<p>I'll expand on @NuclearHoagie's comment.</p>
<p>Generally speaking, when there are <span class="math-container">$N$</span> alternatives, <span class="math-container">$a_1,a_2,\dots,a_N$</span>, and an individual's &quot;net&quot; utility---that is, benefit net of costs---from the <span class="math-container">$n$</span>-th alternative is <span class="math-container">$u(a_n)$</span>, the opportunity cost of alternative <span class="math-container">$a_n$</span> is defined as
<span class="math-container">\begin{equation}
OC(a_n) = \max\;\{u(a_1),\dots,u(a_{n-1}),u(a_{n+1}),\dots,u(a_N)\}.
\end{equation}</span></p>
<p>In your question, <span class="math-container">$N=2$</span> (call them <span class="math-container">$\text{EC}$</span> and <span class="math-container">$\text{BD}$</span>) and the utility function is implicitly assumed to be the willingness-to-pay (<span class="math-container">$WTP$</span>) for a ticket minus the price (<span class="math-container">$P$</span>) of the ticket:
<span class="math-container">\begin{equation}
u(a) = WTP(a) - P(a). 
\end{equation}</span></p>
<p>Applying the definition of <span class="math-container">$OC$</span>, we have
<span class="math-container">\begin{alignat}{4}
OC(\text{EC}) &amp; = u(\text{BD}) &amp;&amp; = WTP(\text{BD}) - P(\text{BD}) &amp;&amp; = 50-40 &amp;&amp;=10 \\
OC(\text{BD}) &amp; = u(\text{EC}) &amp;&amp; = WTP(\text{EC}) - P(\text{EC}) &amp;&amp; = WTP(\text{EC}) - 0 &amp;&amp; =WTP(\text{EC}) 
\end{alignat}</span>
As you see, the <span class="math-container">$OC$</span> for seeing <span class="math-container">$\text{EC}$</span> is <span class="math-container">$10$</span>, and the <span class="math-container">$OC$</span> for seeing <span class="math-container">$\text{BD}$</span> depends on your <span class="math-container">$WTP$</span>, which is not provided in the question.</p>

CC BY-SA 4.0
2024-11-13T04:46:51.580Z
2024-11-13T04:46:51.580Z
Herr K.
<p>My professor gives us a question and solution.</p>
<p>Eric Clapton concert tickets cost <span class="math-container">$\\\$ 45$</span>. You won a free ticket to see the Eric Clapton concert (which is not transferable and has no resale value). Bob Dylan is performing on the same night and is your next-best alternative activity. Both performers are only performing on this one night. Tickets to see Dylan cost <span class="math-container">$\\\$ 40$</span>. You would be willing to pay up to <span class="math-container">$\\\$ 50$</span> to see Dylan if you don't go to the Clapton concert. Assume there are no other costs of seeing either performer. Based on this information, what is your opportunity cost of seeing Eric Clapton?</p>
<p>Solution:</p>
<p>\$10. By seeing the Clapton concert, you give up two things. First, you give up your Clapton ticket which you won. Second, you give up the consumer surplus you would have obtained had you attended the Dylan concert. Because the Clapton ticket is non-transferable, its value if you don't use it is zero. Thus, the opportunity cost o the ticket is zero. The consumer surplus you would have obtained had you gone to the Dylan concert is <span class="math-container">$C S=$</span> <span class="math-container">$50-40=10$</span>. This is an opportunity cost. Add them together and you get the opportunity cost for attending the Clapton concert: <span class="math-container">$0+10=10$</span>.</p>
<p>An aside: I learned of this question and the discussion that follows from Professor Robert Frank. Two researchers, Ferraro and Taylor, used a variant of this question to measure how well opportunity cost is taught and understood by economists. The question they used is simpler because it asked people to choose from four multiple-choice answers. They posed their version of this question to different groups of people to see how well they understood opportunity cost. Surprisingly, the evidence indicates that most economists do not understand opportunity cost. Among professional economists (PhD's, Professors, etc.), only 21.6 percent could answer it correctly, which is less than what a random choice among the four choices would deliver. University students who have completed a course in economics do even worse; only 7.4 percent get it correct. We economists, and I am definitely including myself, need to do a better job teaching this idea. One of my goals is that by the end of this course everyone understands and can apply the concept of opportunity cost.</p>
<p><strong>My question is what if I ask &quot;what is your opportunity cost of seeing Bob Dylan?&quot;</strong></p>

CC BY-SA 4.0
2024-11-12T20:19:55.653Z
This can't be answered without knowing how much you like Eric Clapton - basically, how much more or less valuable is seeing Clapton than the $0 price of the ticket? If you really love Clapton, it is a large opportunity cost to give up a completely free ticket and see Dylan instead at only a slight "discount" below what you'd be willing to pay. But if you hate Clapton, you'd prefer to throw even a free ticket in the trash, whether Dylan is playing or not.
Nuclear Hoagie
<microeconomics>
Ask a question on opportunity cost
Chao
# Ask a question on opportunity cost

(Asked by: username_0 on 2024-11-12)

My professor gives us a question and solution.

