<blockquote>
  <p><strong>The concept of Opportunity Cost is not used in order to <em>net</em> the direct
  benefit of a choice, but in
  order to compare it to the direct benefit of alternative choices.</strong></p>
</blockquote>

<p><strong>How do we go about using it in Economics?</strong></p>

<p>1) We gather all available alternative choices, say $A, B, C$<br>
2) We measure (in whatever way appropriate for the situation) the benefit from each choice, say $G_A, G_B, G_C$.<br>
3) The opportunity cost of choice $A$, say $OC_A$ is defined as the maximum benefit among the benefits of the alternative choices :</p>

<p>$$OC_A \equiv \max \{G_B, G_C\}$$</p>

<p>If $G_A - OC_A &lt;0$ obviously we will be better off by choosing something else, and not $A$. And that's that.</p>

<p>Standard example: you have some money and the only choices available are $A$ to put it in a bank account yielding $3\%$ interest and $B$ to put it in another bank account that yields $4\%$ interest.</p>

<p>The direct benefit of choice $A$ is $3\%$ and its opportunity cost is the direct benefit from the alternative choice $B$, i.e. $4\%$.</p>

<p><em>This does not mean</em> that  $A$'s "net benefit" is $3\% - 4\% = -1\%$. This operation just tells us that we have better choices than $A$. Again, it does <em>not</em>, in any meaningful way, say something like "so the net benefit from choosing $A$ is $-1\%$. It only says "if we choose $A$ we will actually get $3\%$ direct benefit, but we would have get $1$ percentage point more if we had chosen $B$" (an even funnier fallacy here is to say, "so I got $3\%$ and I foregone $1\%$, so my "true benefit = gains (-) losses" therefore true benefit is $3\%-1\%=2\%$" -so sir, can you please hand me this $1\%$ the bank gave you on top of your true benefit? Thank you so much).</p>

<p>Turning to your example, the direct benefit of choosing $x^*=0$ is $3$. The highest opportunity cost of choosing $x^*$ will come from choosing $x'=\epsilon&gt;0$. This will have direct benefit $3-\epsilon$, which is the highest opportunity cost of choosing $x^*$.</p>

<p>Perform if you want the subtracting operation, $3-(3-\epsilon) = \epsilon &gt;0$. The important result is that we get a positive number: so the benefit from choosing $x^*$ is greater than the benefit from choosing any available alternative. It is <em>not</em> the case that the "net benefit" from choosing $x$ is $\epsilon$ (again, since you will get $3$, can you please give me the $3-\epsilon$ which is above your "net benefit"?)</p>

<p>My impression is that this confusion surrounding the correct use of opportunity costs has psychological roots together with the use of the word "opportunity" in a different context: the "feelings of disappointment"(disutility) from "missed opportunities", that one may experience when he learns that he <em>could have gotten more</em>, which appear to "subtract" from the utility gained from what he actually got. Indeed, but in such a case, <em>the missed opportunity was not known/available as an alternative choice during the time of decision</em>. One could attempt to construct a utility function accommodating such behavior, but this is a totally different issue, it has nothing to do with how "opportunity cost" is defined and used in Economics.</p>

