is magic?
Giskard
CC BY-SA 4.0
2021-06-30T12:41:21.043Z
I tried to lay out more detailed examples in my two part comment. Perhaps you could explain where mutual exclusivity in my 2/2 comment disappears? I am guessing at 0 fewer M&Ms, but why?
Giskard
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2021-06-30T12:46:04.407Z
@Giskard 1. Okay, first in your comments you expand on the problem a bit, in your comment there is a difference in the joke there isnt. If in the store there are two completely identical bags of M&M then choosing between them is not mutually exclusive choice (I hope we can at least agree on that). 2. In your example with red vs other color M&Ms (lets say red vs  blue), there would be a meaningful choice, but the problem would be more complex. There you have two sets A={M&M, blue} B={M&M, red} here I think you can reasonably use for opportunity cost calculation only on the difference between
1muflon1
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2021-06-30T12:46:43.643Z
Could you please explain where mutual exclusivity in my [2/2 comment](https://economics.stackexchange.com/questions/45670/what-is-the-problem-with-this-opportunity-cost-example/45672?noredirect=1#comment74342_45672) disappears? I am guessing at 0 fewer M&Ms, but why?
Giskard
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2021-06-30T12:49:22.947Z
I see another mutual-exclusivity debate upcoming...
VARulle
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2021-06-30T12:52:08.523Z
@giskard the two subsets. The way how I think about this is that every set can be further subset, and for opportunity cost calculation you should subset the sets until you have smaller non-overlapping sets (as overlapping sets are not fully mutually exclusive). so set A is just set A1={M&M} ∪ A2={blue} and B is just set B1={M&M} ∪ B2={red} and so here really the underlying choice is just between A2 and B2 since A1=B1 so we can rewrite the problem as A={A1,A2} B={A1,B2}, and you simply use the difference between values of A2 and B2 for the OC calculation
1muflon1
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2021-06-30T12:54:43.073Z
@1muflon1 Yes, but the labeling is arbitrary. If we have M&M bag 1 and M&M bag 2, then they are different elements of the set. Similarly, you could just label Snickers and M&Ms both as "Candy" and claim the there is no real choice there either. The set theory approach only works if the input is correct.
Giskard
CC BY-SA 4.0
2021-06-30T12:58:08.737Z
@Giskard right but this is just then an empirical question if they are different or not. We have to set some parameters for example how you define red color (since there are multiple shades) etc, and once we have proper definitions of characteristics we can measure if they are different. I used to study physics and there we learned that two atoms of hydrogen (or any other atoms) are literally identical. Break it into atoms and check atom by atom if you need to, the point is that two things can be physically identical and in the joke or in a thought experiment you can use 2 identical M&M bags
1muflon1
CC BY-SA 4.0
2021-06-30T13:00:42.590Z
and if they are identical, which is not just semantics, as things *physically* can be identical  there is no meaningful choice (although I think that this would even be unnecessarily strong requirements as two harry potter books with the same cover length font etc can be *practically* identical even if they have some difference in molecular composition, so we can also just work with weaker concept of being identical in relevant characteristics)
1muflon1
CC BY-SA 4.0
2021-06-30T13:02:07.240Z
Allright, I think we took this as far as we could. Guess we just have to agree to disagree on what characteristics are relevant for the mutual exclusivity definition.
Giskard
CC BY-SA 4.0
2021-06-30T13:04:15.423Z
@Giskard I am not sure if we even disagree, because as I mentioned before if the M&M bags have different color there would be a difference (although I think there is a nuance in there as there is only *some* difference they are not completely different).
1muflon1
CC BY-SA 4.0
2021-06-30T13:05:20.650Z
We do disagree; I think in the event of being offered a *choice* (you can only take one) between two perfectly identical M&M bags, there is mutual exclusivity.
Giskard
CC BY-SA 4.0
2021-06-30T13:08:04.287Z
@Giskard care to elaborate how is that mutually exclusive? At that point I do not see difference. If I offer you choice between transferring you 1 USD and transferring you 1USD (you can only choose one) are according to you these two choices mutually exclusive as well, or is here just an issue that you implicitly assume the M&M bags have some hidden difference otherwise I do not understand the argument.
1muflon1
CC BY-SA 4.0
2021-06-30T13:09:41.070Z
**It is mutually exclusive because you can only take one bag, not both.** This does not conflict with the opportunity cost definition at all. It captures the notion that there is no additional benefit to the choice, you are just as happy as if you were given one of the bags without the option of choosing. Yes, I also consider the choices in the 1 USD example to be mutually exclusive, as long as you are unwilling to transfer both dollars to me. (You miser.)
Giskard
CC BY-SA 4.0
2021-06-30T13:13:45.217Z
