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

Question

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.

Answer 1

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.