<p>You have make a simple model to understand it more easily:</p>

<p>Jack, Diane and you all bought coupons called "share of the cake".
If you go to redeem it you will get 1/3 of the cake, because there are 3 coupons in existence.</p>

<p>But then you had your laundry disaster and suddenly there are only 2 coupons so Jack and Diane can now get 1/2 of the cake for one coupon.</p>

<p>So the answer is: other money holders benefit.
By the same principle the money holders lose purchasing power when inflation strikes. </p>

CC BY-SA 3.0
2015-08-24T03:03:08.950Z
This is exactly right.  To the OP:  You had exactly the right intuition --- clearly nothing of actual value has been destroyed, so your loss must be offset by someone else's gain.  And you had exactly the right instinct --- namely, that one ought to be able to figure out who that other person is.  This answer does that.  Note in particular that the total gain to all the other moneyholders must come to exactly $100.  You can prove this with a bunch of algebra, but you can prove it more simply by noticing, as before, that nothing's been destroyed so their gain must exactly equal your loss.
Steven Landsburg
CC BY-SA 3.0
2015-08-24T08:55:23.800Z
It's not that easy. In partial equilibrium, yes - but what if monetary authorities respond?
FooBar
CC BY-SA 3.0
2015-08-24T09:26:51.187Z
If the price of a 1/3 of the cake is 1 note, why would the price of a piece of cake fall? Issue a new note? Keep a third of the cake? The answer is intuitive but builds on non-state assumptions.
Thorst
CC BY-SA 3.0
2015-08-24T10:56:15.970Z
@StevenLandsburg I read The armchair economist long time age and I guess I learned something :)
SimZal
CC BY-SA 3.0
2015-08-24T14:04:45.810Z
@FooBar:   Yes, the monetary authorities might respond,in which case the gain is transferred to whoever gets the seignorage.  But of course, one could make the same objection to any answer to any question. "What would happen if I flipped this switch?"  "The light would go on".  "Yes, in partial equilibrium --- but what if the light attracts a burglar who cuts off the main electrical line?".  You could (quite reasonably) argue that the monetary authorities are more ubiquitous than burglars, but it still seems to me that they are outside the spirit of the question.
Steven Landsburg
CC BY-SA 3.0
2015-08-23T07:09:55.710Z
2015-08-23T07:09:55.710Z
SimZal
<p>The central bank that issues the currency won; they can now issue an additional $100 without increasing the price level. This is similar to seignorage rents due to <a href="https://en.wikipedia.org/wiki/Seigniorage#Overseas_circulation">overseas circulation</a>— in fact, to a central bank, the two are indistinguishable, as the central bank would be unaware that your note had been destroyed.</p>

CC BY-SA 3.0
2016-09-08T19:43:13.547Z
*"they can now issue an additional $100"* - yes, but how do they know they can? By statistics monitoring the average rate of the flow of money, and if that drops by a significant enough amount, they know that enough money has been withdrawn from circulation that they can issue more?
vsz
CC BY-SA 3.0
2016-09-10T00:36:05.237Z
obviously its hard to notice $100, but if you destroy enough currency it will start deflating prices and that will act as a signal to print more money.
Revoltic
CC BY-SA 3.0
2015-08-22T18:46:01.457Z
2015-08-23T21:58:41.597Z
2015-08-23T21:58:41.597Z
Revoltic
<p>Nobody won, you have just lost 100 \$  :) you made a contractionnary monetary policy with a $10^{-1000000000000}$ amplitude on economy. It means that you have reduced the quantity of money in whole economy which will have the same effects (but very very tiny) of a contractionnary monetary policy of a central bank.</p>