@Giskard okay, so I see where the issue lies, we have different meanings of mutual exclusivity. Fair enough, but let me point out that rigorously in math mutual exclusivity is defined in terms of set theory, for example in a coin toss where you have heads or tails heads is mutually exclusive with tails, as they cannot occur at the same time, but if you would have just some (hypothetical) one sided coin where its only heads then there is no mutual exclusivity. Here I think there is only illusion of mutual exclusivity, choice A & B are just by labeling set to be different but actually
1muflon1
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2021-06-30T13:14:08.337Z
"*Guess we just have to agree to disagree on what characteristics are relevant for the mutual exclusivity definition.*"
Giskard
CC BY-SA 4.0
2021-06-30T13:16:18.027Z
its just choice A vs A. Let me give you a thought experiment to chew on. Imagine I offer you choice between M&M and M&M, and we have two scenarios, in scenario one there actually are 2 M&M bags, in the scenario two there is just one M&M bag but I will just state choose this bag or this bag again. Is there any difference between the two? Is there opportunity cost in one not second one, or is in both of them just because person conducting experiment declares there is an choice there?
1muflon1
CC BY-SA 4.0
2021-06-30T13:22:18.093Z
As I write in my answer I am not a fan of the concept of opportunity costs. Scenario two is murky, what does it mean to "choose" "this bag or this bag again". I am afraid we are wading into semantics territory here. If you wish you can post a new question where people argue about the what opportunity costs *ought to* describe, and then you can reason about the definition. Without this I don't see the point of continuing. I believe I understand your interpretation, it could be internally consistent, but I disagree that it is useful as a concept. This is fine, I can be wrong.
Giskard
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2021-06-30T13:23:51.063Z
And now I am gonna go flag your comments "as chatty" to start a constitutional crisis (:   (Not really.)
Giskard
CC BY-SA 4.0
2021-06-30T13:25:06.833Z
@Giskard fair enough, just to clarify since you ask about it when I say choose this bag or this bag again imagine following experiment I tell you to choose M&M bag vs M&M bag, but I do not show you the bags at the same time I will first show you M&M bag and say you can choose this or, wait for it, I put the M&M bag away and then put it up again you can choose this M&M bag. Contrast it with a situation where I do exactly the same antics but now there actually are two perfectly identical M&M bags
1muflon1
CC BY-SA 4.0
2021-06-30T13:26:13.010Z
This is, in my opinion, not a useful experiment. From my (imperfectly informed, misinformed even) point of view an opportunity cost clearly exists in both cases.
Giskard
CC BY-SA 4.0
2021-06-30T10:14:16.103Z
2021-06-30T10:14:16.103Z
1muflon1
<p>The &quot;stand-up economist&quot; Yoram Bauman used the concept of opportunity cost to make the following joke:</p>
<blockquote>
<p>[S]omebody offers you a choice between a Snickers bar and a package of M&amp;Ms. Suppose, for the sake of argument, that you take the M&amp;Ms. According to Mankiw, the cost of those M&amp;Ms is the Snickers bar that you had to give up to get the M&amp;Ms. Your gain from this situation—what economists call “economic profit”—is therefore the difference between the value you gain from getting the M&amp;Ms (say, \$.75) and the value you lose from giving up the Snickers bar (say, \$.40). In other words, your economic profit is only \$.35. Although you value the M&amp;Ms at \$.75, having the choice of the Snickers bar reduces your gain by \$.40….</p>
</blockquote>
<blockquote>
<p>Indeed, the more choices you have, the worse off you are. The worst situation of all would be somebody coming up to you and offering you a choice between two identical packages of M&amp;Ms. Since choosing one package (which you value at \$.75) means giving up the other package (which you also value at \$.75), your economic profit is exactly zero! So being offered a choice between two identical packages of M&amp;Ms is in fact equivalent to being offered nothing.</p>
</blockquote>
<p>There are two problematic claims here:</p>
<ol>
<li><em>Being offered a choice between two identical packages of M&amp;Ms is equivalent to being offered nothing.</em></li>
</ol>
<p>The resolution to this is, I think, fairly straightforward - Bauman is intertwining utility and opportunity cost in a deliberately erroneous manner. In most standard utility functions, one's utility depends on absolute consumption rather than the value of the next best alternative. As such, one's utility from a choice between two identical packages of M&amp;Ms is identical to utility from one package of M&amp;Ms (without choice), and is strictly greater than consuming nothing at all.</p>
<ol start="2">
<li><em>The more choices you have, the worse off you are.</em></li>
</ol>
<p>I'm having a hard time finding the exact problem with this statement as it is constructed in the joke. The reason is because consumer surplus (though not utility) does fall as the value of the next best alternative increases. As such, as long as new choices do not dominate the current best choice, additional choices can only decrease consumer surplus. What is wrong with this line of reasoning?</p>