CC BY-SA 3.0
2015-11-06T14:28:19.540Z
Sorry, you've missed the point of my question. You're obsessing over the word *true* in the context of the phrase "true benefit." That's not my point at all. My point is that **in my opinion,** this is a mathematically artificial concept, and that economically, I think it muddies the conceptual waters. I assure you, I'm not confused; at least, not in the way you describe. Now you may agree with my contention that this concept merely muddies the waters or you may disagree, but that's not the question. The question is whether or not any economist has argued this.
goblin GONE
CC BY-SA 3.0
2015-11-06T14:31:14.897Z
Now on the other hand, if I've fundamentally misunderstood the notion of opportunity cost, then explaining *how and in what way* would constitute an answer. But you haven't done that at all - all you've done is to describe *exactly* my current understanding of opportunity cost, and then gone on to state that you think the issue is psychological or linguistic. Umm, what issue? That I apparently understand it? So I don't think this really qualifies as an answer.
goblin GONE
CC BY-SA 3.0
2015-11-06T14:43:05.057Z
Your question explicitly mentions the "factoring in of opportunity costs", and their subtraction from the benefit. And then you move on to say "_So under the viewpoint of opportunity cost, the true payoff of choosing x=0 is not 3, its 0_". I clearly stated in my answer that this is not the "viewpoint of opportunity cost", as regards how the concept is used in Economics. It may be your way of understanding and using the concept, which is perfectly fine by me, but it is not the Economics' way.
Alecos Papadopoulos
CC BY-SA 3.0
2015-11-06T14:45:41.623Z
But your just focusing on the word "true" again. You can replace "true payoff" with "post-opportunity-cost-subtraction payoff" and the thrust will remain unchanged, except that now we've substituted a long phrase in place of a short word.
goblin GONE
CC BY-SA 3.0
2015-11-06T20:03:16.047Z
You can do that, sure. Still, you will be understanding and using the concept in a way that is not understood and not used in Economics. I added in my answer a more formal description of how the concept is defined and used in Economics.
Alecos Papadopoulos
CC BY-SA 3.0
2015-11-06T14:18:40.217Z
2015-11-06T20:02:21.950Z
2015-11-06T20:02:21.950Z
Alecos Papadopoulos
<p>I hold the opinion that the notion of opportunity cost "muddies the intellectual waters" so to speak, and I'd like to know if any professional economists have expressed this sentiment, or similar.</p>

<blockquote>
  <p><strong>Question.</strong> Have any economists ever argued that the notion of opportunity cost is problematic, or that it should be done away with?</p>
</blockquote>

<p>Let me illustrate with an example. Define a function $f : \mathbb{R} \rightarrow \mathbb{R}$ as follows: $$f(x) = 3-x^2$$</p>

<p>Pretend we get to choose $x,$ and that the resulting payoff is $f(x)$. Then obviously, the optimal choice of $x$ is $x=0$, and this gives a payoff (or "benefit", or "utility") of $3$. Seems simple enough.</p>

<p>Okay, but now look what happens once we admit opportunity cost into the issue. It <em>could</em> be argued that by choosing $x=0$ and getting a payoff of $3$, we forgo the benefit associated with choosing $x=1$ at getting a payoff of $2$. So the <em>true</em> payoff of choosing $x=0$, once opportunity costs have been factored in, is at most $3-1$, which is $2$. Proceeding in this way, we can show that the true payoff, after subtracting all the relevant opportunity costs, is at most $3-(3-\varepsilon^2)$, for any choice of $\varepsilon$, no matter how small. Hence the <em>true</em> payoff is at most $\varepsilon^2$ for each choice of $\varepsilon$. So under the viewpoint of opportunity cost, the true payoff of choosing $x=0$ is not $3$, its $0$. </p>

<p>The is a general principle; if we take the concept of opportunity cost seriously, then every continuous decision problem (involving continuous functions) has a maximum payoff of at most $0$, and most choices actually yield a <em>negative</em> payoff. Obviously, this is pretty artificial. With discrete problems, its even worse; the maximum payoff of any decision is vastly reduced, but its only $0$ at the second-best choice(s); the best choice(s) yield a positive payoff.</p>

<p>Anyway, I'd like to know whether any professional economists have ever argued against using this concept.</p>

