What is Opportunity Cost?

Question

Suppose you have 2 activities, A and B. Doing activity A gives a return of 100 dollars, doing activity B gives a return of -50 dollars. What would be the opportunity cost of choosing activity B? 100 dollars or 150 dollars.

Oxford American Dictionary gives a pretty standard definition of opportunity cost: "the loss of potential gain from other alternatives when one alternative is chosen".

Looking at it one way, the loss of potential gain by picking B is 100 dollars, as that is the gain that would be had from doing A. However, by choosing B, not only are you missing out on 100 dollars, you're also losing 50 dollars by doing B itself. The difference in the gain between the two activities is 100 - - 50 = 150 dollars. This is the foregone value when activity B is chosen, and seems to give the full picture as to what is lost by choosing B. This term "The value foregone.." seems to appear in many definitions of opportunity cost online as well.

Different sites and sources seem to fall on either one side or the other. There are example questions and solutions online which show both methods of approach.

So, in an assignment which requires calculations of opportunity cost, which definition of opportunity cost will get me the marks- the value of the next best alternative, or the difference between the value of the next best alternative and the value of the chosen activity? Or both?

Answer 1

As other answers clarified, the Opportunity Cost has been defined as the value of the best alternative foregone.
Assume that the gain in activity B will be positive, say USD 20. This too does not affect the Opportunity Cost, it does not make it equal to $100-20 = 80$.

In other words, the Opportunity Cost does NOT reflect the "net change of financial position if a switch from my current choice to the alternative". This would be, well, "net change in financial position", not opportunity cost.

Of course, these are labels, and one could conceivably go on and define "opportunity cost" in some other way. What I am writing here is what is its historically established definition in Economics.

Is it a "reasonable" definition? It is, if one realizes that it essentially respects the distinction between "cost (foregone direct gain) from NOT undertaking activity A", and "direct cost/gain by undertaking activity B". These are two different things conceptually, so it is reasonable to have a concept that does not net their effect.

So, again, It is NOT the full/net cost/gain of a choice.

Think also about the following: assume that there are only these two activities, and you can undertake both. What is the Opportunity Cost of choosing both? Answer: Zero. What is the total cost/gain of undertaking both? Answer 100-50 = 50.

Answer 2

Opportunity cost is what you forgo for choosing something else. Commonly thought of in economic terms as follows:

Opportunity cost refers to a benefit that a person could have received, but gave up, to take another course of action. Stated differently, an opportunity cost represents an alternative given up when a decision is made. This cost is, therefore, most relevant for two mutually exclusive events. In investing, it is the difference in return between a chosen investment and one that is necessarily passed up.

The term is, as above, used when thinking about investments or purchases. Therefore, you can have a negative or positive investment return or outcome, or a monetary cost or gain.

If you spent 50 dollars which meant that you could not gain 100 dollars, your opportunity cost is 100 dollars. If you gained 100 dollars but instead you did not lose 50 dollars, your opportunity cost is negative 50 dollars (there's no opportunity cost for taking the 100 dollars, as the opportunity cost is negative). It was worthwhile that you obviously didn't lose the 50 dollars. You may claim that it's of value to lose the most money and in that case having the largest negative opportunity cost is the best. But that's a bit nonsensical.

The total opportunity cost isn't 150 dollars because we’re only interested in the forgone investment or monetary opportunity (the 100 dollars or negative 50 dollars.

Opportunity cost is about what you could gain or lose (but what we could have gained is more often used when opportunity costs are calculated) because you sacrificed or spent money on something else. There's really an infinite number of things you could bring into the opportunity cost equation. You don't work so you can paint art; you buy a house but can’t go overseas on a trip; and so on. Not everything can be thought of in strict economic terms, so opportunity cost is best left to discussions about monetary investments. Otherwise, this discussion will tie into what you value, and what provides you with the most utility. In that sense, there’s no right or wrong to it. What you see as a gain may be an absolute ’waste’ to others; therefore, your opportunity cost and another persons opportunity cost may vary wildly. That's why, again, it’s clearest to only stick to monetary investments and purchases when thinking about economic opportunity cost.

Answer 3

Definition. The opportunity cost (OC) of any alternative is the value you place on the best of the forgone alternatives.

If we adopt the above definition (and I do), the OC of $B$ is the value of $A$, which is simply $\$100$.