<utility><welfare-economics><social-welfare><consumer-surplus><opportunity-cost>
What is the problem with this opportunity cost example?
pythonuser
# What is the problem with this opportunity cost example?

(Asked by: username_0 on 2021-06-30)

The "stand-up economist" Yoram Bauman used the concept of opportunity cost to make the following joke:

> [S]omebody offers you a choice between a Snickers bar and a package of M&Ms. Suppose, for the sake of argument, that you take the M&Ms. According to Mankiw, the cost of those M&Ms is the Snickers bar that you had to give up to get the M&Ms. Your gain from this situation—what economists call “economic profit”—is therefore the difference between the value you gain from getting the M&Ms (say, \$.75) and the value you lose from giving up the Snickers bar (say, \$.40). In other words, your economic profit is only \$.35. Although you value the M&Ms at \$.75, having the choice of the Snickers bar reduces your gain by \$.40….

> Indeed, the more choices you have, the worse off you are. The worst situation of all would be somebody coming up to you and offering you a choice between two identical packages of M&Ms. Since choosing one package (which you value at \$.75) means giving up the other package (which you also value at \$.75), your economic profit is exactly zero! So being offered a choice between two identical packages of M&Ms is in fact equivalent to being offered nothing.

There are two problematic claims here:

1. *Being offered a choice between two identical packages of M&Ms is equivalent to being offered nothing.*

The resolution to this is, I think, fairly straightforward - Bauman is intertwining utility and opportunity cost in a deliberately erroneous manner. In most standard utility functions, one's utility depends on absolute consumption rather than the value of the next best alternative. As such, one's utility from a choice between two identical packages of M&Ms is identical to utility from one package of M&Ms (without choice), and is strictly greater than consuming nothing at all.

2. *The more choices you have, the worse off you are.*

I'm having a hard time finding the exact problem with this statement as it is constructed in the joke. The reason is because consumer surplus (though not utility) does fall as the value of the next best alternative increases. As such, as long as new choices do not dominate the current best choice, additional choices can only decrease consumer surplus. What is wrong with this line of reasoning?