CC BY-SA 3.0
2015-11-06T13:38:32.367Z
You're muddling concepts - opportunity cost is not what you think it is.  If $f(x)$ is your objective function, the payoff at every $x$ should already be taking into account various opportunity cost. If I have time I might expand on this.
FooBar
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2015-11-06T14:22:33.087Z
@FooBar, I'd like that.
goblin GONE
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2015-11-06T15:23:46.793Z
Obviously, this is pretty stupid question to downvote. The downvoter seems to be saying: "Don't think about things, don't have opinions, and *definitely* don't try to find out whether or not any experts share your opinions." Unfortunately, we get these kind of attitudes on math.stackexchange, too. I think they're repugnant.
goblin GONE
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2015-11-06T15:41:49.193Z
I agree that this question doesn't deserve a downvote. My only question is what is the problem with the "true payoff" (or the post-opportunity-cost-subtraction payoff) having a max of 0? It isn't clear to me what you mean by muddy the "intellectual" waters. Could you be precise about what the problem with that is?
cc7768
CC BY-SA 3.0
2015-11-06T16:01:12.180Z
@goblin Actually I disagree. I didn't down vote it, but not understanding a concept and jumping to the strict conclusion ("everyone seems to be using the notion of opportunity-cost, but here's my handwaving argument why it is broken *by general principle*, is anyone actually as smart as me?") is downvote-worthy. The question itself is okay, but it is packaged in a *much*  to overconfident way.
FooBar
CC BY-SA 3.0
2015-11-06T16:02:50.513Z
"Here is how I think about opportunity-costs, but it doesn't really make sense - where am I wrong?" is a **much** better way of phrasing it.
FooBar
CC BY-SA 3.0
2015-11-06T16:04:21.310Z
Or in other words "If many smart people in their discipline - outside of yours - do something which doesn't make sense to you, your prior should be that you're not understanding fully what they're doing, not that they're making some mistake you - as an outsider - immediately spotted".
FooBar
CC BY-SA 3.0
2015-11-06T16:09:45.693Z
@FooBar, in my view, interpreting the phrase "I hold opinion x..." as overconfidence is a bit like interpreting a dove as a declaration of war. And recall that I'm *asking* whether or not expert(s) hold my opinion. In short, I think the way you're interpreting my question is pretty crazy.
goblin GONE
CC BY-SA 3.0
2015-11-06T16:11:48.900Z
Quite frankly, if I was certain the consensus was wrong, I would just say: "The consensus says A, but in fact B is true." I wouldn't mention opinions. I certainly wouldn't bother asking a question about it at a Q&A site. I'd just accept that sometimes people are wrong about things and that is that.
goblin GONE
CC BY-SA 3.0
2015-11-06T16:42:04.530Z
I still think it would be useful if you could answer my previous questions: 'What is the problem with the "true payoff" (or the post-opportunity-cost-subtraction payoff) having a max of 0? It isn't clear to me what you mean by muddy the "intellectual" waters. Could you be precise about what the problem with that is?'
cc7768
CC BY-SA 3.0
2015-11-07T03:00:30.930Z
@cc7768, well one reason is that its only in the continuous case that the new max is $0$; in the discrete case, the new max might be vastly reduced, but it will still be positive. But more generally, why bother introducing this normalizing factor? Even if the normalizing factor was defined more usefully and/or simply, it would still just overcomplicate things mathematically. And linguistically, its a nightmare; we always have to be wondering whether the other person means "payoff" or "normalized payoff."
goblin GONE
<reference-request><theory><opportunity-cost>
Have any economists ever argued that the notion of opportunity cost should be done away with?
goblin GONE
# Have any economists ever argued that the notion of opportunity cost should be done away with?

(Asked by: username_0 on 2015-11-06)

I hold the opinion that the notion of opportunity cost "muddies the intellectual waters" so to speak, and I'd like to know if any professional economists have expressed this sentiment, or similar.

> **Question.** Have any economists ever argued that the notion of opportunity cost is problematic, or that it should be done away with?

Let me illustrate with an example. Define a function $f : \mathbb{R} \rightarrow \mathbb{R}$ as follows: $$f(x) = 3-x^2$$

Pretend we get to choose $x,$ and that the resulting payoff is $f(x)$. Then obviously, the optimal choice of $x$ is $x=0$, and this gives a payoff (or "benefit", or "utility") of $3$. Seems simple enough.

Okay, but now look what happens once we admit opportunity cost into the issue. It *could* be argued that by choosing $x=0$ and getting a payoff of $3$, we forgo the benefit associated with choosing $x=1$ at getting a payoff of $2$. So the *true* payoff of choosing $x=0$, once opportunity costs have been factored in, is at most $3-1$, which is $2$. Proceeding in this way, we can show that the true payoff, after subtracting all the relevant opportunity costs, is at most $3-(3-\varepsilon^2)$, for any choice of $\varepsilon$, no matter how small. Hence the *true* payoff is at most $\varepsilon^2$ for each choice of $\varepsilon$. So under the viewpoint of opportunity cost, the true payoff of choosing $x=0$ is not $3$, its $0$.

