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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?

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    $\begingroup$ 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? $\endgroup$ – EnergyNumbers Aug 22 '15 at 17:21
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    $\begingroup$ @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. $\endgroup$ – Michael Greinecker Aug 22 '15 at 19:27
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    $\begingroup$ Perhaps the question should instead be more simply and less sensationally: "what are the effects?" "Who won?" would seem to presume that someone necessarily benefited from your loss. $\endgroup$ – Kenny LJ Aug 24 '15 at 8:30
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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— in fact, to a central bank, the two are indistinguishable, as the central bank would be unaware that your note had been destroyed.

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  • $\begingroup$ "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rate of the flow of money, and if that drops by a significant enough amount, they know that enough money has been withdrawn from circulation that they can issue more? $\endgroup$ – vsz Sep 8 '16 at 19:43
  • $\begingroup$ 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. $\endgroup$ – Revoltic Sep 10 '16 at 0:36
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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.

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    $\begingroup$ 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. $\endgroup$ – Steven Landsburg Aug 24 '15 at 3:03
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    $\begingroup$ It's not that easy. In partial equilibrium, yes - but what if monetary authorities respond? $\endgroup$ – FooBar Aug 24 '15 at 8:55
  • $\begingroup$ 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. $\endgroup$ – Thorst Aug 24 '15 at 9:26
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    $\begingroup$ @StevenLandsburg I read The armchair economist long time age and I guess I learned something :) $\endgroup$ – SimZal Aug 24 '15 at 10:56
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    $\begingroup$ @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. $\endgroup$ – Steven Landsburg Aug 24 '15 at 14:04
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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.

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    $\begingroup$ 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. $\endgroup$ – Steven Landsburg Aug 24 '15 at 3:10
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    $\begingroup$ it is just a symbolic thing in order to show how small the effect will be. There are no calculations behind. $\endgroup$ – optimal control Aug 24 '15 at 9:00
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    $\begingroup$ If you really believe that a \$100 transfer has essentially zero effect on anything that might interest anyone, then please send me \$100. $\endgroup$ – Steven Landsburg Aug 24 '15 at 14:49
  • $\begingroup$ 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. $\endgroup$ – optimal control Aug 24 '15 at 22:10
  • $\begingroup$ 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? $\endgroup$ – BCLC Aug 26 '15 at 8:49
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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.

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