**Tags:** utility, welfare-economics, social-welfare, consumer-surplus, opportunity-cost


---

## 2 answers

### Answer by username_1 on 2021-06-30. Score: 2 | Accepted answer

The joke is conflating the value of the item you get and the value of the option to determine which item you get.

---

1. Suppose I value the Snickers at $\\\$.4$ and the M&Ms at $\\\$.75$.
   If I am offered a Snickers for free my economic profit is $\\\$.4$. If I could get the *additional* option to choose between the Snickers and a bag of M&Ms, rather than just get a Snickers for free, that would be worth an *extra* $\\\$.35$ to me. The entire event of getting the Snickers or a bag of M&Ms for free is still worth $\\\$.75$.
     
     
   If, instead of the Snickers, I was offered a free bag of M&Ms, then the *additional* option to choose from two identical bags of M&Ms would not yield any benefit. The economic profit resulting from the *additional option to choose* is indeed 0.   
   Note that compared to getting nothing you are better off if you can choose from two identical bag of M&Ms, but you are not better off compared to getting one bag without the option to choose. This is how we could deduce the value of the option to choose.

  

2. Similarly, if your options broaden in a decision situation, it is possible that the *additional* benefit each new option yields diminishes. This is captured by the increasing opportunity cost. It does not mean that the entire value of getting to choose from a wide variety is approaching zero.

---

I usually find that opportunity cost examples are overly complicated, perhaps to make the notion seem more intellectually demanding than it really is - therefore I can relate to the joke.

I used to teach microeconomics. With sunk costs it is important to get people to accept that the sunk costs are lost, hence doing something could be worthwhile even if the final outcome yields a loss, as long as the loss is smaller than the sunk cost.

In my experience most students understand the above two sentences perfectly, but they can be greatly confused when trying to pin down opportunity costs. Because of this I was never sure if this was a useful concept to teach.

> **Comments:**
> **username_2**: In the meanwhile I'm almost convinced that the concept is rather vague and impossible to formalize. I never teach it.  
> **username_3**: @username_2 I agree, I always found the concept of opportunity costs very "ambiguous", and I've never seen it formalized in a good way. In addition, if you know the value of the second best option, then by definition, you should also know what the best option is. If so, what's the point?  

---

### Answer by username_4 on 2021-06-30. Score: 2

1. First of all its all just joke so you should not read too much into it. Most jokes are based on some false/overly simplified premise.
2. You are right:

> There are two problematic claims here:

> Being offered a choice between two identical packages of M&Ms is equivalent to being offered nothing.

This is erroneous argument if for no other reason than that in such case there is no opportunity cost. In fact if you read papers on opportunity cost such as [Buchanan (1991)](https://link.springer.com/chapter/10.1007/978-1-349-21315-3_69), opportunity cost requires some choice between mutually exclusive options. Thus having option M&M vs M&M is not an option at all. So in that case there is no opportunity cost.

Next you are also correct that your absolute utility depends on absolute consumption of goods and services.

In addition, the most valued option might not be in your original choice set. For example, you might value chocolate at whooping \$5. Thus if you expand your choice set you might discover that suddenly M&M is not the best option. It is also sometimes argued consumers have preferences for diversity where they derive utility just from having more options (e.g. monopolistic competition models with consumer preferences for product differentiation).

This being said you can construct games\* or there are behavioral experiments that show that *sometimes* having more choices can be worse, and sometimes people might purposefully constrain their choices to deal with behavioral biases. For example, in response to hyperbolic discounting one might purposefully install some program that restricts your access to the internet when you want to study, but you know that you suffer from hyperbolic discounting. In addition, there is some experimental evidence from psychology that having more choice can be sometimes demotivating [(see Iyengar & Lepper 2000)](https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.79.6.995&source=post_page---------------------------), although I think results there can be interpreted with caution, it is possible that having more choice is not *always* strictly better in behavioral setting.