The is a general principle; if we take the concept of opportunity cost seriously, then every continuous decision problem (involving continuous functions) has a maximum payoff of at most $0$, and most choices actually yield a *negative* payoff. Obviously, this is pretty artificial. With discrete problems, its even worse; the maximum payoff of any decision is vastly reduced, but its only $0$ at the second-best choice(s); the best choice(s) yield a positive payoff.

Anyway, I'd like to know whether any professional economists have ever argued against using this concept.

**Tags:** reference-request, theory, opportunity-cost

> **Comments:**
> **username_1**: You're muddling concepts - opportunity cost is not what you think it is.  If $f(x)$ is your objective function, the payoff at every $x$ should already be taking into account various opportunity cost. If I have time I might expand on this.  
> **username_0**: @username_1, I'd like that.  
> **username_0**: Obviously, this is pretty stupid question to downvote. The downvoter seems to be saying: "Don't think about things, don't have opinions, and *definitely* don't try to find out whether or not any experts share your opinions." Unfortunately, we get these kind of attitudes on math.stackexchange, too. I think they're repugnant.  
> **username_2**: I agree that this question doesn't deserve a downvote. My only question is what is the problem with the "true payoff" (or the post-opportunity-cost-subtraction payoff) having a max of 0? It isn't clear to me what you mean by muddy the "intellectual" waters. Could you be precise about what the problem with that is?  
> **username_1**: @goblin Actually I disagree. I didn't down vote it, but not understanding a concept and jumping to the strict conclusion ("everyone seems to be using the notion of opportunity-cost, but here's my handwaving argument why it is broken *by general principle*, is anyone actually as smart as me?") is downvote-worthy. The question itself is okay, but it is packaged in a *much*  to overconfident way.  
> **username_1**: "Here is how I think about opportunity-costs, but it doesn't really make sense - where am I wrong?" is a **much** better way of phrasing it.  
> **username_1**: Or in other words "If many smart people in their discipline - outside of yours - do something which doesn't make sense to you, your prior should be that you're not understanding fully what they're doing, not that they're making some mistake you - as an outsider - immediately spotted".  
> **username_0**: @username_1, in my view, interpreting the phrase "I hold opinion x..." as overconfidence is a bit like interpreting a dove as a declaration of war. And recall that I'm *asking* whether or not expert(s) hold my opinion. In short, I think the way you're interpreting my question is pretty crazy.  
> **username_0**: Quite frankly, if I was certain the consensus was wrong, I would just say: "The consensus says A, but in fact B is true." I wouldn't mention opinions. I certainly wouldn't bother asking a question about it at a Q&A site. I'd just accept that sometimes people are wrong about things and that is that.  
> **username_2**: I still think it would be useful if you could answer my previous questions: 'What is the problem with the "true payoff" (or the post-opportunity-cost-subtraction payoff) having a max of 0? It isn't clear to me what you mean by muddy the "intellectual" waters. Could you be precise about what the problem with that is?'  
> **username_0**: @username_2, well one reason is that its only in the continuous case that the new max is $0$; in the discrete case, the new max might be vastly reduced, but it will still be positive. But more generally, why bother introducing this normalizing factor? Even if the normalizing factor was defined more usefully and/or simply, it would still just overcomplicate things mathematically. And linguistically, its a nightmare; we always have to be wondering whether the other person means "payoff" or "normalized payoff."  

---

## 1 answers

### Answer by username_3 on 2015-11-06. Score: 8

> **The concept of Opportunity Cost is not used in order to *net* the direct
> benefit of a choice, but in
> order to compare it to the direct benefit of alternative choices.**

**How do we go about using it in Economics?**

1) We gather all available alternative choices, say $A, B, C$  
2) We measure (in whatever way appropriate for the situation) the benefit from each choice, say $G\_A, G\_B, G\_C$.  
3) The opportunity cost of choice $A$, say $OC\_A$ is defined as the maximum benefit among the benefits of the alternative choices :

$$OC\_A \equiv \max \{G\_B, G\_C\}$$

If $G\_A - OC\_A <0$ obviously we will be better off by choosing something else, and not $A$. And that's that.

