# Have any economists ever argued that the notion of opportunity cost should be done away with?

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.

• 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 Nov 6 '15 at 13:38
• @FooBar, I'd like that. – goblin Nov 6 '15 at 14:22
• @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 Nov 6 '15 at 16:01
• "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 Nov 6 '15 at 16:02
• 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 Nov 6 '15 at 16:04

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.

• 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 Nov 6 '15 at 14:28
• 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 Nov 6 '15 at 14:31
• 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 Nov 6 '15 at 14:43
• 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 Nov 6 '15 at 14:45
• 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 Nov 6 '15 at 20:03