CC BY-SA 3.0
2015-08-24T03:10:17.283Z
I'd like very much to know a) what "amplitude on the economy" means, b) how you calculated that exponent, and c) whether the same exponent would apply to any other transfer of $100.
Steven Landsburg
CC BY-SA 3.0
2015-08-24T09:00:54.540Z
it is just a symbolic thing in order to show how small the effect will be. There are no calculations behind.
optimal control
CC BY-SA 3.0
2015-08-24T14:49:09.633Z
If you really believe that a \$100 transfer has essentially zero effect on anything that might interest anyone, then please send me \$100.
Steven Landsburg
CC BY-SA 3.0
2015-08-24T22:10:46.560Z
I think you are deviating the conversation :) I don't think that you are naive to believe that destroyed 100 \$ (as OP said in his question) could have some considerable effects on whole economy. The effect is so minor. Also, there does not exist any transfer according to OP's question. The money is destroyed in laundry which means that there is a reduction of quantity of money in circulation.
optimal control
CC BY-SA 3.0
2015-08-26T08:49:53.750Z
Initially you said nobody won. Later you said there is a small effect. Seems like a contradiction since the first statement seems to imply that there is no effect?
BCLC
CC BY-SA 3.0
2015-08-26T08:52:14.610Z
@BCLC Nobody won this money (in the sense that there is not a transfer and nobody took this 100 \$ ) because it is destroyed. However, there is a very very tiny effect on the whole economy beaucause the amount of money in circulation decreases. That's the idea.
optimal control
CC BY-SA 3.0
2015-08-26T08:58:14.497Z
Well no [ONE](http://economics.stackexchange.com/a/6971/4483) person won the WHOLE 100 dollars. Is that what you mean?
BCLC
CC BY-SA 3.0
2015-08-26T09:08:48.730Z
@BCLC yes no one won the whole 100 \$ but agents in economy will see the effect on their wallet ! As this 100 \$ is destroyed, the quantity of money in circulation is decreased, which will increase the value of \$ with respect to other currencies
Let' say person A holds 10.000 € and person B holds 10.000 \$. In this case, person B will win (By the way, I don't think the word win is appropriate) and person A will loose as the value of \$ increases according to €.
optimal control
CC BY-SA 3.0
2015-08-26T09:11:33.650Z
'Benefited from' instead of 'won' ?
BCLC
CC BY-SA 3.0
2015-08-26T09:13:30.927Z
@BCLC Yes, I think it fits better.
optimal control
CC BY-SA 3.0
2015-08-22T20:21:29.073Z
2015-08-22T20:21:29.073Z
optimal control
<p>My intuition says that theoretically the disappearance of 100 $ from the money supply should increase the value of all other money in circulation so everyone else with any money gains a marginal benefit that is higher the more money they have.</p>

<p>The benefit a person gains = (100$/total money supply)*(amount of money held by the person)</p>

<p>The disappearance has to be public knowledge, though, so the market can take it into account.</p>

CC BY-SA 3.0
2015-08-24T10:32:12.297Z
2015-08-24T10:32:12.297Z
John L.
<p>I lost a 100 dollars bill in the laundry (it was destroyed).
I clearly lost 100 dollars.
Where are they now? Who won 100 dollars?</p>

CC BY-SA 3.0
2015-08-22T17:21:45.840Z
Why do you think someone else won 100 dollars? What is the actual economics principle that you are trying to get to the bottom of?
410 gone
CC BY-SA 3.0
2015-08-22T19:27:43.530Z
@EnergyNumbers Arguably, real output should be uneffected, so if no real output is wasted, this should have redistributive effects. I think this is a really good question.
Michael Greinecker
<currency>
I lost $100 in the laundry, who won?
user5498
# I lost $100 in the laundry, who won?

(Asked by: username_0 on 2015-08-22)

I lost a 100 dollars bill in the laundry (it was destroyed).
I clearly lost 100 dollars.
Where are they now? Who won 100 dollars?

**Tags:** currency

> **Comments:**
> **username_1**: Why do you think someone else won 100 dollars? What is the actual economics principle that you are trying to get to the bottom of?  
> **username_2**: @EnergyNumbers Arguably, real output should be uneffected, so if no real output is wasted, this should have redistributive effects. I think this is a really good question.  

---

## 4 answers

### Answer by username_7 on 2015-08-22. Score: 13

The central bank that issues the currency won; they can now issue an additional $100 without increasing the price level. This is similar to seignorage rents due to [overseas circulation](https://en.wikipedia.org/wiki/Seigniorage#Overseas_circulation)— in fact, to a central bank, the two are indistinguishable, as the central bank would be unaware that your note had been destroyed.

> **Comments:**
> **username_8**: *"they can now issue an additional $100"* - yes, but how do they know they can? By statistics monitoring the average rate of the flow of money, and if that drops by a significant enough amount, they know that enough money has been withdrawn from circulation that they can issue more?  
> **username_7**: obviously its hard to notice $100, but if you destroy enough currency it will start deflating prices and that will act as a signal to print more money.  