With the above definition, the alternative you choose ($B$ in this case) is completely irrelevant when calculating its OC. All that matters is the best of the forgone alternatives.

To illustrate this point, consider this pair of examples:

Example #1. $A$ and $B$ are the only two alternatives. $A$: "Pay $\$500$ to get back $\$600$ in return." $B$: "Pay $\$500$ to get back $\$450$ in return." The OC of $B$ is the value of $A$, which is $\$100$.

Example #2. Everything is exactly the same as before, except that now $B$ is changed to "Pay $\$500$ to get back $\$1,000$ in return." The OC of $B$ is again the value of $A$, which is $\$100$.

In the above examples, the value of $B$ changes (from $-\$50$ to $\$500$) but that of $A$ doesn't. And so, the OC of $B$ is $\$100$ in both examples.

An alternative's value is completely irrelevant to its OC. What's relevant is the value of the best alternative forgone.

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Notes. "What exactly is OC?"

This seemingly-simple question was discussed in the past (see e.g. Alchian, 1968). Then like many of the most important questions in economics, it was then forgotten/glossed over until Ferraro & Taylor (2005) and the susbequent literature spawned (see in particular the 2016 JEE Symposium).

It all boils down to which definition you use. My view (and I believe also that of Alchian and Buchanan, 1987) is that the above definition is the "most correct" one that "everyone should use". Of course, whoever's marking your homework may disagree.

Answer 4

My answer is different to the others, though I don't think their definitions of opportunity cost are incorrect, only their interpretations of the problem. But based on my interpretation of your question, I would indeed say that the opportunity cost of activity B is $150.

This is a trick question because it is playing on the differences between economics and math and misleading wording, making it an ambiguous scenario leading to different assumptions/interpretations of the underlying circumstances. This ambiguity means that some clarifications and assumptions need to be made to answer the question.

In reality, a gain of -$50 does not make sense on its own, because there is no such thing as negative money. Opportunity cost only makes sense when there is a choice in the first place, and choosing to lose \$50 to perform some activity is the very definition of a cost. A net gain (or profit) of -\$50 can make sense, but that implies more than one factor. In a situation where you pay \$50 and get \$0 back, that is a cost of \$50 and an output of \$0. This is often the case when you spend money for immaterial gains, such as entertainment.

With that out of the way, there are 3 assumptions that need to be made to answer the question:

Assumption 1: You can only choose activity A OR activity B, but not both. If you could choose to both, then the opportunity costs would not depend on each other as you are not foregoing either option by choosing the other one.

Assumption 2: We are evaluating the opportunity cost of the output of partaking in activity B, and are not differentiating between gaining the right to partake in an activity, with actually partaking in it. This is an important distinction, because if we are discussing gaining rights to perform the activities, then gaining the right to activity B over activity A would trivially have an opportunity cost of $100, because you could then choose to not partake in activity B, and you would have lost no money. However, partaking in activity B would then have a further opportunity cost.

Assumption 3: Activity B has a cost of \$50 and an output of \$0. This is important because we are evaluating the opportunity cost of the output, so the cost needs to be differentiated from the output. If you buy a \$50 bill for \$100, you would say that the \$50 bill cost you \$100, not \$50, but your net gain (or profit) was -\$50. This is clearly different from the situation where you pay $50 for entertainment, even though the net gain is the same.

With these 3 assumptions the answer becomes clear, that the opportunity cost in partaking in activity B is \$150. The opportunity cost is equal to the potential $100 you could have gained from partaking in activity A (implicit cost), plus the explicit cost of \$50 from partaking in activity B.

As an equation, we can say that:

Net gain compared to best alternative(B) = Output(B) - Opportunity Cost(B)
Opportunity Cost(B) = Output(B) - Net gain compared to best alternative(B)
Opportunity Cost(B) = \$0 - (Net gain(B) - Net gain(A))
Opportunity Cost(B) = \$0 - (-\$50 - \$100)
Opportunity Cost(B) = \$150

Side note: "Net gain compared to best alternative(x)" is only positive when x will give the most net gain. That also means that the opportunity cost of x will always be greater than the output of x unless x gives the most net gain. This intuitively makes sense, because if the output of an option is greater than its opportunity cost, this means the value we get from this option is greater the value we are foregoing by picking the next best option.