---

\* I recall seeing some examples of that in Tadelis Game Theory: An Introduction

> **Comments:**
> **username_1**: 1/2 > "Being offered a choice between two identical packages of M&Ms is equivalent to being offered nothing."  This is erroneous argument if for no other reason than that in such case there is no opportunity cost. [...] opportunity cost requires some choice between mutually exclusive options.< The two M&M bags are mutually exclusive options even though they are identical. You could make arbitrary alterations, where one bag is red and the other blue, but they are valued equally, or you could have two different types of candies that are valued equally.  
> **username_1**: 2/2 Perhaps you would not dispute mutual exclusivity if one of the (otherwise identical) bags contained 10 fewer M&M pieces. Or 5. Or 1. Or $\epsilon$. Why would this change with at 0?  
> **username_4**: @username_1 I think of mutual exclusivity in terms of sets of characteristics. If there are red M&Ms then the color is different and there you do have a choice but its not really between M&Ms as a whole as you still get the same chocolate, but between coloring. In any case, if you look at the literature like the paper I cited, textbooks etc you see that all definitions of opportunity cost either explicitly or implicitly require some mutually exclusive choice. In the joke itself though its even simpler since the comedian does not say M&M packs are different  
> **username_1**: I do not dispute the requirement, I dispute your claim that this (the one between two identical bags) is not a mutually exclusive choice.  
> **username_4**: @username_1  Well but lets think about it in terms of set theory. You have choice set A = { M&M}, You have choice set B={M&M}, these two sets are identical A=B, so you are in essence just choosing between A and A, you just rename A B, that does not make it mutually exclusive. Or think of it in terms of Venn diagrams, the set A and B completely overlap each others  
> **username_1**: Come on man. You seem to be saying that each set contains 1 element as  does their union. So if there are two identical bags of M&Ms in the supermarket, are there even two bags or just one and the world is magic?  
> **username_1**: I tried to lay out more detailed examples in my two part comment. Perhaps you could explain where mutual exclusivity in my 2/2 comment disappears? I am guessing at 0 fewer M&Ms, but why?  
> **username_4**: @username_1 1. Okay, first in your comments you expand on the problem a bit, in your comment there is a difference in the joke there isnt. If in the store there are two completely identical bags of M&M then choosing between them is not mutually exclusive choice (I hope we can at least agree on that). 2. In your example with red vs other color M&Ms (lets say red vs  blue), there would be a meaningful choice, but the problem would be more complex. There you have two sets A={M&M, blue} B={M&M, red} here I think you can reasonably use for opportunity cost calculation only on the difference between  
> **username_1**: Could you please explain where mutual exclusivity in my [2/2 comment](https://economics.stackexchange.com/questions/45670/what-is-the-problem-with-this-opportunity-cost-example/45672?noredirect=1#comment74342_45672) disappears? I am guessing at 0 fewer M&Ms, but why?  
> **username_2**: I see another mutual-exclusivity debate upcoming...  
> **username_4**: @username_1 the two subsets. The way how I think about this is that every set can be further subset, and for opportunity cost calculation you should subset the sets until you have smaller non-overlapping sets (as overlapping sets are not fully mutually exclusive). so set A is just set A1={M&M} ∪ A2={blue} and B is just set B1={M&M} ∪ B2={red} and so here really the underlying choice is just between A2 and B2 since A1=B1 so we can rewrite the problem as A={A1,A2} B={A1,B2}, and you simply use the difference between values of A2 and B2 for the OC calculation  
> **username_1**: @username_4 Yes, but the labeling is arbitrary. If we have M&M bag 1 and M&M bag 2, then they are different elements of the set. Similarly, you could just label Snickers and M&Ms both as "Candy" and claim the there is no real choice there either. The set theory approach only works if the input is correct.  
> **username_4**: @username_1 right but this is just then an empirical question if they are different or not. We have to set some parameters for example how you define red color (since there are multiple shades) etc, and once we have proper definitions of characteristics we can measure if they are different. I used to study physics and there we learned that two atoms of hydrogen (or any other atoms) are literally identical. Break it into atoms and check atom by atom if you need to, the point is that two things can be physically identical and in the joke or in a thought experiment you can use 2 identical M&M bags  