---

### Answer by username_3 on 2015-08-23. Score: 8

You have make a simple model to understand it more easily:

Jack, Diane and you all bought coupons called "share of the cake".
If you go to redeem it you will get 1/3 of the cake, because there are 3 coupons in existence.

But then you had your laundry disaster and suddenly there are only 2 coupons so Jack and Diane can now get 1/2 of the cake for one coupon.

So the answer is: other money holders benefit.
By the same principle the money holders lose purchasing power when inflation strikes.

> **Comments:**
> **username_4**: This is exactly right.  To the OP:  You had exactly the right intuition --- clearly nothing of actual value has been destroyed, so your loss must be offset by someone else's gain.  And you had exactly the right instinct --- namely, that one ought to be able to figure out who that other person is.  This answer does that.  Note in particular that the total gain to all the other moneyholders must come to exactly $100.  You can prove this with a bunch of algebra, but you can prove it more simply by noticing, as before, that nothing's been destroyed so their gain must exactly equal your loss.  
> **username_5**: It's not that easy. In partial equilibrium, yes - but what if monetary authorities respond?  
> **username_6**: If the price of a 1/3 of the cake is 1 note, why would the price of a piece of cake fall? Issue a new note? Keep a third of the cake? The answer is intuitive but builds on non-state assumptions.  
> **username_3**: @StevenLandsburg I read The armchair economist long time age and I guess I learned something :)  
> **username_4**: @username_5:   Yes, the monetary authorities might respond,in which case the gain is transferred to whoever gets the seignorage.  But of course, one could make the same objection to any answer to any question. "What would happen if I flipped this switch?"  "The light would go on".  "Yes, in partial equilibrium --- but what if the light attracts a burglar who cuts off the main electrical line?".  You could (quite reasonably) argue that the monetary authorities are more ubiquitous than burglars, but it still seems to me that they are outside the spirit of the question.  

---

### Answer by username_9 on 2015-08-22. Score: 5

Nobody won, you have just lost 100 \$ :) you made a contractionnary monetary policy with a $10^{-1000000000000}$ amplitude on economy. It means that you have reduced the quantity of money in whole economy which will have the same effects (but very very tiny) of a contractionnary monetary policy of a central bank.

> **Comments:**
> **username_4**: I'd like very much to know a) what "amplitude on the economy" means, b) how you calculated that exponent, and c) whether the same exponent would apply to any other transfer of $100.  
> **username_9**: it is just a symbolic thing in order to show how small the effect will be. There are no calculations behind.  
> **username_4**: If you really believe that a \$100 transfer has essentially zero effect on anything that might interest anyone, then please send me \$100.  
> **username_9**: I think you are deviating the conversation :) I don't think that you are naive to believe that destroyed 100 \$ (as OP said in his question) could have some considerable effects on whole economy. The effect is so minor. Also, there does not exist any transfer according to OP's question. The money is destroyed in laundry which means that there is a reduction of quantity of money in circulation.  
> **username_10**: Initially you said nobody won. Later you said there is a small effect. Seems like a contradiction since the first statement seems to imply that there is no effect?  
> **username_9**: @username_10 Nobody won this money (in the sense that there is not a transfer and nobody took this 100 \$ ) because it is destroyed. However, there is a very very tiny effect on the whole economy beaucause the amount of money in circulation decreases. That's the idea.  
> **username_10**: Well no [ONE](http://economics.stackexchange.com/a/6971/4483) person won the WHOLE 100 dollars. Is that what you mean?  
> **username_9**: @username_10 yes no one won the whole 100 \$ but agents in economy will see the effect on their wallet ! As this 100 \$ is destroyed, the quantity of money in circulation is decreased, which will increase the value of \$ with respect to other currencies Let' say person A holds 10.000 € and person B holds 10.000 \$. In this case, person B will win (By the way, I don't think the word win is appropriate) and person A will loose as the value of \$ increases according to €.  
> **username_10**: 'Benefited from' instead of 'won' ?  
> **username_9**: @username_10 Yes, I think it fits better.  

---

### Answer by username_11 on 2015-08-24. Score: 2

My intuition says that theoretically the disappearance of 100 $ from the money supply should increase the value of all other money in circulation so everyone else with any money gains a marginal benefit that is higher the more money they have.

The benefit a person gains = (100$/total money supply)\*(amount of money held by the person)

The disappearance has to be public knowledge, though, so the market can take it into account.


---