Eric Clapton concert tickets cost $\\\$ 45$. You won a free ticket to see the Eric Clapton concert (which is not transferable and has no resale value). Bob Dylan is performing on the same night and is your next-best alternative activity. Both performers are only performing on this one night. Tickets to see Dylan cost $\\\$ 40$. You would be willing to pay up to $\\\$ 50$ to see Dylan if you don't go to the Clapton concert. Assume there are no other costs of seeing either performer. Based on this information, what is your opportunity cost of seeing Eric Clapton?

Solution:

\$10. By seeing the Clapton concert, you give up two things. First, you give up your Clapton ticket which you won. Second, you give up the consumer surplus you would have obtained had you attended the Dylan concert. Because the Clapton ticket is non-transferable, its value if you don't use it is zero. Thus, the opportunity cost o the ticket is zero. The consumer surplus you would have obtained had you gone to the Dylan concert is $C S=$ $50-40=10$. This is an opportunity cost. Add them together and you get the opportunity cost for attending the Clapton concert: $0+10=10$.

An aside: I learned of this question and the discussion that follows from Professor Robert Frank. Two researchers, Ferraro and Taylor, used a variant of this question to measure how well opportunity cost is taught and understood by economists. The question they used is simpler because it asked people to choose from four multiple-choice answers. They posed their version of this question to different groups of people to see how well they understood opportunity cost. Surprisingly, the evidence indicates that most economists do not understand opportunity cost. Among professional economists (PhD's, Professors, etc.), only 21.6 percent could answer it correctly, which is less than what a random choice among the four choices would deliver. University students who have completed a course in economics do even worse; only 7.4 percent get it correct. We economists, and I am definitely including myself, need to do a better job teaching this idea. One of my goals is that by the end of this course everyone understands and can apply the concept of opportunity cost.

**My question is what if I ask "what is your opportunity cost of seeing Bob Dylan?"**

**Tags:** microeconomics
> **Comments:**
> **username_1**: This can't be answered without knowing how much you like Eric Clapton - basically, how much more or less valuable is seeing Clapton than the $0 price of the ticket? If you really love Clapton, it is a large opportunity cost to give up a completely free ticket and see Dylan instead at only a slight "discount" below what you'd be willing to pay. But if you hate Clapton, you'd prefer to throw even a free ticket in the trash, whether Dylan is playing or not.  

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## 1 answers

### Answer by username_2 on 2024-11-13. Score: 1 | Accepted answer

I'll expand on @NuclearHoagie's comment.

Generally speaking, when there are $N$ alternatives, $a\_1,a\_2,\dots,a\_N$, and an individual's "net" utility---that is, benefit net of costs---from the $n$-th alternative is $u(a\_n)$, the opportunity cost of alternative $a\_n$ is defined as
\begin{equation}
OC(a\_n) = \max\;\{u(a\_1),\dots,u(a\_{n-1}),u(a\_{n+1}),\dots,u(a\_N)\}.
\end{equation}

In your question, $N=2$ (call them $\text{EC}$ and $\text{BD}$) and the utility function is implicitly assumed to be the willingness-to-pay ($WTP$) for a ticket minus the price ($P$) of the ticket:
\begin{equation}
u(a) = WTP(a) - P(a).
\end{equation}

Applying the definition of $OC$, we have
\begin{alignat}{4}
OC(\text{EC}) & = u(\text{BD}) && = WTP(\text{BD}) - P(\text{BD}) && = 50-40 &&=10 \\
OC(\text{BD}) & = u(\text{EC}) && = WTP(\text{EC}) - P(\text{EC}) && = WTP(\text{EC}) - 0 && =WTP(\text{EC})
\end{alignat}
As you see, the $OC$ for seeing $\text{EC}$ is $10$, and the $OC$ for seeing $\text{BD}$ depends on your $WTP$, which is not provided in the question.


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