<p>A completely full stadium does somewhat imply that there would have been other people willing to pay that much or more. It's almost certain that almost any one of ticketholders would have paid a penny more than they actually did, meaning there is some profit left &quot;on the table&quot;. It's simply unfathomable that all 50k attendants at a sold-out game paid the absolute maximum they would have been willing to, and furthermore also likely that there were other people who wanted tickets but couldn't get them due to availability rather than price - in other words, you possibly could have raised the price, earned more profit, and still have gotten 50k attendants. On the other hand, the existence of empty seats implies that the going rate did, in fact, exceed what people were willing to pay.</p>
<p>A full stadium does mean it's possible (but not guaranteed) that you charged too little for some people. A not-full stadium means you definitely charged too much for some people. Ideally, you'd sell seats from the not-full stadium for a lower price, allowing you to recoup some profit for those seats (so long as the purchase price is more than the operating price for that one additional seat). In a perfect world, you'd find each individual willing to pay the highest price and sell the final seat at the highest price that anyone in the world would pay for it, but that's not really realistic. It may be better to be sure you can sell the seat at a somewhat lower price, than to try to sell it at a higher price and possibly not sell it at all.</p>

CC BY-SA 4.0
2024-10-18T19:07:30.953Z
2024-10-18T19:07:30.953Z
Nuclear Hoagie
<p>You've assumed ticket prices must be constant across all seats. If ticket prices can be varied then it would be more profitable to fill all seats through variable pricing.</p>
<p>We can use your example to illustrate this. 49,000 tickets at \$210 gives a total revenue of (<span class="math-container">$49000\cdot210=$</span>) \$10,290,000. However, there are 1,000 seats unfilled. We know that we could fill the stadium if tickets were priced at \$200, therefore the sales manager could lower the price of tickets to fill the remaining seats and therefore gain an extra revenue of (<span class="math-container">$1000\cdot200=$</span>) \$200,000.</p>
<p>Under variable pricing, it would only be profitable to leave seats empty when the costs of filling remaining seats (e.g. additional staff) outweigh the price of the ticket - factoring the additional spread of sunk costs.</p>

CC BY-SA 4.0
2024-10-20T20:36:19.650Z
Fair enough, this is a commonly used solution to this problem. But does the point of my question stand if we assume there is fixed pricing? Or did I overlook something there?
Jumboman
CC BY-SA 4.0
2024-10-18T18:45:14.263Z
2024-10-18T18:56:57.830Z
2024-10-18T18:56:57.830Z
williams-ji
<p>My question is about the equilibrium where supply meets demand in a way that profits are maximized. It seems to me that if a soccer match sells out, the stadium manager did a poor job: they underestimated demand, and they could have made more profit by increasing the price, even if that meant they would not sell all the tickets. After all, if a stadium has 50.000 seats, it would be more profitable to sell 49.000 tickets at \$210 than 50.000 at \$200, and even more profitable to sell 47.000 tickets at \$220.
Does this mean that some percentage of every stadium, theater, airplane etc. is <em>supposed</em> to remain empty and only exists to catch imperfect demand estimates?</p>

CC BY-SA 4.0
2024-10-18T22:51:42.100Z
Why the tag 'general equilibrium'? It seems more like a monopoly problem the way you have phrased the question.
Jesper Hybel
CC BY-SA 4.0
2024-10-20T20:40:04.607Z
@JesperHybel Because the optimal profit for the stadium manager is when supply and demand are in equlibrium, right? Sure, in this case the supply is fixed, but the demand can be managed by raising or lowering the price.
Jumboman
CC BY-SA 4.0
2024-10-20T23:50:11.583Z
Ok, so I have edited the tag to equilibrium. General equilibrium is primarily used when there is more than one market. As far as I understand your question you are only concerned with one market - correct me if I'm wrong.
Jesper Hybel
<equilibrium>
Does supply and demand result in empty seats?
Jumboman
# Does supply and demand result in empty seats?

(Asked by: username_0 on 2024-10-17)

My question is about the equilibrium where supply meets demand in a way that profits are maximized. It seems to me that if a soccer match sells out, the stadium manager did a poor job: they underestimated demand, and they could have made more profit by increasing the price, even if that meant they would not sell all the tickets. After all, if a stadium has 50.000 seats, it would be more profitable to sell 49.000 tickets at \$210 than 50.000 at \$200, and even more profitable to sell 47.000 tickets at \$220.
Does this mean that some percentage of every stadium, theater, airplane etc. is *supposed* to remain empty and only exists to catch imperfect demand estimates?

**Tags:** equilibrium
> **Comments:**
> **username_1**: Why the tag 'general equilibrium'? It seems more like a monopoly problem the way you have phrased the question.  
> **username_0**: @JesperHybel Because the optimal profit for the stadium manager is when supply and demand are in equlibrium, right? Sure, in this case the supply is fixed, but the demand can be managed by raising or lowering the price.  
> **username_1**: Ok, so I have edited the tag to equilibrium. General equilibrium is primarily used when there is more than one market. As far as I understand your question you are only concerned with one market - correct me if I'm wrong.  

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## 2 answers

### Answer by username_2 on 2024-10-18. Score: 0

A completely full stadium does somewhat imply that there would have been other people willing to pay that much or more. It's almost certain that almost any one of ticketholders would have paid a penny more than they actually did, meaning there is some profit left "on the table". It's simply unfathomable that all 50k attendants at a sold-out game paid the absolute maximum they would have been willing to, and furthermore also likely that there were other people who wanted tickets but couldn't get them due to availability rather than price - in other words, you possibly could have raised the price, earned more profit, and still have gotten 50k attendants. On the other hand, the existence of empty seats implies that the going rate did, in fact, exceed what people were willing to pay.

A full stadium does mean it's possible (but not guaranteed) that you charged too little for some people. A not-full stadium means you definitely charged too much for some people. Ideally, you'd sell seats from the not-full stadium for a lower price, allowing you to recoup some profit for those seats (so long as the purchase price is more than the operating price for that one additional seat). In a perfect world, you'd find each individual willing to pay the highest price and sell the final seat at the highest price that anyone in the world would pay for it, but that's not really realistic. It may be better to be sure you can sell the seat at a somewhat lower price, than to try to sell it at a higher price and possibly not sell it at all.


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### Answer by username_3 on 2024-10-18. Score: 0

You've assumed ticket prices must be constant across all seats. If ticket prices can be varied then it would be more profitable to fill all seats through variable pricing.

We can use your example to illustrate this. 49,000 tickets at \$210 gives a total revenue of ($49000\cdot210=$) \$10,290,000. However, there are 1,000 seats unfilled. We know that we could fill the stadium if tickets were priced at \$200, therefore the sales manager could lower the price of tickets to fill the remaining seats and therefore gain an extra revenue of ($1000\cdot200=$) \$200,000.

Under variable pricing, it would only be profitable to leave seats empty when the costs of filling remaining seats (e.g. additional staff) outweigh the price of the ticket - factoring the additional spread of sunk costs.

> **Comments:**
> **username_0**: Fair enough, this is a commonly used solution to this problem. But does the point of my question stand if we assume there is fixed pricing? Or did I overlook something there?  

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