> **username_4**: and if they are identical, which is not just semantics, as things *physically* can be identical  there is no meaningful choice (although I think that this would even be unnecessarily strong requirements as two harry potter books with the same cover length font etc can be *practically* identical even if they have some difference in molecular composition, so we can also just work with weaker concept of being identical in relevant characteristics)  
> **username_1**: Allright, I think we took this as far as we could. Guess we just have to agree to disagree on what characteristics are relevant for the mutual exclusivity definition.  
> **username_4**: @username_1 I am not sure if we even disagree, because as I mentioned before if the M&M bags have different color there would be a difference (although I think there is a nuance in there as there is only *some* difference they are not completely different).  
> **username_1**: We do disagree; I think in the event of being offered a *choice* (you can only take one) between two perfectly identical M&M bags, there is mutual exclusivity.  
> **username_4**: @username_1 care to elaborate how is that mutually exclusive? At that point I do not see difference. If I offer you choice between transferring you 1 USD and transferring you 1USD (you can only choose one) are according to you these two choices mutually exclusive as well, or is here just an issue that you implicitly assume the M&M bags have some hidden difference otherwise I do not understand the argument.  
> **username_1**: **It is mutually exclusive because you can only take one bag, not both.** This does not conflict with the opportunity cost definition at all. It captures the notion that there is no additional benefit to the choice, you are just as happy as if you were given one of the bags without the option of choosing. Yes, I also consider the choices in the 1 USD example to be mutually exclusive, as long as you are unwilling to transfer both dollars to me. (You miser.)  
> **username_4**: @username_1 okay, so I see where the issue lies, we have different meanings of mutual exclusivity. Fair enough, but let me point out that rigorously in math mutual exclusivity is defined in terms of set theory, for example in a coin toss where you have heads or tails heads is mutually exclusive with tails, as they cannot occur at the same time, but if you would have just some (hypothetical) one sided coin where its only heads then there is no mutual exclusivity. Here I think there is only illusion of mutual exclusivity, choice A & B are just by labeling set to be different but actually  
> **username_1**: "*Guess we just have to agree to disagree on what characteristics are relevant for the mutual exclusivity definition.*"  
> **username_4**: its just choice A vs A. Let me give you a thought experiment to chew on. Imagine I offer you choice between M&M and M&M, and we have two scenarios, in scenario one there actually are 2 M&M bags, in the scenario two there is just one M&M bag but I will just state choose this bag or this bag again. Is there any difference between the two? Is there opportunity cost in one not second one, or is in both of them just because person conducting experiment declares there is an choice there?  
> **username_1**: As I write in my answer I am not a fan of the concept of opportunity costs. Scenario two is murky, what does it mean to "choose" "this bag or this bag again". I am afraid we are wading into semantics territory here. If you wish you can post a new question where people argue about the what opportunity costs *ought to* describe, and then you can reason about the definition. Without this I don't see the point of continuing. I believe I understand your interpretation, it could be internally consistent, but I disagree that it is useful as a concept. This is fine, I can be wrong.  
> **username_1**: And now I am gonna go flag your comments "as chatty" to start a constitutional crisis (:   (Not really.)  
> **username_4**: @username_1 fair enough, just to clarify since you ask about it when I say choose this bag or this bag again imagine following experiment I tell you to choose M&M bag vs M&M bag, but I do not show you the bags at the same time I will first show you M&M bag and say you can choose this or, wait for it, I put the M&M bag away and then put it up again you can choose this M&M bag. Contrast it with a situation where I do exactly the same antics but now there actually are two perfectly identical M&M bags  
> **username_1**: This is, in my opinion, not a useful experiment. From my (imperfectly informed, misinformed even) point of view an opportunity cost clearly exists in both cases.  

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