Standard example: you have some money and the only choices available are $A$ to put it in a bank account yielding $3\%$ interest and $B$ to put it in another bank account that yields $4\%$ interest.

The direct benefit of choice $A$ is $3\%$ and its opportunity cost is the direct benefit from the alternative choice $B$, i.e. $4\%$.

*This does not mean* that $A$'s "net benefit" is $3\% - 4\% = -1\%$. This operation just tells us that we have better choices than $A$. Again, it does *not*, in any meaningful way, say something like "so the net benefit from choosing $A$ is $-1\%$. It only says "if we choose $A$ we will actually get $3\%$ direct benefit, but we would have get $1$ percentage point more if we had chosen $B$" (an even funnier fallacy here is to say, "so I got $3\%$ and I foregone $1\%$, so my "true benefit = gains (-) losses" therefore true benefit is $3\%-1\%=2\%$" -so sir, can you please hand me this $1\%$ the bank gave you on top of your true benefit? Thank you so much).

Turning to your example, the direct benefit of choosing $x^\*=0$ is $3$. The highest opportunity cost of choosing $x^\*$ will come from choosing $x'=\epsilon>0$. This will have direct benefit $3-\epsilon$, which is the highest opportunity cost of choosing $x^\*$.

Perform if you want the subtracting operation, $3-(3-\epsilon) = \epsilon >0$. The important result is that we get a positive number: so the benefit from choosing $x^\*$ is greater than the benefit from choosing any available alternative. It is *not* the case that the "net benefit" from choosing $x$ is $\epsilon$ (again, since you will get $3$, can you please give me the $3-\epsilon$ which is above your "net benefit"?)

My impression is that this confusion surrounding the correct use of opportunity costs has psychological roots together with the use of the word "opportunity" in a different context: the "feelings of disappointment"(disutility) from "missed opportunities", that one may experience when he learns that he *could have gotten more*, which appear to "subtract" from the utility gained from what he actually got. Indeed, but in such a case, *the missed opportunity was not known/available as an alternative choice during the time of decision*. One could attempt to construct a utility function accommodating such behavior, but this is a totally different issue, it has nothing to do with how "opportunity cost" is defined and used in Economics.

> **Comments:**
> **username_0**: Sorry, you've missed the point of my question. You're obsessing over the word *true* in the context of the phrase "true benefit." That's not my point at all. My point is that **in my opinion,** this is a mathematically artificial concept, and that economically, I think it muddies the conceptual waters. I assure you, I'm not confused; at least, not in the way you describe. Now you may agree with my contention that this concept merely muddies the waters or you may disagree, but that's not the question. The question is whether or not any economist has argued this.  
> **username_0**: Now on the other hand, if I've fundamentally misunderstood the notion of opportunity cost, then explaining *how and in what way* would constitute an answer. But you haven't done that at all - all you've done is to describe *exactly* my current understanding of opportunity cost, and then gone on to state that you think the issue is psychological or linguistic. Umm, what issue? That I apparently understand it? So I don't think this really qualifies as an answer.  
> **username_3**: Your question explicitly mentions the "factoring in of opportunity costs", and their subtraction from the benefit. And then you move on to say "_So under the viewpoint of opportunity cost, the true payoff of choosing x=0 is not 3, its 0_". I clearly stated in my answer that this is not the "viewpoint of opportunity cost", as regards how the concept is used in Economics. It may be your way of understanding and using the concept, which is perfectly fine by me, but it is not the Economics' way.  
> **username_0**: But your just focusing on the word "true" again. You can replace "true payoff" with "post-opportunity-cost-subtraction payoff" and the thrust will remain unchanged, except that now we've substituted a long phrase in place of a short word.  
> **username_3**: You can do that, sure. Still, you will be understanding and using the concept in a way that is not understood and not used in Economics. I added in my answer a more formal description of how the concept is defined and used in Economics.  

---

